WorldWideScience

Sample records for geometrical gauge theory

  1. Physical principles, geometrical aspects, and locality properties of gauge field theories

    International Nuclear Information System (INIS)

    Mack, G.; Hamburg Univ.

    1981-01-01

    Gauge field theories, particularly Yang - Mills theories, are discussed at a classical level from a geometrical point of view. The introductory chapters are concentrated on physical principles and mathematical tools. The main part is devoted to locality problems in gauge field theories. Examples show that locality problems originate from two sources in pure Yang - Mills theories (without matter fields). One is topological and the other is related to the existence of degenerated field configurations of the infinitesimal holonomy groups on some extended region of space or space-time. Nondegenerate field configurations in theories with semisimple gauge groups can be analysed with the help of the concept of a local gauge. Such gauges play a central role in the discussion. (author)

  2. On the motion of matter in the geometrical gauge field theory

    International Nuclear Information System (INIS)

    Konopleva, N.P.

    2005-01-01

    In the geometrical gauge field theory, the motion equations of matter (elementary particles) are connected with the field equations. The problems arising from this connection are discussed. For the first time, such problems arose in Einstein's General Relativity. Einstein hoped that solution of these problems will allow explanation of elementary particles nature without making use of quantum mechanics. But, as it turned out, the situation is more difficult. Here the corresponding problems are formulated for the connection of equations of particle motion and field equations in the geometrical gauge field theory. It is shown that appearance of the problems under discussion is an inevitable effect of passage to relativism and local symmetries

  3. On the Motion of Matter in the Geometrical Gauge Field Theory

    CERN Document Server

    Konopleva, N P

    2005-01-01

    In the geometrical gauge field theory, the motion equations of matter (elementary particles) are connected with the field equations. In the talk, the problems arising from this connection are discussed. For the first time, such problems arose in Einstein's General Relativity. Einstein hoped that solution of these problems will allow explanation of elementary particles nature without making use of quantum mechanics. But, as it turned out, the situation is more difficult. Here the corresponding problems are formulated for the connection of equations of particle motion and field equations in the geometrical gauge field theory. It is shown that appearance of the problems under discussion is an inevitable effect of passage to relativism and local symmetries.

  4. On N = 1 gauge models from geometric engineering in M-theory

    International Nuclear Information System (INIS)

    Belhaj, A; Drissi, L B; Rasmussen, J

    2003-01-01

    We study geometric engineering of four-dimensional N = 1 gauge models from M-theory on a seven-dimensional manifold with G 2 holonomy. The manifold is constructed as a K3 fibration over a three-dimensional base space with ADE geometry. The resulting gauge theory is discussed in the realm of (p, q) webs. We discuss how the anomaly cancellation condition translates into a condition on the associated affine ADE Lie algebras

  5. Geometrical and topological formulation of local gauge and supergauge theories

    International Nuclear Information System (INIS)

    Macrae, K.I.

    1976-01-01

    A geometrical and topological formulation of local gauge and supergauge invariance is presented. Analysis of experiments of the type described by Bohm and Aharanov and in the attempt to understand immersed submanifolds such as the string with internal symmetry, in a geometric setting, are led to the introduction of fiber bundles, superspaces. Many exact classical solutions to the equations of motion were considered for these gauge theories with specific choices of gauge group such as SU 4 . We describe some exact soliton solutions to these theories which have linear Regge trajectories, i.e., their angular momentum is a linear function of their mass squared. Next one discusses the actions and equations of motion for gauge theories whose base manifolds can have arbitrarily dimensioned submanifolds excised from them, manifolds with holes were discussed. These holes can have fractional quark charges when the structure group is, for example, SU 3 or SU 4 . By extending the concept of conservation of energy to include the excised submanifolds, their actions, and their equations of motion were derived showing that they can act as charged particles. Using the fractionality of the quark charges, are led to suggest a topological confinement mechanism for these particles. One also derives the actions and equations of motion for the string from this viewpoint. Some new Lie algebras which have anticommuting elements are introduced. Their gauge theories are described, and the possibility of fermionic actions for the anticommuting pieces is examined. Supersymmetric strings and their supergauge transformations were discussed and an extension was suggested of supersymmetry to immersed minimal submanifolds other than the string. Both quarklike and vectorlike fermions are included. Finally the invariance of both the equations of motion and the gauge conditions under supersymmetry transformations for these submanifolds were described

  6. Geometrical phases from global gauge invariance of nonlinear classical field theories

    International Nuclear Information System (INIS)

    Garrison, J.C.; Chiao, R.Y.

    1988-01-01

    We show that the geometrical phases recently discovered in quantum mechanics also occur naturally in the theory of any classical complex multicomponent field satisfying nonlinear equations derived from a Lagrangean with is invariant under gauge transformations of the first kind. Some examples are the paraxial wave equation for nonlinear optics, and Ginzburg-Landau equations for complex order parameters in condensed-matter physics

  7. Gauge theory and gravitation

    International Nuclear Information System (INIS)

    Kikkawa, Keiji; Nakanishi, Noboru; Nariai, Hidekazu

    1983-01-01

    These proceedings contain the articles presented at the named symposium. They deal with geometrical aspects of gauge theory and gravitation, special problems in gauge theories, quantum field theory in curved space-time, quantum gravity, supersymmetry including supergravity, and grand unification. See hints under the relevant topics. (HSI)

  8. Gauge field vacuum structure in geometrical aspect

    International Nuclear Information System (INIS)

    Konopleva, N.P.

    2003-01-01

    Vacuum conception is one of the main conceptions of quantum field theory. Its meaning in classical field theory is also very profound. In this case the vacuum conception is closely connected with ideas of the space-time geometry. The global and local geometrical space-time conceptions lead to different vacuum definitions and therefore to different ways of physical theory construction. Some aspects of the gauge field vacuum structure are analyzed. It is shown that in the gauge field theory the vacuum Einstein equation solutions describe the relativistic vacuum as common vacuum of all gauge fields and its sources. Instantons (both usual and hyperbolical) are regarded as nongravitating matter, because they have zero energy-momentum tensors and correspond to vacuum Einstein equations

  9. Gauge theories and monopoles

    International Nuclear Information System (INIS)

    Cabibbo, N.

    1983-01-01

    This chapter attempts to present some of the fundamental geometrical ideas at the basis of gauge theories. Describes Dirac Monopoles and discusses those ideas that are not usually found in more ''utilitarian'' presentations which concentrate on QCD or on the Glashow-Salam-Weinberg model. This topic was chosen because of the announcement of the possible detection of a Dirac monopole. The existence of monopoles depends on topological features of gauge theories (i.e., on global properties of field configurations which are unique to gauge theories). Discusses global symmetry-local symmetry; the connection; path dependence and the gauge fields; topology and monopoles; the case of SU(3) x U(1); and the 't Hooft-Polyakov monopole

  10. Gauge theory loop operators and Liouville theory

    International Nuclear Information System (INIS)

    Drukker, Nadav; Teschner, Joerg

    2009-10-01

    We propose a correspondence between loop operators in a family of four dimensional N=2 gauge theories on S 4 - including Wilson, 't Hooft and dyonic operators - and Liouville theory loop operators on a Riemann surface. This extends the beautiful relation between the partition function of these N=2 gauge theories and Liouville correlators found by Alday, Gaiotto and Tachikawa. We show that the computation of these Liouville correlators with the insertion of a Liouville loop operator reproduces Pestun's formula capturing the expectation value of a Wilson loop operator in the corresponding gauge theory. We prove that our definition of Liouville loop operators is invariant under modular transformations, which given our correspondence, implies the conjectured action of S-duality on the gauge theory loop operators. Our computations in Liouville theory make an explicit prediction for the exact expectation value of 't Hooft and dyonic loop operators in these N=2 gauge theories. The Liouville loop operators are also found to admit a simple geometric interpretation within quantum Teichmueller theory as the quantum operators representing the length of geodesics. We study the algebra of Liouville loop operators and show that it gives evidence for our proposal as well as providing definite predictions for the operator product expansion of loop operators in gauge theory. (orig.)

  11. Gravitation as Gauge theory of Poincare Group

    International Nuclear Information System (INIS)

    Stedile, E.

    1982-08-01

    The geometrical approach to gauge theories, based on fiber-bundles, is shown in detail. Several gauge formalisms for gravitation are examined. In particular, it is shown how to build gauge theories for non-semisimple groups. A gravitational theory for the Poincare group, with all the essential characteristics of a Yang-Mills theory is proposed. Inonu-Wigner contractions of gauge theories are introduced, which provide a Lagrangian formalism, equivalent to a Lagrangian de Sitter theory supplemented by weak constraints. Yang and Einstein theories for gravitation become particular cases of a Yang-Mills theory. The classical limit of the proposed formalism leads to the Poisson equation, for the static case. (Author) [pt

  12. Non-Abelian gauge field theory in scale relativity

    International Nuclear Information System (INIS)

    Nottale, Laurent; Celerier, Marie-Noeelle; Lehner, Thierry

    2006-01-01

    Gauge field theory is developed in the framework of scale relativity. In this theory, space-time is described as a nondifferentiable continuum, which implies it is fractal, i.e., explicitly dependent on internal scale variables. Owing to the principle of relativity that has been extended to scales, these scale variables can themselves become functions of the space-time coordinates. Therefore, a coupling is expected between displacements in the fractal space-time and the transformations of these scale variables. In previous works, an Abelian gauge theory (electromagnetism) has been derived as a consequence of this coupling for global dilations and/or contractions. We consider here more general transformations of the scale variables by taking into account separate dilations for each of them, which yield non-Abelian gauge theories. We identify these transformations with the usual gauge transformations. The gauge fields naturally appear as a new geometric contribution to the total variation of the action involving these scale variables, while the gauge charges emerge as the generators of the scale transformation group. A generalized action is identified with the scale-relativistic invariant. The gauge charges are the conservative quantities, conjugates of the scale variables through the action, which find their origin in the symmetries of the ''scale-space.'' We thus found in a geometric way and recover the expression for the covariant derivative of gauge theory. Adding the requirement that under the scale transformations the fermion multiplets and the boson fields transform such that the derived Lagrangian remains invariant, we obtain gauge theories as a consequence of scale symmetries issued from a geometric space-time description

  13. Supersymmetric quiver gauge theories on the lattice

    International Nuclear Information System (INIS)

    Joseph, Anosh

    2013-12-01

    In this paper we detail the lattice constructions of several classes of supersymmetric quiver gauge theories in two and three Euclidean spacetime dimensions possessing exact supersymmetry at finite lattice spacing. Such constructions are obtained through the methods of topological twisting and geometric discretization of Euclidean Yang-Mills theories with eight and sixteen supercharges in two and three dimensions. We detail the lattice constructions of two-dimensional quiver gauge theories possessing four and eight supercharges and three-dimensional quiver gauge theories possessing eight supercharges.

  14. Gauge theory loop operators and Liouville theory

    Energy Technology Data Exchange (ETDEWEB)

    Drukker, Nadav [Humboldt Univ. Berlin (Germany). Inst. fuer Physik; Gomis, Jaume; Okuda, Takuda [Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada); Teschner, Joerg [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

    2009-10-15

    We propose a correspondence between loop operators in a family of four dimensional N=2 gauge theories on S{sup 4} - including Wilson, 't Hooft and dyonic operators - and Liouville theory loop operators on a Riemann surface. This extends the beautiful relation between the partition function of these N=2 gauge theories and Liouville correlators found by Alday, Gaiotto and Tachikawa. We show that the computation of these Liouville correlators with the insertion of a Liouville loop operator reproduces Pestun's formula capturing the expectation value of a Wilson loop operator in the corresponding gauge theory. We prove that our definition of Liouville loop operators is invariant under modular transformations, which given our correspondence, implies the conjectured action of S-duality on the gauge theory loop operators. Our computations in Liouville theory make an explicit prediction for the exact expectation value of 't Hooft and dyonic loop operators in these N=2 gauge theories. The Liouville loop operators are also found to admit a simple geometric interpretation within quantum Teichmueller theory as the quantum operators representing the length of geodesics. We study the algebra of Liouville loop operators and show that it gives evidence for our proposal as well as providing definite predictions for the operator product expansion of loop operators in gauge theory. (orig.)

  15. A geometric view on topologically massive gauge theories

    International Nuclear Information System (INIS)

    Horvathy, P.A.; Nash, C.

    1985-01-01

    The topologically massive gauge theory of Deser, Jackiw and Templeton is understood from Souriau's Principle of General Covariance. The non-gauge invariant mass term corresponds to a non-trivial class in the first cohomology group of configuration space, generated by the Chern-Simons secondary characteristic class. Quantization requires this class to be integral

  16. The mathematical foundations of gauge theories

    International Nuclear Information System (INIS)

    Marathe, K.B.; Martucci, G.

    1992-01-01

    Theoretical physicists tend to discuss their theories in the language of mathematics. However, the adequate mathematical formulation may not yet be available when the physical law is first discovered. Mathematical physicists trying to develop the relevant mathematics for these theories, may obtain new insights into old mathematical structures. Gauge Theory is such a gift from physics to mathematics. This book presents a self-contained development of a differential geometric formulation of gauge theories, in particular, the theory of Yang-Mills fields. (author). refs.; figs.; tabs

  17. Geometrodynamics of gauge fields on the geometry of Yang-Mills and gravitational gauge theories

    CERN Document Server

    Mielke, Eckehard W

    2016-01-01

    This monograph aims to provide a unified, geometrical foundation of gauge theories of elementary particle physics. The underlying geometrical structure is unfolded in a coordinate-free manner via the modern mathematical notions of fibre bundles and exterior forms. Topics such as the dynamics of Yang-Mills theories, instanton solutions and topological invariants are included. By transferring these concepts to local space-time symmetries, generalizations of Einstein's theory of gravity arise in a Riemann-Cartan space with curvature and torsion. It provides the framework in which the (broken) Poincaré gauge theory, the Rainich geometrization of the Einstein-Maxwell system, and higher-dimensional, non-abelian Kaluza-Klein theories are developed. Since the discovery of the Higgs boson, concepts of spontaneous symmetry breaking in gravity have come again into focus, and, in this revised edition, these will be exposed in geometric terms. Quantizing gravity remains an open issue: formulating it as a de Sitter t...

  18. Sp(2) covariant quantisation of general gauge theories

    Energy Technology Data Exchange (ETDEWEB)

    Vazquez-Bello, J L

    1994-11-01

    The Sp(2) covariant quantization of gauge theories is studied. The geometrical interpretation of gauge theories in terms of quasi principal fibre bundles Q(M{sub s}, G{sub s}) is reviewed. It is then described the Sp(2) algebra of ordinary Yang-Mills theory. A consistent formulation of covariant Lagrangian quantisation for general gauge theories based on Sp(2) BRST symmetry is established. The original N = 1, ten dimensional superparticle is considered as an example of infinitely reducible gauge algebras, and given explicitly its Sp(2) BRST invariant action. (author). 18 refs.

  19. Sp(2) covariant quantisation of general gauge theories

    International Nuclear Information System (INIS)

    Vazquez-Bello, J.L.

    1994-11-01

    The Sp(2) covariant quantization of gauge theories is studied. The geometrical interpretation of gauge theories in terms of quasi principal fibre bundles Q(M s , G s ) is reviewed. It is then described the Sp(2) algebra of ordinary Yang-Mills theory. A consistent formulation of covariant Lagrangian quantisation for general gauge theories based on Sp(2) BRST symmetry is established. The original N = 1, ten dimensional superparticle is considered as an example of infinitely reducible gauge algebras, and given explicitly its Sp(2) BRST invariant action. (author). 18 refs

  20. Supersymmetric gauge theories from string theory

    International Nuclear Information System (INIS)

    Metzger, St.

    2005-12-01

    This thesis presents various ways to construct four-dimensional quantum field theories from string theory. In a first part we study the generation of a supersymmetric Yang-Mills theory, coupled to an adjoint chiral superfield, from type IIB string theory on non-compact Calabi-Yau manifolds, with D-branes wrapping certain sub-cycles. Properties of the gauge theory are then mapped to the geometric structure of the Calabi-Yau space. Even if the Calabi-Yau geometry is too complicated to evaluate the geometric integrals explicitly, one can then always use matrix model perturbation theory to calculate the effective superpotential. The second part of this work covers the generation of four-dimensional super-symmetric gauge theories, carrying several important characteristic features of the standard model, from compactifications of eleven-dimensional supergravity on G 2 -manifolds. If the latter contain conical singularities, chiral fermions are present in the four-dimensional gauge theory, which potentially lead to anomalies. We show that, locally at each singularity, these anomalies are cancelled by the non-invariance of the classical action through a mechanism called 'anomaly inflow'. Unfortunately, no explicit metric of a compact G 2 -manifold is known. Here we construct families of metrics on compact weak G 2 -manifolds, which contain two conical singularities. Weak G 2 -manifolds have properties that are similar to the ones of proper G 2 -manifolds, and hence the explicit examples might be useful to better understand the generic situation. Finally, we reconsider the relation between eleven-dimensional supergravity and the E 8 x E 8 -heterotic string. This is done by carefully studying the anomalies that appear if the supergravity theory is formulated on a ten-manifold times the interval. Again we find that the anomalies cancel locally at the boundaries of the interval through anomaly inflow, provided one suitably modifies the classical action. (author)

  1. Gauge theory and the topology of four-manifolds

    CERN Document Server

    Friedman, Robert Marc

    1998-01-01

    The lectures in this volume provide a perspective on how 4-manifold theory was studied before the discovery of modern-day Seiberg-Witten theory. One reason the progress using the Seiberg-Witten invariants was so spectacular was that those studying SU(2)-gauge theory had more than ten years' experience with the subject. The tools had been honed, the correct questions formulated, and the basic strategies well understood. The knowledge immediately bore fruit in the technically simpler environment of the Seiberg-Witten theory. Gauge theory long predates Donaldson's applications of the subject to 4-manifold topology, where the central concern was the geometry of the moduli space. One reason for the interest in this study is the connection between the gauge theory moduli spaces of a Kähler manifold and the algebro-geometric moduli space of stable holomorphic bundles over the manifold. The extra geometric richness of the SU(2)-moduli spaces may one day be important for purposes beyond the algebraic invariants that ...

  2. Geometric phases and hidden local gauge symmetry

    International Nuclear Information System (INIS)

    Fujikawa, Kazuo

    2005-01-01

    The analysis of geometric phases associated with level crossing is reduced to the familiar diagonalization of the Hamiltonian in the second quantized formulation. A hidden local gauge symmetry, which is associated with the arbitrariness of the phase choice of a complete orthonormal basis set, becomes explicit in this formulation (in particular, in the adiabatic approximation) and specifies physical observables. The choice of a basis set which specifies the coordinate in the functional space is arbitrary in the second quantization, and a subclass of coordinate transformations, which keeps the form of the action invariant, is recognized as the gauge symmetry. We discuss the implications of this hidden local gauge symmetry in detail by analyzing geometric phases for cyclic and noncyclic evolutions. It is shown that the hidden local symmetry provides a basic concept alternative to the notion of holonomy to analyze geometric phases and that the analysis based on the hidden local gauge symmetry leads to results consistent with the general prescription of Pancharatnam. We however note an important difference between the geometric phases for cyclic and noncyclic evolutions. We also explain a basic difference between our hidden local gauge symmetry and a gauge symmetry (or equivalence class) used by Aharonov and Anandan in their definition of generalized geometric phases

  3. Spin foam model for pure gauge theory coupled to quantum gravity

    International Nuclear Information System (INIS)

    Oriti, Daniele; Pfeiffer, Hendryk

    2002-01-01

    We propose a spin foam model for pure gauge fields coupled to Riemannian quantum gravity in four dimensions. The model is formulated for the triangulation of a four-manifold which is given merely combinatorially. The Riemannian Barrett-Crane model provides the gravity sector of our model and dynamically assigns geometric data to the given combinatorial triangulation. The gauge theory sector is a lattice gauge theory living on the same triangulation and obtains from the gravity sector the geometric information which is required to calculate the Yang-Mills action. The model is designed so that one obtains a continuum approximation of the gauge theory sector at an effective level, similarly to the continuum limit of lattice gauge theory, when the typical length scale of gravity is much smaller than the Yang-Mills scale

  4. On low rank classical groups in string theory, gauge theory and matrix models

    International Nuclear Information System (INIS)

    Intriligator, Ken; Kraus, Per; Ryzhov, Anton V.; Shigemori, Masaki; Vafa, Cumrun

    2004-01-01

    We consider N=1 supersymmetric U(N), SO(N), and Sp(N) gauge theories, with two-index tensor matter and added tree-level superpotential, for general breaking patterns of the gauge group. By considering the string theory realization and geometric transitions, we clarify when glueball superfields should be included and extremized, or rather set to zero; this issue arises for unbroken group factors of low rank. The string theory results, which are equivalent to those of the matrix model, refer to a particular UV completion of the gauge theory, which could differ from conventional gauge theory results by residual instanton effects. Often, however, these effects exhibit miraculous cancellations, and the string theory or matrix model results end up agreeing with standard gauge theory. In particular, these string theory considerations explain and remove some apparent discrepancies between gauge theories and matrix models in the literature

  5. Indefinite harmonic forms and gauge theory

    International Nuclear Information System (INIS)

    Nakashima, M.

    1988-01-01

    Indecomposable representations have been extensively used in the construction of conformal and de Sitter gauge theories. It is thus noteworthy that certain unitary highest weight representations have been given a geometric realization as the unitary quotient of an indecomposable representation using indefinite harmonic forms [RSW]. We apply this construction to SU(2,2) and the de Sitter group. The relation is established between these representations and the massless, positive energy representations of SU(2,2) obtained in the physics literature. We investigate the extent to which this construction allows twistors to be viewed as a gauge theory of SU(2,2). For the de Sitter group, on which the gauge theory of singletons is based, we find that this construction is not directly applicable. (orig.)

  6. Invariant structures in gauge theories and confinement

    International Nuclear Information System (INIS)

    Prokhorov, L.V.; Shabanov, S.V.

    1991-01-01

    The problem of finding all gauge invariants is considered in connection with the problem of confinement. Polylocal gauge tensors are introduced and studied. It is shown (both in physical and pure geometrical approaches) that the path-ordered exponent is the only fundamental bilocal gauge tensor, which means that any irreducible polylocal gauge tensor is built of P-exponents and local tensors (matter fields). The simplest invariant structures in electrodynamics, chromodynamics and a theory with the gauge group SU(2) are considered separately. 23 refs.; 2 figs

  7. A new geometrical gravitational theory

    International Nuclear Information System (INIS)

    Obata, T.; Chiba, J.; Oshima, H.

    1981-01-01

    A geometrical gravitational theory is developed. The field equations are uniquely determined apart from one unknown dimensionless parameter ω 2 . It is based on an extension of the Weyl geometry, and by the extension the gravitational coupling constant and the gravitational mass are made to be dynamical and geometrical. The fundamental geometrical objects in the theory are a metric gsub(μν) and two gauge scalars phi and psi. The theory satisfies the weak equivalence principle, but breaks the strong one generally. u(phi, psi) = phi is found out on the assumption that the strong one keeps holding good at least for bosons of low spins. Thus there is the simple correspondence between the geometrical objects and the gravitational objects. Since the theory satisfies the weak one, the inertial mass is also dynamical and geometrical in the same way as is the gravitational mass. Moreover, the cosmological term in the theory is a coscalar of power -4 algebraically made of psi and u(phi, psi), so it is dynamical, too. Finally spherically symmetric exact solutions are given. The permissible range of the unknown parameter ω 2 is experimentally determined by applying the solutions to the solar system. (author)

  8. Meta fluid dynamic as a gauge field theory

    International Nuclear Information System (INIS)

    Mendes, A.C.R.; Neves, C.; Oliveira, W.; Takakura, F.I.

    2003-01-01

    In this paper, the analog of Maxwell electromagnetism for hydrodynamic turbulence, the meta fluid dynamics, is extended in order to reformulate the meta fluid dynamics as a gauge field theory. That analogy opens up the possibility to investigate this theory as a constrained system. Having this possibility in mind, we propose a Lagrangian to describe this new theory of turbulence and, subsequently, analyze it from the symplectic point of view. From this analysis, a hidden gauge symmetry is revealed, providing a clear interpretation and meaning of the physics behind the meta fluid theory. Also, the geometrical interpretation to the gauge symmetries is discussed. (author)

  9. Geometric derivation of string field theory from first principles: Closed strings and modular invariance

    International Nuclear Information System (INIS)

    Kaku, M.

    1988-01-01

    We present an entirely new approach to closed-string field theory, called Igeometric string field theory R, which avoids the complications found in Becchi-Rouet-Stora-Tyutin string field theory (e.g., ghost counting, infinite overcounting of diagrams, midpoints, lack of modular invariance). Following the analogy with general relativity and Yang-Mills theory, we define a new infinite-dimensional local gauge group, called the unified string group, which uniquely specifies the connection fields, the curvature tensor, the measure and tensor calculus, and finally the action itself. Geometric field theory, when gauge fixed, yields an entirely new class of gauges called the interpolating gauge which allows us to smoothly interpolate between the midpoint gauge and the end-point gauge (''covariantized light-cone gauge''). We can show that geometric string field theory reproduces one copy of the Shapiro-Virasoro model. Surprisingly, after the gauge is broken, a new Iclosed four-string interactionR emerges as the counterpart of the instantaneous four-fermion Coulomb term in QED. This term restores modular invariance and precisely fills the missing region of the complex plane

  10. Gauging of 1D-space translations for nonrelativistic matter - Geometric bags

    International Nuclear Information System (INIS)

    Stichel, P.C.

    2000-01-01

    We develop in a systematic fashion the idea of gauging 1D-space translations with fixed Newtonian time for nonrelativistic matter (particles and fields). By starting with a nonrelativistic free theory we obtain its minimal gauge invariant extension by introducing two gauge fields with a Maxwellian self interaction. We fix the gauge so that the residual symmetry group is the Galilei group and construct a representation of the extended Galilei algebra. The reduced N-particle Lagrangian describes geodesic motion in a (N-1)-dimensional (Pseudo-) Riemannian space. The singularity of the metric for negative gauge coupling leads in classical dynamics to the formation of geometric bags in the case of two or three particles. The ordering problem within the quantization scheme for N-particles is solved by canonical quantization of a pseudoclassical Schroedinger theory obtained by adding to the continuum generalization of the point-particle Lagrangian an appropriate quantum correction. We solve the two-particle bound state problem for both signs of the gauge coupling. At the end we speculate on the possible physical relevance of the new interaction induced by the gauge fields

  11. An N=2 gauge theory and its supergravity dual

    CERN Document Server

    Brandhuber, A

    2000-01-01

    We study flows on the scalar manifold of N=8 gauged supergravity in five dimensions which are dual to certain mass deformations of N=4 super Yang-Mill theory. In particular, we consider a perturbation of the gauge theory by a mass term for the adjoint hyper-multiplet, giving rise to an N=2 theory. The exact solution of the 5-dim gauged supergravity equations of motion is found and the metric is uplifted to a ten-dimensional background of type-IIB supergravity. Using these geometric data and the AdS/CFT correspondence we analyze the spectra of certain operators as well as Wilson loops on the dual gauge theory side. The physical flows are parametrized by a single non-positive constant and describe part of the Coulomb branch of the N=2 theory at strong coupling.

  12. Gauge theories

    International Nuclear Information System (INIS)

    Lee, B.W.

    1976-01-01

    Some introductory remarks to Yang-Mills fields are given and the problem of the Coulomb gauge is considered. The perturbation expansion for quantized gauge theories is discussed and a survey of renormalization schemes is made. The role of Ward-Takahashi identities in gauge theories is discussed. The author then discusses the renormalization of pure gauge theories and theories with spontaneously broken symmetry. (B.R.H.)

  13. Deriving the four-string and open-closed string interactions from geometric string field theory

    International Nuclear Information System (INIS)

    Kaku, M.

    1990-01-01

    One of the questions concerning the covariant open string field theory is why there are two distinct BRST theories and why the four-string interaction appears in one version but not the other. The authors solve this mystery by showing that both theories are gauge-fixed versions of a higher gauge theory, called the geometric string field theory, with a new field, a string verbein e μσ νρ , which allows us to gauge the string length and σ parametrization. By fixing the gauge, the authors can derive the endpoint gauge (the covariantized light cone gauge), the midpoint gauge of Witten, or the interpolating gauge with arbitrary string length. The authors show explicitly that the four-string interaction is a gauge artifact of the geometric theory (the counterpart of the four-fermion instantaneous Coulomb term of QED). By choosing the interpolating gauge, they produce a new class of four-string interactions which smoothly interpolate between the endpoint gauge and the midpoint gauge (where it vanishes). Similarly, they can extract the closed string as a bound state of the open string, which appears in the endpoint gauge but vanishes in the midpoint gauge. Thus, the four-string and open-closed string interactions do not have to be added to the action as long as the string vierbein is included

  14. Gauge theory of gravity and supergravity on a group manifold

    International Nuclear Information System (INIS)

    Ne'eman, Y.; Regge, T.

    1977-12-01

    The natural arena for the physics of gravity, supergravity and their enlargements appears to be the group manifold of the Poincare group P, the graded Poincare group GP of supersymmetry, and the corresponding enlargements. The dynamics of these theories correspond to geometrical algorithms in P and GP. Differential geometry on Lie groups is reviewed and results applied to P and GP. Curvature, gauge transformations and factorization are introduced. Also reviewed is the general coordinate transformation group and a hybrid gauge transformation, the anholonomized G.C.T. gauge. A study is made of the construction of an action, including the introduction of a set of special 2 forms, the ''pseudo curvatures.'' The possibilities of factorization in supersymmetry are analyzed. The version of supergravity is present which has now become a completely geometrical theory

  15. Lattice formulations of supersymmetric gauge theories with matter fields

    International Nuclear Information System (INIS)

    Joseph, Anosh

    2014-12-01

    Certain classes of supersymmetric gauge theories, including the well known N=4 supersymmetric Yang-Mills theory, that takes part in the AdS/CFT correspondence, can be formulated on a Euclidean spacetime lattice using the techniques of exact lattice supersymmetry. Great ideas such as topological field theories, Dirac-Kaehler fermions, geometric discretization all come together to create supersymmetric lattice theories that are gauge-invariant, doubler free, local and exact supersymmetric. We discuss the recent lattice constructions of supersymmetric Yang-Mills theories in two and three dimensions coupled to matter fields in various representations of the color group.

  16. Chern-Simons as a geometrical set up for three dimensional gauge theories

    International Nuclear Information System (INIS)

    Lemes, V.E.R; Jesus, C. Linhares de; Sorella, S.P.; Villar, L.C.Q.; Ventura, O.S.

    1997-12-01

    Three dimensional Yang-Mills gauge theories in the presence of the Chern-Simons action are seen as being generated by the pure topological Chern-Simons term through nonlinear covariant redefinitions of the gauge field. (author)

  17. Five-dimensional gauge theory and compactification on a torus

    NARCIS (Netherlands)

    Haghighat, B.; Vandoren, S.J.G.

    2011-01-01

    We study five-dimensional minimally supersymmetric gauge theory compactified on a torus down to three dimensions, and its embedding into string/M-theory using geometric engineering. The moduli space on the Coulomb branch is hyperkaehler equipped with a metric with modular transformation properties.

  18. Geometrical theory of the relativistic string in t=tau gauge

    International Nuclear Information System (INIS)

    Barbashov, B.M.; Nesterenko, V.V.

    1982-01-01

    Using the co-moving frame method and the exterior differential forms in the surface theory the classical theory of the relativistic string in the gauge is constructed. The moving frame on the string world-sheet is chosen in a special form. As a result, the theory of the free relativistic string in the four-dimensional space-time is reduced to the D'Alembert equation for one scalar function

  19. High energy behaviour of nonabelian gauge theories

    International Nuclear Information System (INIS)

    Bartels, J.

    1979-10-01

    The high energy behavior (in the Regge limit) of nonabelian gauge theories is reviewed. After a general remark concerning the question to what extent the Regge limit can be approached within perturbation theory, we first review the reggeization of elementary particles within nonabelian gauge theories. Then the derivation of a unitary high energy description of a massive (= spontaneously broken) nonabelian gauge model is described, which results in a complete reggeon calculus. There is strong evidence that the zero mass limit of this reggeon calculus exists, thus giving rise to the hope that the Regge behavior in pure Yang-Mills theories (QCD) can be reached in this way. In the final part of these lectures two possible strategies for solving this reggeon calculus (both for the massive and the massless case) are outlined. One of them leads to a geometrical picture in which the distribution of the wee partons obeys a diffusion law. The other one makes contact with reggeon field theory and predicts that QCD in the high energy limit is described by critical reggeon field theory. (orig.)

  20. Gauge theories of Yang-Mills vector fields coupled to antisymmetric tensor fields

    International Nuclear Information System (INIS)

    Anco, Stephen C.

    2003-01-01

    A non-Abelian class of massless/massive nonlinear gauge theories of Yang-Mills vector potentials coupled to Freedman-Townsend antisymmetric tensor potentials is constructed in four space-time dimensions. These theories involve an extended Freedman-Townsend-type coupling between the vector and tensor fields, and a Chern-Simons mass term with the addition of a Higgs-type coupling of the tensor fields to the vector fields in the massive case. Geometrical, field theoretic, and algebraic aspects of the theories are discussed in detail. In particular, the geometrical structure mixes and unifies features of Yang-Mills theory and Freedman-Townsend theory formulated in terms of Lie algebra valued curvatures and connections associated to the fields and nonlinear field strengths. The theories arise from a general determination of all possible geometrical nonlinear deformations of linear Abelian gauge theory for one-form fields and two-form fields with an Abelian Chern-Simons mass term in four dimensions. For this type of deformation (with typical assumptions on the allowed form considered for terms in the gauge symmetries and field equations), an explicit classification of deformation terms at first-order is obtained, and uniqueness of deformation terms at all higher orders is proven. This leads to a uniqueness result for the non-Abelian class of theories constructed here

  1. Spin Gauge Theory of Gravity in Clifford Space

    International Nuclear Information System (INIS)

    Pavsic, Matej

    2006-01-01

    A theory in which 16-dimensional curved Clifford space (C-space) provides a realization of Kaluza-Klein theory is investigated. No extra dimensions of spacetime are needed: 'extra dimensions' are in C-space. We explore the spin gauge theory in C-space and show that the generalized spin connection contains the usual 4-dimensional gravity and Yang-Mills fields of the U(1) x SU(2) x SU(3) gauge group. The representation space for the latter group is provided by 16-component generalized spinors composed of four usual 4-component spinors, defined geometrically as the members of four independent minimal left ideals of Clifford algebra

  2. Geometric symmetries and topological terms in F-theory and field theory

    Energy Technology Data Exchange (ETDEWEB)

    Kapfer, Andreas

    2016-08-25

    suggest a new geometric group structure on resolved elliptic fibrations. In the same way we also propose a novel group operation for multi-sections in genus-one fibrations without a proper section. We stress that these arithmetic structures ensure the cancelation of all gauge anomalies in F-theory compactifications on Calabi-Yau manifolds.

  3. Strings - Links between conformal field theory, gauge theory and gravity

    International Nuclear Information System (INIS)

    Troost, J.

    2009-05-01

    String theory is a candidate framework for unifying the gauge theories of interacting elementary particles with a quantum theory of gravity. The last years we have made considerable progress in understanding non-perturbative aspects of string theory, and in bringing string theory closer to experiment, via the search for the Standard Model within string theory, but also via phenomenological models inspired by the physics of strings. Despite these advances, many deep problems remain, amongst which a non-perturbative definition of string theory, a better understanding of holography, and the cosmological constant problem. My research has concentrated on various theoretical aspects of quantum theories of gravity, including holography, black holes physics and cosmology. In this Habilitation thesis I have laid bare many more links between conformal field theory, gauge theory and gravity. Most contributions were motivated by string theory, like the analysis of supersymmetry preserving states in compactified gauge theories and their relation to affine algebras, time-dependent aspects of the holographic map between quantum gravity in anti-de-Sitter space and conformal field theories in the bulk, the direct quantization of strings on black hole backgrounds, the embedding of the no-boundary proposal for a wave-function of the universe in string theory, a non-rational Verlinde formula and the construction of non-geometric solutions to supergravity

  4. The master space of N = 1 gauge theories

    International Nuclear Information System (INIS)

    Forcella, Davide; Hanany, Amihay; He Yanghui; Zaffaroni, Alberto

    2008-01-01

    The full moduli space M of a class of N = 1 supersymmetric gauge theories is studied. For gauge theories living on a stack of D3-branes at Calabi-Yau singularities X, M is a combination of the mesonic and baryonic branches. In consonance with the mathematical literature, the single brane moduli space is called the master space F b . Illustrating with a host of explicit examples, we exhibit many algebro-geometric properties of the master space such as when F b is toric Calabi-Yau, behaviour of its Hilbert series, its irreducible components and its symmetries. In conjunction with the plethystic programme, we investigate the counting of BPS gauge invariants, baryonic and mesonic, using the geometry of F b and show how its refined Hilbert series not only engenders the generating functions for the counting but also beautifully encode 'hidden' global symmetries of the gauge theory which manifest themselves as symmetries of the complete moduli space M for N number of branes.

  5. Abelian gauge symmetries in F-theory and dual theories

    Science.gov (United States)

    Song, Peng

    In this dissertation, we focus on important physical and mathematical aspects, especially abelian gauge symmetries, of F-theory compactifications and its dual formulations within type IIB and heterotic string theory. F-theory is a non-perturbative formulation of type IIB string theory which enjoys important dualities with other string theories such as M-theory and E8 x E8 heterotic string theory. One of the main strengths of F-theory is its geometrization of many physical problems in the dual string theories. In particular, its study requires a lot of mathematical tools such as advanced techniques in algebraic geometry. Thus, it has also received a lot of interests among mathematicians, and is a vivid area of research within both the physics and the mathematics community. Although F-theory has been a long-standing theory, abelian gauge symmetry in Ftheory has been rarely studied, until recently. Within the mathematics community, in 2009, Grassi and Perduca first discovered the possibility of constructing elliptically fibered varieties with non-trivial toric Mordell-Weil group. In the physics community, in 2012, Morrison and Park first made a major advancement by constructing general F-theory compactifications with U(1) abelian gauge symmetry. They found that in such cases, the elliptically-fibered Calabi-Yau manifold that F-theory needs to be compactified on has its fiber being a generic elliptic curve in the blow-up of the weighted projective space P(1;1;2) at one point. Subsequent developments have been made by Cvetic, Klevers and Piragua extended the works of Morrison and Park and constructed general F-theory compactifications with U(1) x U(1) abelian gauge symmetry. They found that in the U(1) x U(1) abelian gauge symmetry case, the elliptically-fibered Calabi-Yau manifold that F-theory needs to be compactified on has its fiber being a generic elliptic curve in the del Pezzo surface dP2. In chapter 2 of this dissertation, I bring this a step further by

  6. Anomaly matching conditions and the moduli space of supersymmetric gauge theories

    International Nuclear Information System (INIS)

    Dotti, G.; Manohar, A.V.

    1998-01-01

    The structure of the moduli space of N=1 supersymmetric gauge theories is analyzed from an algebraic geometric viewpoint. The connection between the fundamental fields of the ultraviolet theory, and the gauge-invariant composite fields of the infrared theory is explained in detail. The results are then used to prove an anomaly matching theorem. The theorem is used to study anomaly matching for supersymmetric QCD, and can explain all the known anomaly matching results for this case. (orig.)

  7. The arithmetic of elliptic fibrations in gauge theories on a circle

    Energy Technology Data Exchange (ETDEWEB)

    Grimm, Thomas W. [Max-Planck-Institut für Physik,Föhringer Ring 6, 80805 Munich (Germany); Institute for Theoretical Physics,Utrecht University, Leuvenlaan 4, 3584 CE Utrecht (Netherlands); Center for Extreme Matter and Emergent Phenomena,Utrecht University, Leuvenlaan 4, 3584 CE Utrecht (Netherlands); Kapfer, Andreas [Max-Planck-Institut für Physik,Föhringer Ring 6, 80805 Munich (Germany); Klevers, Denis [Theory Group, Physics Department, CERN,CH-1211, Geneva 23 (Switzerland)

    2016-06-20

    The geometry of elliptic fibrations translates to the physics of gauge theories in F-theory. We systematically develop the dictionary between arithmetic structures on elliptic curves as well as desingularized elliptic fibrations and symmetries of gauge theories on a circle. We show that the Mordell-Weil group law matches integral large gauge transformations around the circle in Abelian gauge theories and explain the significance of Mordell-Weil torsion in this context. We also use Higgs transitions and circle large gauge transformations to introduce a group law for genus-one fibrations with multi-sections. Finally, we introduce a novel arithmetic structure on elliptic fibrations with non-Abelian gauge groups in F-theory. It is defined on the set of exceptional divisors resolving the singularities and divisor classes of sections of the fibration. This group structure can be matched with certain integral non-Abelian large gauge transformations around the circle when studying the theory on the lower-dimensional Coulomb branch. Its existence is required by consistency with Higgs transitions from the non-Abelian theory to its Abelian phases in which it becomes the Mordell-Weil group. This hints towards the existence of a new underlying geometric symmetry.

  8. The arithmetic of elliptic fibrations in gauge theories on a circle

    Science.gov (United States)

    Grimm, Thomas W.; Kapfer, Andreas; Klevers, Denis

    2016-06-01

    The geometry of elliptic fibrations translates to the physics of gauge theories in F-theory. We systematically develop the dictionary between arithmetic structures on elliptic curves as well as desingularized elliptic fibrations and symmetries of gauge theories on a circle. We show that the Mordell-Weil group law matches integral large gauge transformations around the circle in Abelian gauge theories and explain the significance of Mordell-Weil torsion in this context. We also use Higgs transitions and circle large gauge transformations to introduce a group law for genus-one fibrations with multi-sections. Finally, we introduce a novel arithmetic structure on elliptic fibrations with non-Abelian gauge groups in F-theory. It is defined on the set of exceptional divisors resolving the singularities and divisor classes of sections of the fibration. This group structure can be matched with certain integral non-Abelian large gauge transformations around the circle when studying the theory on the lower-dimensional Coulomb branch. Its existence is required by consistency with Higgs transitions from the non-Abelian theory to its Abelian phases in which it becomes the Mordell-Weil group. This hints towards the existence of a new underlying geometric symmetry.

  9. The arithmetic of elliptic fibrations in gauge theories on a circle

    International Nuclear Information System (INIS)

    Grimm, Thomas W.; Kapfer, Andreas; Klevers, Denis

    2016-01-01

    The geometry of elliptic fibrations translates to the physics of gauge theories in F-theory. We systematically develop the dictionary between arithmetic structures on elliptic curves as well as desingularized elliptic fibrations and symmetries of gauge theories on a circle. We show that the Mordell-Weil group law matches integral large gauge transformations around the circle in Abelian gauge theories and explain the significance of Mordell-Weil torsion in this context. We also use Higgs transitions and circle large gauge transformations to introduce a group law for genus-one fibrations with multi-sections. Finally, we introduce a novel arithmetic structure on elliptic fibrations with non-Abelian gauge groups in F-theory. It is defined on the set of exceptional divisors resolving the singularities and divisor classes of sections of the fibration. This group structure can be matched with certain integral non-Abelian large gauge transformations around the circle when studying the theory on the lower-dimensional Coulomb branch. Its existence is required by consistency with Higgs transitions from the non-Abelian theory to its Abelian phases in which it becomes the Mordell-Weil group. This hints towards the existence of a new underlying geometric symmetry.

  10. Gauge theories

    International Nuclear Information System (INIS)

    Kenyon, I.R.

    1986-01-01

    Modern theories of the interactions between fundamental particles are all gauge theories. In the case of gravitation, application of this principle to space-time leads to Einstein's theory of general relativity. All the other interactions involve the application of the gauge principle to internal spaces. Electromagnetism serves to introduce the idea of a gauge field, in this case the electromagnetic field. The next example, the strong force, shows unique features at long and short range which have their origin in the self-coupling of the gauge fields. Finally the unification of the description of the superficially dissimilar electromagnetic and weak nuclear forces completes the picture of successes of the gauge principle. (author)

  11. Continuum gauge fields from lattice gauge fields

    International Nuclear Information System (INIS)

    Goeckeler, M.; Kronfeld, A.S.; Schierholz, G.; Wiese, U.J.

    1993-01-01

    On the lattice some of the salient features of pure gauge theories and of gauge theories with fermions in complex representations of the gauge group seem to be lost. These features can be recovered by considering part of the theory in the continuum. The prerequisite for that is the construction of continuum gauge fields from lattice gauge fields. Such a construction, which is gauge covariant and complies with geometrical constructions of the topological charge on the lattice, is given in this paper. The procedure is explicitly carried out in the U(1) theory in two dimensions, where it leads to simple results. (orig.)

  12. Lattice gauge theory

    International Nuclear Information System (INIS)

    Mack, G.

    1982-01-01

    After a description of a pure Yang-Mills theory on a lattice, the author considers a three-dimensional pure U(1) lattice gauge theory. Thereafter he discusses the exact relation between lattice gauge theories with the gauge groups SU(2) and SO(3). Finally he presents Monte Carlo data on phase transitions in SU(2) and SO(3) lattice gauge models. (HSI)

  13. Geometric continuum regularization of quantum field theory

    International Nuclear Information System (INIS)

    Halpern, M.B.

    1989-01-01

    An overview of the continuum regularization program is given. The program is traced from its roots in stochastic quantization, with emphasis on the examples of regularized gauge theory, the regularized general nonlinear sigma model and regularized quantum gravity. In its coordinate-invariant form, the regularization is seen as entirely geometric: only the supermetric on field deformations is regularized, and the prescription provides universal nonperturbative invariant continuum regularization across all quantum field theory. 54 refs

  14. Gravitational Goldstone fields from affine gauge theory

    Science.gov (United States)

    Tresguerres, Romualdo; Mielke, Eckehard W.

    2000-08-01

    In order to facilitate the application of standard renormalization techniques, gravitation should be described, in the pure connection formalism, as a Yang-Mills theory of a certain spacetime group, say the Poincaré or the affine group. This embodies the translational as well as the linear connection. However, the coframe is not the standard Yang-Mills-type gauge field of the translations, since it lacks the inhomogeneous gradient term in the gauge transformations. By explicitly restoring this ``hidden'' piece within the framework of nonlinear realizations, the usual geometrical interpretation of the dynamical theory becomes possible, and in addition one can avoid the metric or coframe degeneracy which would otherwise interfere with the integrations within the path integral. We claim that nonlinear realizations provide the general mathematical scheme for the foundation of gauge theories of spacetime symmetries. When applied to construct the Yang-Mills theory of the affine group, tetrads become identified with nonlinear translational connections; the anholonomic metric no longer constitutes an independent gravitational potential, since its degrees of freedom reveal a correspondence to eliminateable Goldstone bosons. This may be an important advantage for quantization.

  15. Enhanced gauge symmetry in type II string theory

    International Nuclear Information System (INIS)

    Katz, S.; Ronen Plesser, M.

    1996-01-01

    We show how enhanced gauge symmetry in type II string theory compactified on a Calabi-Yau threefold arises from singularities in the geometry of the target space. When the target space of the type IIA string acquires a genus g curve C of A N-1 singularities, we find that an SU(N) gauge theory with g adjoint hypermultiplets appears at the singularity. The new massless states correspond to solitons wrapped about the collapsing cycles, and their dynamics is described by a twisted supersymmetric gauge theory on C x R 4 . We reproduce this result from an analysis of the S-dual D-manifold. We check that the predictions made by this model about the nature of the Higgs branch, the monodromy of period integrals, and the asymptotics of the one-loop topological amplitude are in agreement with geometrical computations. In one of our examples we find that the singularity occurs at strong coupling in the heterotic dual proposed by Kachru and Vafa. (orig.)

  16. Supersymmetric gauge theories from string theory; Theorie de jauge supersymetrique de la theorie des cordes

    Energy Technology Data Exchange (ETDEWEB)

    Metzger, St

    2005-12-15

    This thesis presents various ways to construct four-dimensional quantum field theories from string theory. In a first part we study the generation of a supersymmetric Yang-Mills theory, coupled to an adjoint chiral superfield, from type IIB string theory on non-compact Calabi-Yau manifolds, with D-branes wrapping certain sub-cycles. Properties of the gauge theory are then mapped to the geometric structure of the Calabi-Yau space. Even if the Calabi-Yau geometry is too complicated to evaluate the geometric integrals explicitly, one can then always use matrix model perturbation theory to calculate the effective superpotential. The second part of this work covers the generation of four-dimensional super-symmetric gauge theories, carrying several important characteristic features of the standard model, from compactifications of eleven-dimensional supergravity on G{sub 2}-manifolds. If the latter contain conical singularities, chiral fermions are present in the four-dimensional gauge theory, which potentially lead to anomalies. We show that, locally at each singularity, these anomalies are cancelled by the non-invariance of the classical action through a mechanism called 'anomaly inflow'. Unfortunately, no explicit metric of a compact G{sub 2}-manifold is known. Here we construct families of metrics on compact weak G{sub 2}-manifolds, which contain two conical singularities. Weak G{sub 2}-manifolds have properties that are similar to the ones of proper G{sub 2}-manifolds, and hence the explicit examples might be useful to better understand the generic situation. Finally, we reconsider the relation between eleven-dimensional supergravity and the E{sub 8} x E{sub 8}-heterotic string. This is done by carefully studying the anomalies that appear if the supergravity theory is formulated on a ten-manifold times the interval. Again we find that the anomalies cancel locally at the boundaries of the interval through anomaly inflow, provided one suitably modifies the

  17. Direct gauging of the Poincare group V. Group scaling, classical gauge theory, and gravitational corrections

    International Nuclear Information System (INIS)

    Edelen, D.G.B.

    1986-01-01

    Homogeneous scaling of the group space of the Poincare group, P 10 , is shown to induce scalings of all geometric quantities associated with the local action of P 10 . The field equations for both the translation and the Lorentz rotation compensating fields reduce to O(1) equations if the scaling parameter is set equal to the general relativistic gravitational coupling constant 8πGc -4 . Standard expansions of all field variables in power series in the scaling parameter give the following results. The zeroth-order field equations are exactly the classical field equations for matter fields on Minkowski space subject to local action of an internal symmetry group (classical gauge theory). The expansion process is shown to break P 10 -gauge covariance of the theory, and hence solving the zeroth-order field equations imposes an implicit system of P 10 -gauge conditions. Explicit systems of field equations are obtained for the first- and higher-order approximations. The first-order translation field equations are driven by the momentum-energy tensor of the matter and internal compensating fields in the zeroth order (classical gauge theory), while the first-order Lorentz rotation field equations are driven by the spin currents of the same classical gauge theory. Field equations for the first-order gravitational corrections to the matter fields and the gauge fields for the internal symmetry group are obtained. Direct Poincare gauge theory is thus shown to satisfy the first two of the three-part acid test of any unified field theory. Satisfaction of the third part of the test, at least for finite neighborhoods, seems probable

  18. A Unified Field Theory of Gravity, Electromagnetism, and the Yang-Mills Gauge Field

    Directory of Open Access Journals (Sweden)

    Suhendro I.

    2008-01-01

    Full Text Available In this work, we attempt at constructing a comprehensive four-dimensional unified field theory of gravity, electromagnetism, and the non-Abelian Yang-Mills gauge field in which the gravitational, electromagnetic, and material spin fields are unified as intrinsic geometric objects of the space-time manifold S4 via the connection, with the general- ized non-Abelian Yang-Mills gauge field appearing in particular as a sub-field of the geometrized electromagnetic interaction.

  19. Nonlocal gauge theories

    International Nuclear Information System (INIS)

    Krasnikov, N.V.

    1987-01-01

    Nonlocal gauge theories including gravity are considered. It is shown that the introduction of the additional nonlocal interaction makes γ 5 -anomalous theories meaningful. The introduction of such interaction leads to macrocausal unitary theory, which describes the interaction of massive vector fields with fermion fields. It is shown that nonlocal gauge theories with nonlocal scale Λ nl ≤(1-10) TeV can solve the gauge hierarchy problem. An example of nonlinear grand unified gauge model in which topologically nontrivial finite energy monopole solutions are absent is found

  20. Quantization of the Hitchin moduli spaces, Liouville theory, and the geometric Langlands correspondence I

    Energy Technology Data Exchange (ETDEWEB)

    Teschner, J. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Gruppe Theorie

    2010-05-15

    It was in particular recently argued that the gauge theory in the presence of a certain one-parameter deformation can at low energies effectively be described in terms the quantization of an algebraically integrable system, which is canonically associated to this theory. It seems, however, that the deeper reasons for this relationship between a two- and a fourdimensional theory remain to be understood. A clue in this direction may be seen in the fact that the instanton partition functions which represent the building blocks of the partition functions are obtained by specializing a two-parameter family Z(a,{epsilon}{sub 1},{epsilon}{sub 2};q) of instanton partition functions. These functions were identified with the conformal blocks of Liouville theory. This indicates that the relationship between certain gauge theories and Liouville theory involves in particular a two-parametric deformation of the algebraically integrable model associated to the gauge theories on R{sup 4} which ultimately produces Liouville theory as a result. One of my intentions in this paper is to clarify in which sense this point of view is correct. Another piece of motivation comes from relations between fourdimensional gauge theories and the geometric Langlands correspondence. The author feels that the mentioned relations between gauge theory and conformal field theory offer new clues in this regard. It is therefore my second main aim to clarify the relations between the quantization of the Hitchin system, the geometric Langlands correspondence and the Liouville conformal field theory. (orig.)

  1. Quantization of the Hitchin moduli spaces, Liouville theory, and the geometric Langlands correspondence I

    International Nuclear Information System (INIS)

    Teschner, J.

    2010-05-01

    It was in particular recently argued that the gauge theory in the presence of a certain one-parameter deformation can at low energies effectively be described in terms the quantization of an algebraically integrable system, which is canonically associated to this theory. It seems, however, that the deeper reasons for this relationship between a two- and a fourdimensional theory remain to be understood. A clue in this direction may be seen in the fact that the instanton partition functions which represent the building blocks of the partition functions are obtained by specializing a two-parameter family Z(a,ε 1 ,ε 2 ;q) of instanton partition functions. These functions were identified with the conformal blocks of Liouville theory. This indicates that the relationship between certain gauge theories and Liouville theory involves in particular a two-parametric deformation of the algebraically integrable model associated to the gauge theories on R 4 which ultimately produces Liouville theory as a result. One of my intentions in this paper is to clarify in which sense this point of view is correct. Another piece of motivation comes from relations between fourdimensional gauge theories and the geometric Langlands correspondence. The author feels that the mentioned relations between gauge theory and conformal field theory offer new clues in this regard. It is therefore my second main aim to clarify the relations between the quantization of the Hitchin system, the geometric Langlands correspondence and the Liouville conformal field theory. (orig.)

  2. A Kaluza-Klein interpretation of an extended gauge theory

    International Nuclear Information System (INIS)

    Doria, C.M.

    1987-01-01

    A possible geometric justification for the inclusion of three vector potentials transforming under a common compact and simple gauge group is presented in terms of the spontaneous compactification of a higher-dimensional theory of coupled Yang-Mills-gravity with non-trivial torsion. (author) [pt

  3. Hyperunified field theory and gravitational gauge-geometry duality

    International Nuclear Information System (INIS)

    Wu, Yue-Liang

    2018-01-01

    A hyperunified field theory is built in detail based on the postulates of gauge invariance and coordinate independence along with the conformal scaling symmetry. All elementary particles are merged into a single hyper-spinor field and all basic forces are unified into a fundamental interaction governed by the hyper-spin gauge symmetry SP(1, D h - 1). The dimension D h of hyper-spacetime is conjectured to have a physical origin in correlation with the hyper-spin charge of elementary particles. The hyper-gravifield fiber bundle structure of biframe hyper-spacetime appears naturally with the globally flat Minkowski hyper-spacetime as a base spacetime and the locally flat hyper-gravifield spacetime as a fiber that is viewed as a dynamically emerged hyper-spacetime characterized by a non-commutative geometry. The gravitational origin of gauge symmetry is revealed with the hyper-gravifield that plays an essential role as a Goldstone-like field. The gauge-gravity and gravity-geometry correspondences bring about the gravitational gauge-geometry duality. The basic properties of hyperunified field theory and the issue on the fundamental scale are analyzed within the framework of quantum field theory, which allows us to describe the laws of nature in deriving the gauge gravitational equation with the conserved current and the geometric gravitational equations of Einstein-like type and beyond. (orig.)

  4. Hyperunified field theory and gravitational gauge-geometry duality

    Energy Technology Data Exchange (ETDEWEB)

    Wu, Yue-Liang [International Centre for Theoretical Physics Asia-Pacific (ICTP-AP), Beijing (China); Chinese Academy of Sciences, Institute of Theoretical Physics, Beijing (China); University of Chinese Academy of Sciences (UCAS), Beijing (China)

    2018-01-15

    A hyperunified field theory is built in detail based on the postulates of gauge invariance and coordinate independence along with the conformal scaling symmetry. All elementary particles are merged into a single hyper-spinor field and all basic forces are unified into a fundamental interaction governed by the hyper-spin gauge symmetry SP(1, D{sub h} - 1). The dimension D{sub h} of hyper-spacetime is conjectured to have a physical origin in correlation with the hyper-spin charge of elementary particles. The hyper-gravifield fiber bundle structure of biframe hyper-spacetime appears naturally with the globally flat Minkowski hyper-spacetime as a base spacetime and the locally flat hyper-gravifield spacetime as a fiber that is viewed as a dynamically emerged hyper-spacetime characterized by a non-commutative geometry. The gravitational origin of gauge symmetry is revealed with the hyper-gravifield that plays an essential role as a Goldstone-like field. The gauge-gravity and gravity-geometry correspondences bring about the gravitational gauge-geometry duality. The basic properties of hyperunified field theory and the issue on the fundamental scale are analyzed within the framework of quantum field theory, which allows us to describe the laws of nature in deriving the gauge gravitational equation with the conserved current and the geometric gravitational equations of Einstein-like type and beyond. (orig.)

  5. Hyperunified field theory and gravitational gauge-geometry duality

    Science.gov (United States)

    Wu, Yue-Liang

    2018-01-01

    A hyperunified field theory is built in detail based on the postulates of gauge invariance and coordinate independence along with the conformal scaling symmetry. All elementary particles are merged into a single hyper-spinor field and all basic forces are unified into a fundamental interaction governed by the hyper-spin gauge symmetry SP(1, D_h-1). The dimension D_h of hyper-spacetime is conjectured to have a physical origin in correlation with the hyper-spin charge of elementary particles. The hyper-gravifield fiber bundle structure of biframe hyper-spacetime appears naturally with the globally flat Minkowski hyper-spacetime as a base spacetime and the locally flat hyper-gravifield spacetime as a fiber that is viewed as a dynamically emerged hyper-spacetime characterized by a non-commutative geometry. The gravitational origin of gauge symmetry is revealed with the hyper-gravifield that plays an essential role as a Goldstone-like field. The gauge-gravity and gravity-geometry correspondences bring about the gravitational gauge-geometry duality. The basic properties of hyperunified field theory and the issue on the fundamental scale are analyzed within the framework of quantum field theory, which allows us to describe the laws of nature in deriving the gauge gravitational equation with the conserved current and the geometric gravitational equations of Einstein-like type and beyond.

  6. A new gauge for supersymmetric abelian gauge theories

    International Nuclear Information System (INIS)

    Smith, A.W.; Barcelos Neto, J.

    1984-01-01

    A new gauge for supersymmetric abelian gauge theories is presented. It is shown that this new gauge allows us to obtain terms which usually come as radiative corrections to the supersymmetric abelian gauge theories when one uses the Wess-Zumino gauge. (Author) [pt

  7. Nonlocal gauge theories

    International Nuclear Information System (INIS)

    Partovi, M.H.

    1982-01-01

    From a generalization of the covariant derivative, nonlocal gauge theories are developed. These theories enjoy local gauge invariance and associated Ward identities, a corresponding locally conserved current, and a locally conserved energy-momentum tensor, with the Ward identities implying the masslessness of the gauge field as in local theories. Their ultraviolet behavior allows the presence as well as the absence of the Adler-Bell-Jackiw anomaly, the latter in analogy with lattice theories

  8. Geometrical theory of ghost and Higgs fields and SU(2/1)

    International Nuclear Information System (INIS)

    Ne'eman, Y.; Thierry-Mieg, J.

    1979-10-01

    That a Principal Fiber Bundle provides a precise geometrical representation of Yang-Mills gauge theories has been known since 1963 and used since 1975. This work presents an entirely new domain of applications. The Feynman-DeWitt-Fadeev-Popov ghost-fields required in the renormalization procedure are identified with geometrical objects in the Principal Bundle. This procedure directly yields the BRS equations guaranteeing unitarity and Slavnov-Taylor invariance of the quantum effective Lagrangian. Except for one ghost field and its variation, this entire symmetry thus corresponds to classical notions, in that it is geometrical, and completely independent of the gauge-fixing procedure, which determines the quantized Lagrangian. These results may be used to fix the signs associated with the various ghost loops of quantum supergravity. The result is based upon the identification of a geometrical Z(2) x Z(2) double-gradation of the generalized fields in supergravity: [physical/ghost] fields and [integer/half integer] spins. Then the case of a supergroup as an internal symmetry gauge is considered. Ghosts geometrically associated to odd generators may be identified with the Goldstone-Nambu Higgs-Kibble scalar fields of conventional models with spontaneous symmetry breakdown. As an example, the chiral SU(3)/sub L/ x SU(3)/sub R/ flavor symmetry is realized by gauging the supergroup Q(3).Lastly, the main results concerning asthenodynamics (Weak-EM Unification) as given by the ghost-gauge SU(2/1) supergroup are recalled. 1 table

  9. Supersymmetric gauged double field theory: systematic derivation by virtue of twist

    International Nuclear Information System (INIS)

    Cho, Wonyoung; Fernández-Melgarejo, J.J.; Jeon, Imtak; Park, Jeong-Hyuck

    2015-01-01

    In a completely systematic and geometric way, we derive maximal and half-maximal supersymmetric gauged double field theories in lower than ten dimensions. To this end, we apply a simple twisting ansatz to the D=10 ungauged maximal and half-maximal supersymmetric double field theories constructed previously within the so-called semi-covariant formalism. The twisting ansatz may not satisfy the section condition. Nonetheless, all the features of the semi-covariant formalism, including its complete covariantizability, are still valid after the twist under alternative consistency conditions. The twist allows gaugings as supersymmetry preserving deformations of the D=10 untwisted theories after Scherk-Schwarz-type dimensional reductions. The maximal supersymmetric twist requires an extra condition to ensure both the Ramond-Ramond gauge symmetry and the 32 supersymmetries unbroken.

  10. Dual geometric-gauge field aspects of gravity

    International Nuclear Information System (INIS)

    Huei Peng; Wang, K.

    1992-01-01

    We propose that the geometric and standard gauge field aspects of gravity are equally essential for a complete description of gravity and can be reconciled. We show that this dualism of gravity resolves the dimensional Newtonian constant problem in both quantum gravity and unification schemes involving gravity (i.e., the Newtonian constant is no longer the coupling constant in the gauge aspect of gravity) and reveals the profound similarity between gravity and other fields. 23 refs., 3 tabs

  11. Gauge field condensation in geometric quantum chromodynamics

    International Nuclear Information System (INIS)

    Guendelman, E.I.

    1991-09-01

    In odd number of dimensions, it is possible to construct general covariant gauge theories, where the metric is not an independent variable, but local function of the gauge fields. Starting from standardly defined gauge theory, upon functional integration of some variables, we could end up with such moodels. For models with SU(2) and SU(3) symmetry in three dimensions, gauge field condensation take place in the vacuum, which is nevertheless homogeneous and isotropic up to a gauge transformation, provided the space is flat. Introducing Higgs fields that spontaneously break the gauge symmetry, we get a breakdown of the homogenity and isotropy of the vacuum. Finally, we discuss how some of this ideas can be generalized to four and other even dimensions. (author)

  12. From lattice BF gauge theory to area-angle Regge calculus

    International Nuclear Information System (INIS)

    Bonzom, Valentin

    2009-01-01

    We consider Riemannian 4D BF lattice gauge theory, on a triangulation of spacetime. Introducing the simplicity constraints which turn BF theory into simplicial gravity, some geometric quantities of Regge calculus, areas, and 3D and 4D dihedral angles, are identified. The parallel transport conditions are taken care of to ensure a consistent gluing of simplices. We show that these gluing relations, together with the simplicity constraints, contain the constraints of area-angle Regge calculus in a simple way, via the group structure of the underlying BF gauge theory. This provides a precise road from constrained BF theory to area-angle Regge calculus. Doing so, a framework combining variables of lattice BF theory and Regge calculus is built. The action takes a form a la Regge and includes the contribution of the Immirzi parameter. In the absence of simplicity constraints, the standard spin foam model for BF theory is recovered. Insertions of local observables are investigated, leading to Casimir insertions for areas and reproducing for 3D angles known results obtained through angle operators on spin networks. The present formulation is argued to be suitable for deriving spin foam models from discrete path integrals and to unravel their geometric content.

  13. Nambu–Poisson gauge theory

    Energy Technology Data Exchange (ETDEWEB)

    Jurčo, Branislav, E-mail: jurco@karlin.mff.cuni.cz [Charles University in Prague, Faculty of Mathematics and Physics, Mathematical Institute, Prague 186 75 (Czech Republic); Schupp, Peter, E-mail: p.schupp@jacobs-university.de [Jacobs University Bremen, 28759 Bremen (Germany); Vysoký, Jan, E-mail: vysokjan@fjfi.cvut.cz [Jacobs University Bremen, 28759 Bremen (Germany); Czech Technical University in Prague, Faculty of Nuclear Sciences and Physical Engineering, Prague 115 19 (Czech Republic)

    2014-06-02

    We generalize noncommutative gauge theory using Nambu–Poisson structures to obtain a new type of gauge theory with higher brackets and gauge fields. The approach is based on covariant coordinates and higher versions of the Seiberg–Witten map. We construct a covariant Nambu–Poisson gauge theory action, give its first order expansion in the Nambu–Poisson tensor and relate it to a Nambu–Poisson matrix model.

  14. Nambu–Poisson gauge theory

    International Nuclear Information System (INIS)

    Jurčo, Branislav; Schupp, Peter; Vysoký, Jan

    2014-01-01

    We generalize noncommutative gauge theory using Nambu–Poisson structures to obtain a new type of gauge theory with higher brackets and gauge fields. The approach is based on covariant coordinates and higher versions of the Seiberg–Witten map. We construct a covariant Nambu–Poisson gauge theory action, give its first order expansion in the Nambu–Poisson tensor and relate it to a Nambu–Poisson matrix model.

  15. Chemical potentials in gauge theories

    International Nuclear Information System (INIS)

    Actor, A.; Pennsylvania State Univ., Fogelsville

    1985-01-01

    One-loop calculations of the thermodynamic potential Ω are presented for temperature gauge and non-gauge theories. Prototypical formulae are derived which give Ω as a function of both (i) boson and/or fermion chemical potential, and in the case of gauge theories (ii) the thermal vacuum parameter Asub(O)=const (Asub(μ) is the euclidean gauge potential). From these basic abelian gauge theory formulae, the one-loop contribution to Ω can readily be constructed for Yang-Mills theories, and also for non-gauge theories. (orig.)

  16. Geometry from Gauge Theory

    International Nuclear Information System (INIS)

    Correa, Diego H.; Silva, Guillermo A.

    2008-01-01

    We discuss how geometrical and topological aspects of certain (1/2)-BPS type IIB geometries are captured by their dual operators in N = 4 Super Yang-Mills theory. The type IIB solutions are characterized by arbitrary droplet pictures in a plane and we consider, in particular, axially symmetric droplets. The 1-loop anomalous dimension of the dual gauge theory operators probed with single traces is described by some bosonic lattice Hamiltonians. These Hamiltonians are shown to encode the topology of the droplets. In appropriate BMN limits, the Hamiltonians spectrum reproduces the spectrum of near-BPS string excitations propagating along each of the individual edges of the droplet. We also study semiclassical regimes for the Hamiltonians. For droplets having disconnected constituents, the Hamiltonian admits different complimentary semiclassical descriptions, each one replicating the semiclassical description for closed strings extending in each of the constituents

  17. Introduction to gauge theories

    International Nuclear Information System (INIS)

    Wit, B. de

    1983-01-01

    In these lectures we present the key ingredients of theories with local gauge invariance. We introduce gauge invariance as a starting point for the construction of a certain class of field theories, both for abelian and nonabelian gauge groups. General implications of gauge invariance are discussed, and we outline in detail how gauge fields can acquire masses in a spontaneous fashion. (orig./HSI)

  18. Unification of gauge and gravity Chern-Simons theories in 3-D space-time

    Energy Technology Data Exchange (ETDEWEB)

    Saghir, Chireen A.; Shamseddine, Laurence W. [American University of Beirut, Physics Department, Beirut (Lebanon)

    2017-11-15

    Chamseddine and Mukhanov showed that gravity and gauge theories could be unified in one geometric construction provided that a metricity condition is imposed on the vielbein. In this paper we are going to show that by enlarging the gauge group we are able to unify Chern-Simons gauge theory and Chern-Simons gravity in 3-D space-time. Such a unification leads to the quantization of the coefficients for both Chern-Simons terms for compact groups but not for non-compact groups. Moreover, it leads to a topological invariant quantity of the 3-dimensional space-time manifold on which they are defined. (orig.)

  19. A Unified Field Theory of Gravity, Electromagnetism, and theA Unified Field Theory of Gravity, Electromagnetism, and the Yang-Mills Gauge Field

    Directory of Open Access Journals (Sweden)

    Suhendro I.

    2008-01-01

    Full Text Available In this work, we attempt at constructing a comprehensive four-dimensional unified field theory of gravity, electromagnetism, and the non-Abelian Yang-Mills gauge field in which the gravitational, electromagnetic, and material spin fields are unified as intrinsic geometric objects of the space-time manifold $S_4$ via the connection, with the generalized non-Abelian Yang-Mills gauge field appearing in particular as a sub-field of the geometrized electromagnetic interaction.

  20. Group-geometric methods in supergravity and superstring theories

    International Nuclear Information System (INIS)

    Castellani, L.

    1992-01-01

    The purpose of this paper is to give a brief and pedagogical account of the group-geometric approach to (super)gravity and superstring theories. The authors summarize the main ideas and apply them to selected examples. Group geometry provides a natural and unified formulation of gravity and gauge theories. The invariance of both are interpreted as diffeomorphisms on a suitable group manifold. This geometrical framework has a fruitful output, in that it provides a systematic algorithm for the gauging of Lie algebras and the construction of (super)gravity or (super)string Lagrangians. The basic idea is to associate fundamental fields to the group generators. This is done by considering first a basis of tangent vectors on the group manifold. These vectors close on the same algebra as the abstract group generators. The dual basis, i.e. the vielbeins (cotangent basis of one-forms) is then identified with the set of fundamental fields. Thus, for example, the vielbein V a and the spin connection ω ab of ordinary Einstein-Cartan gravity are seen as the duals of the tangent vectors corresponding to translations and Lorentz rotations, respectively

  1. Gauge theories as string theories: the first results

    International Nuclear Information System (INIS)

    Gorsky, Aleksandr S

    2005-01-01

    The gauge/string theory duality in curved space is discussed mainly using a non-Abelian conformal N = 4 supersymmetric gauge theory and the theory of a closed superstring in the AdS 5 x S 5 metric as an example. It is shown that in the supergravity approximation, string duality yields the characteristics of a strong-coupling gauge theory. For a special shape of the contour, a Wilson loop expression is derived in the classical superstring approximation. The role of the hidden integrability in lower-loop calculations in gauge theory and in different approximations of string theory is discussed. It is demonstrated that in the large quantum-number limit, gauge theory operators can be described in terms of the dual string picture. Examples of metrics providing the dual description of gauge theories with broken conformal symmetry are presented, and formulations of the vacuum structure of such theories in terms of gravity are discussed. (reviews of topical problems)

  2. Gauge invariance rediscovered

    International Nuclear Information System (INIS)

    Moriyasu, K.

    1978-01-01

    A pedagogical approach to gauge invariance is presented which is based on the analogy between gauge transformations and relativity. By using the concept of an internal space, purely geometrical arguments are used to teach the physical ideas behind gauge invariance. Many of the results are applicable to general gauge theories

  3. The geometry and physics of Abelian gauge groups in F-theory

    Energy Technology Data Exchange (ETDEWEB)

    Keitel, Jan

    2015-07-14

    In this thesis we study the geometry and the low-energy effective physics associated with Abelian gauge groups in F-theory compactifications. To construct suitable torus-fibered Calabi-Yau manifolds, we employ the framework of toric geometry. By identifying appropriate building blocks of Calabi-Yau manifolds that can be studied independently, we devise a method to engineer large numbers of manifolds that give rise to a specified gauge group and achieve a partial classification of toric gauge groups. Extending our analysis from gauge groups to matter spectra, we prove that the matter content of the most commonly studied F-theory set-ups is rather constrained. To circumvent such limitations, we introduce an algorithm to analyze torus-fibrations defined as complete intersections and present several novel kinds of F-theory compactifications. Finally, we show how torus-fibrations without section are linked to fibrations with multiple sections through a network of successive geometric transitions. In order to investigate the low-energy effective physics resulting from our compactifications, we apply M- to F-theory duality. After determining the effective action of F-theory with Abelian gauge groups in six dimensions, we compare the loop-corrected Chern-Simons terms to topological quantities of the compactification manifold to read off the massless matter content. Under certain assumptions, we show that all gravitational and mixed anomalies are automatically canceled in F-theory. Furthermore, we compute the low-energy effective action of F-theory compactifications without section and suggest that the absence of a section signals the presence of an additional massive Abelian gauge field. Adjusting our analysis to four dimensions, we show that remnants of this massive gauge field survive as discrete symmetries that impose selection rules on the Yukawa couplings of the effective theory.

  4. The geometry and physics of Abelian gauge groups in F-theory

    International Nuclear Information System (INIS)

    Keitel, Jan

    2015-01-01

    In this thesis we study the geometry and the low-energy effective physics associated with Abelian gauge groups in F-theory compactifications. To construct suitable torus-fibered Calabi-Yau manifolds, we employ the framework of toric geometry. By identifying appropriate building blocks of Calabi-Yau manifolds that can be studied independently, we devise a method to engineer large numbers of manifolds that give rise to a specified gauge group and achieve a partial classification of toric gauge groups. Extending our analysis from gauge groups to matter spectra, we prove that the matter content of the most commonly studied F-theory set-ups is rather constrained. To circumvent such limitations, we introduce an algorithm to analyze torus-fibrations defined as complete intersections and present several novel kinds of F-theory compactifications. Finally, we show how torus-fibrations without section are linked to fibrations with multiple sections through a network of successive geometric transitions. In order to investigate the low-energy effective physics resulting from our compactifications, we apply M- to F-theory duality. After determining the effective action of F-theory with Abelian gauge groups in six dimensions, we compare the loop-corrected Chern-Simons terms to topological quantities of the compactification manifold to read off the massless matter content. Under certain assumptions, we show that all gravitational and mixed anomalies are automatically canceled in F-theory. Furthermore, we compute the low-energy effective action of F-theory compactifications without section and suggest that the absence of a section signals the presence of an additional massive Abelian gauge field. Adjusting our analysis to four dimensions, we show that remnants of this massive gauge field survive as discrete symmetries that impose selection rules on the Yukawa couplings of the effective theory.

  5. Finsler geometry, relativity and gauge theories

    International Nuclear Information System (INIS)

    Asanov, G.S.

    1985-01-01

    This book provides a self-contained account of the Finslerian techniques which aim to synthesize the ideas of Finslerian metrical generalization of Riemannian geometry to merge with the primary physical concepts of general relativity and gauge field theories. The geometrization of internal symmetries in terms of Finslerian geometry, as well as the formulation of Finslerian generalization of gravitational field equations and equations of motion of matter, are two key points used to expound the techniques. The Clebsch representation of the canonical momentum field is used to formulate the Hamilton-Jacobi theory for homogeneous Lagrangians of classical mechanics. As an auxillary mathematical apparatus, the author uses invariance identities which systematically reflect the covariant properties of geometrical objects. The results of recent studies of special Finsler spaces are also applied. The book adds substantially to the mathematical monographs by Rund (1959) and Rund and Bear (1972), all basic results of the latter being reflected. It is the author's hope that thorough exploration of the materrial presented will tempt the reader to revise the habitual physical concepts supported conventionally by Riemannian geometry. (Auth.)

  6. Self-dual gauge theories

    International Nuclear Information System (INIS)

    Zet, G.

    2002-01-01

    The self-duality equations are important in gauge theories because they show the connection between gauge models with internal symmetry groups and gauge theory of gravity. They are differential equations of the first order and it is easier to investigate the solutions for different particular configurations of the gauge fields and of space-times.One of the most important property of the self-duality equations is that they imply the Yang-Mills field equations. In this paper we will prove this property for the general case of a gauge theory with compact Lie group of symmetry over a 4-dimensional space-time manifold. It is important to remark that there are 3m independent self-duality equations (of the first order) while the number of Yang-Mills equations is equal to 4m, where m is the dimension of the gauge group. Both of them have 4m unknown functions which are the gauge potentials A μ a (x), a = 1, 2, ....,m; μ = 0, 1, 2, 3. But, we have, in addition, m gauge conditions for A μ a (x), (for example Coulomb, Lorentz or axial gauge) which together with the selfduality equation constitute a system of 4m equations. The Bianchi identities for the self-dual stress tensor F μν a coincide with the Yang-Mills equations and do not imply therefore supplementary conditions. We use the axial gauge in order to obtain the self duality equations for a SU(2) gauge theory over a curved space-time. The compatibility between self-duality and Yang-Mills equations is studied and some classes of solutions are obtained. In fact, we will write the Einstein-Yang-Mills equations and we will analyse only the Yang-Mills sector. The Einstein equations can not be obtained of course from self-duality. They should be obtained if we would consider a gauge theory having P x SU(2) as symmetry group, where P is the Poincare group. More generally, a gauge theory of N-extended supersymmetry can be developed by imposing the self-duality condition. (author)

  7. From topological quantum field theories to supersymmetric gauge theories

    International Nuclear Information System (INIS)

    Bossard, G.

    2007-10-01

    This thesis contains 2 parts based on scientific contributions that have led to 2 series of publications. The first one concerns the introduction of vector symmetry in cohomological theories, through a generalization of the so-called Baulieu-Singer equation. Together with the topological BRST (Becchi-Rouet-Stora-Tyutin) operator, this symmetry gives an off-shell closed sub-sector of supersymmetry that permits to determine the action uniquely. The second part proposes a methodology for re-normalizing supersymmetric Yang-Mills theory without assuming a regularization scheme which is both supersymmetry and gauge invariance preserving. The renormalization prescription is derived thanks to the definition of 2 consistent Slavnov-Taylor operators for supersymmetry and gauge invariance, whose construction requires the introduction of the so-called shadow fields. We demonstrate the renormalizability of supersymmetric Yang-Mills theories. We give a fully consistent, regularization scheme independent, proof of the vanishing of the β function and of the anomalous dimensions of the one half BPS operators in maximally supersymmetric Yang-Mills theory. After a short introduction, in chapter two, we give a review of the cohomological Yang-Mills theory in eight dimensions. We then study its dimensional reductions in seven and six dimensions. The last chapter gives quite independent results, about a geometrical interpretation of the shadow fields, an unpublished work about topological gravity in four dimensions, an extension of the shadow formalism to superconformal invariance, and finally the solution of the constraints in a twisted superspace. (author)

  8. Lattice gauge theories

    International Nuclear Information System (INIS)

    Creutz, M.

    1983-04-01

    In the last few years lattice gauge theory has become the primary tool for the study of nonperturbative phenomena in gauge theories. The lattice serves as an ultraviolet cutoff, rendering the theory well defined and amenable to numerical and analytical work. Of course, as with any cutoff, at the end of a calculation one must consider the limit of vanishing lattice spacing in order to draw conclusions on the physical continuum limit theory. The lattice has the advantage over other regulators that it is not tied to the Feynman expansion. This opens the possibility of other approximation schemes than conventional perturbation theory. Thus Wilson used a high temperature expansion to demonstrate confinement in the strong coupling limit. Monte Carlo simulations have dominated the research in lattice gauge theory for the last four years, giving first principle calculations of nonperturbative parameters characterizing the continuum limit. Some of the recent results with lattice calculations are reviewed

  9. Gauge backgrounds and zero-mode counting in F-theory

    Science.gov (United States)

    Bies, Martin; Mayrhofer, Christoph; Weigand, Timo

    2017-11-01

    Computing the exact spectrum of charged massless matter is a crucial step towards understanding the effective field theory describing F-theory vacua in four dimensions. In this work we further develop a coherent framework to determine the charged massless matter in F-theory compactified on elliptic fourfolds, and demonstrate its application in a concrete example. The gauge background is represented, via duality with M-theory, by algebraic cycles modulo rational equivalence. Intersection theory within the Chow ring allows us to extract coherent sheaves on the base of the elliptic fibration whose cohomology groups encode the charged zero-mode spectrum. The dimensions of these cohomology groups are computed with the help of modern techniques from algebraic geometry, which we implement in the software gap. We exemplify this approach in models with an Abelian and non-Abelian gauge group and observe jumps in the exact massless spectrum as the complex structure moduli are varied. An extended mathematical appendix gives a self-contained introduction to the algebro-geometric concepts underlying our framework.

  10. Abelian gauge theories with tensor gauge fields

    International Nuclear Information System (INIS)

    Kapuscik, E.

    1984-01-01

    Gauge fields of arbitrary tensor type are introduced. In curved space-time the gravitational field serves as a bridge joining different gauge fields. The theory of second order tensor gauge field is developed on the basis of close analogy to Maxwell electrodynamics. The notion of tensor current is introduced and an experimental test of its detection is proposed. The main result consists in a coupled set of field equations representing a generalization of Maxwell theory in which the Einstein equivalence principle is not satisfied. (author)

  11. Geometrical Lagrangian for a Supersymmetric Yang-Mills Theory on the Group Manifold

    International Nuclear Information System (INIS)

    Borges, M. F.

    2002-01-01

    Perhaps one of the main features of Einstein's General Theory of Relativity is that spacetime is not flat itself but curved. Nowadays, however, many of the unifying theories like superstrings on even alternative gravity theories such as teleparalell geometric theories assume flat spacetime for their calculations. This article, an extended account of an earlier author's contribution, it is assumed a curved group manifold as a geometrical background from which a Lagrangian for a supersymmetric N=2, d=5 Yang-Mills - SYM, N=2, d=5 - is built up. The spacetime is a hypersurface embedded in this geometrical scenario, and the geometrical action here obtained can be readily coupled to the five-dimensional supergravity action. The essential idea that underlies this work has its roots in the Einstein-Cartan formulation of gravity and in the 'group manifold approach to gravity and supergravity theories'. The group SYM, N=2, d=5, turns out to be the direct product of supergravity and a general gauge group G:G=GxSU(2,2/1)-bar

  12. Two-dimensional N=(2,2) lattice gauge theories with matter in higher representations

    International Nuclear Information System (INIS)

    Joseph, Anosh

    2014-06-01

    We construct two-dimensional N=(2,2) supersymmetric gauge theories on a Euclidean spacetime lattice with matter in the two-index symmetric and anti-symmetric representations of SU(N c ) color group. These lattice theories preserve a subset of the supercharges exact at finite lattice spacing. The method of topological twisting is used to construct such theories in the continuum and then the geometric discretization scheme is used to formulate them on the lattice. The lattice theories obtained this way are gauge-invariant, free from fermion doubling problem and exact supersymmetric at finite lattice spacing. We hope that these lattice constructions further motivate the nonperturbative explorations of models inspired by technicolor, orbifolding and orientifolding in string theories and the Corrigan-Ramond limit.

  13. Some formal problems in gauge theories

    International Nuclear Information System (INIS)

    Magpantay, J.A.

    1980-01-01

    The concerns of this thesis are the problems due to the extra degrees of freedom in gauge-invariant theories. Since gauge-invariant Lagrangians are singular, Dirac's consistency formalism and Fadeev's extension are first reviewed. A clarification on the origin of primary constraints is given, and some of the open problems in singular Lagrangian theory are discussed. The criteria in choosing a gauge, i.e., attainability, maintainability and Poincare invariance are summarized and applied to various linear gauges. The effects of incomplete removal of all gauge freedom on the criteria for gauge conditions are described. A simple example in point mechanics that contains some of the features of gauge field theories is given. Finally, we describe a method of constructing gauge-invariant variables in various gauge field theories. For the Abelian theory, the gauge-invariant, transverse potential and Dirac's gauge-invariant fermion field was derived. For the non-Abelian case we introduce a local set of basis vectors and gauge transformations are interpreted as rotations of the basis vectors introduced. The analysis leads to the reformulation of local SU(2) field theory in terms of path-dependent U(1) x U(1) x U(1). However, the analysis fails to include the matter fields as of now

  14. On the geometrical approach to the relativistic string theory

    International Nuclear Information System (INIS)

    Barbashov, B.M.; Nesterenko, V.V.

    1978-01-01

    In a geometrical approach to the string theory in the four-dimensional Minkowski space the relativistic invariant gauge proposed earlier for the string moving in three-dimensional space-time is used. In contrast to the results of previous paper the system of equations for the coefficients of the fundamental forms of the string model world sheet can be reduced now to one nonlinear Lionville equation again but for a complex valued function u. It is shown that in the case of space-time with arbitrary dimension there are such string motions which are described by one non-linear equation with a real function u. And as a consequence the soliton solutions investigated earlier take place in a geometrical approach to the string theory in any dimensional space-time

  15. Superfield approach to topological features of non-Abelian gauge theory

    International Nuclear Information System (INIS)

    Malik, R.P.

    2002-01-01

    We discuss some of the key topological aspects of a (1+1)-dimensional (2D) self-interacting non-Abelian gauge theory (having no interaction with matter fields) in the framework of chiral superfield formalism. We provide the geometrical interpretation for the Lagrangian density, symmetric energy-momentum tensor, topological invariants, etc, by exploiting the on-shell nilpotent BRST and co-BRST symmetries that emerge after the application of (dual) horizontality conditions. We show that the above physically interesting quantities geometrically correspond to the translation of some local (but composite) chiral superfields along one of the two independent Grassmannian directions of a (2+2)-dimensional supermanifold. This translation is generated by the conserved and on-shell nilpotent (co-)BRST charges that are present in the theory. (author)

  16. Gauge field theories

    International Nuclear Information System (INIS)

    Leite Lopes, J.

    1981-01-01

    The book is intended to explain, in an elementary way, the basic notions and principles of gauge theories. Attention is centred on the Salem-Weinberg model of electro-weak interactions, as well as neutrino-lepton scattering and the parton model. Classical field theory, electromagnetic, Yang-Mills and gravitational gauge fields, weak interactions, Higgs mechanism and the SU(5) model of grand unification are also discussed. (U.K.)

  17. Lattice gauge theory using parallel processors

    International Nuclear Information System (INIS)

    Lee, T.D.; Chou, K.C.; Zichichi, A.

    1987-01-01

    The book's contents include: Lattice Gauge Theory Lectures: Introduction and Current Fermion Simulations; Monte Carlo Algorithms for Lattice Gauge Theory; Specialized Computers for Lattice Gauge Theory; Lattice Gauge Theory at Finite Temperature: A Monte Carlo Study; Computational Method - An Elementary Introduction to the Langevin Equation, Present Status of Numerical Quantum Chromodynamics; Random Lattice Field Theory; The GF11 Processor and Compiler; and The APE Computer and First Physics Results; Columbia Supercomputer Project: Parallel Supercomputer for Lattice QCD; Statistical and Systematic Errors in Numerical Simulations; Monte Carlo Simulation for LGT and Programming Techniques on the Columbia Supercomputer; Food for Thought: Five Lectures on Lattice Gauge Theory

  18. String field theory-inspired algebraic structures in gauge theories

    International Nuclear Information System (INIS)

    Zeitlin, Anton M.

    2009-01-01

    We consider gauge theories in a string field theory-inspired formalism. The constructed algebraic operations lead, in particular, to homotopy algebras of the related Batalin-Vilkovisky theories. We discuss an invariant description of the gauge fixing procedure and special algebraic features of gauge theories coupled to matter fields.

  19. Noncommutative gauge theory for Poisson manifolds

    Energy Technology Data Exchange (ETDEWEB)

    Jurco, Branislav E-mail: jurco@mpim-bonn.mpg.de; Schupp, Peter E-mail: schupp@theorie.physik.uni-muenchen.de; Wess, Julius E-mail: wess@theorie.physik.uni-muenchen.de

    2000-09-25

    A noncommutative gauge theory is associated to every Abelian gauge theory on a Poisson manifold. The semi-classical and full quantum version of the map from the ordinary gauge theory to the noncommutative gauge theory (Seiberg-Witten map) is given explicitly to all orders for any Poisson manifold in the Abelian case. In the quantum case the construction is based on Kontsevich's formality theorem.

  20. Noncommutative gauge theory for Poisson manifolds

    International Nuclear Information System (INIS)

    Jurco, Branislav; Schupp, Peter; Wess, Julius

    2000-01-01

    A noncommutative gauge theory is associated to every Abelian gauge theory on a Poisson manifold. The semi-classical and full quantum version of the map from the ordinary gauge theory to the noncommutative gauge theory (Seiberg-Witten map) is given explicitly to all orders for any Poisson manifold in the Abelian case. In the quantum case the construction is based on Kontsevich's formality theorem

  1. Global gauge fixing in lattice gauge theories

    Energy Technology Data Exchange (ETDEWEB)

    Fachin, S.; Parrinello, C. (Physics Department, New York University, 4 Washington Place, New York, New York (USA))

    1991-10-15

    We propose a covariant, nonperturbative gauge-fixing procedure for lattice gauge theories that avoids the problem of Gribov copies. This is closely related to a recent proposal for a gauge fixing in the continuum that we review. The lattice gauge-fixed model allows both analytical and numerical investigations: on the analytical side, explicit nonperturbative calculations of gauge-dependent quantities can be easily performed in the framework of a generalized strong-coupling expansion, while on the numerical side a stochastic gauge-fixing algorithm is very naturally associated with the scheme. In both applications one can study the gauge dependence of the results, since the model actually provides a smooth'' family of gauge-fixing conditions.

  2. Classical field theory on electrodynamics, non-Abelian gauge theories and gravitation

    CERN Document Server

    Scheck, Florian

    2012-01-01

    The book describes Maxwell's equations first in their integral, directly testable form, then moves on to their local formulation. The first two chapters cover all essential properties of Maxwell's equations, including their symmetries and their covariance in a modern notation. Chapter 3 is devoted to Maxwell theory as a classical field theory and to solutions of the wave equation. Chapter 4 deals with important applications of Maxwell theory. It includes topical subjects such as metamaterials with negative refraction index and solutions of Helmholtz' equation in paraxial approximation relevant for the description of laser beams. Chapter 5 describes non-Abelian gauge theories from a classical, geometric point of view, in analogy to Maxwell theory as a prototype, and culminates in an application to the U(2) theory relevant for electroweak interactions. The last chapter 6 gives a concise summary of semi-Riemannian geometry as the framework for the classical field theory of gravitation. The chapter concludes wit...

  3. 4d quantum geometry from 3d supersymmetric gauge theory and holomorphic block

    International Nuclear Information System (INIS)

    Han, Muxin

    2016-01-01

    A class of 3d N=2 supersymmetric gauge theories are constructed and shown to encode the simplicial geometries in 4-dimensions. The gauge theories are defined by applying the Dimofte-Gaiotto-Gukov construction http://dx.doi.org/10.1007/s00220-013-1863-2 in 3d-3d correspondence to certain graph complement 3-manifolds. Given a gauge theory in this class, the massive supersymmetric vacua of the theory contain the classical geometries on a 4d simplicial complex. The corresponding 4d simplicial geometries are locally constant curvature (either dS or AdS), in the sense that they are made by gluing geometrical 4-simplices of the same constant curvature. When the simplicial complex is sufficiently refined, the simplicial geometries can approximate all possible smooth geometries on 4-manifold. At the quantum level, we propose that a class of holomorphic blocks defined in http://dx.doi.org/10.1007/JHEP12(2014)177 from the 3d N=2 gauge theories are wave functions of quantum 4d simplicial geometries. In the semiclassical limit, the asymptotic behavior of holomorphic block reproduces the classical action of 4d Einstein-Hilbert gravity in the simplicial context.

  4. Duffin-Kemmer formulation of gauge theories

    International Nuclear Information System (INIS)

    Okubo, S.; Tosa, Y.

    1979-01-01

    Gauge theories, including the Yang-Mills theory as well as Einstein's general relativity, are reformulated in first-order differential forms. In this generalized Duffin-Kemmer formalism, gauge theories take very simple forms with only cubic interactions. Moreover, every local gauge transformation, e.g., that of Yang and Mills or Einstein, etc., has an essentially similar form. Other examples comprise a gauge theory akin to the Sugawara theory of currents and the nonlinear realization of chiral symmetry. The octonion algebra is found possibly relevant to the discussion of the Yang-Mills theory

  5. Gauge theories

    International Nuclear Information System (INIS)

    Jarlskog, C.

    An introduction to the unified gauge theories of weak and electromagnetic interactions is given. The ingredients of gauge theories and symmetries and conservation laws lead to discussion of local gauge invariance and QED, followed by weak interactions and quantum flavor dynamics. The construction of the standard SU(2)xU(1) model precedes discussion of the unification of weak and electromagnetic interactions and weak neutral current couplings in this model. Presentation of spontaneous symmetry breaking and spontaneous breaking of a local symmetry leads to a spontaneous breaking scheme for the standard SU(2)xU(1) model. Consideration of quarks, leptons, masses and the Cabibbo angles, of the four quark and six quark models and CP violation lead finally to grand unification, followed by discussion of mixing angles in the Georgi-Glashow model, the Higgses of the SU(5) model and proton/ neutron decay in SU(5). (JIW)

  6. Higher spin gauge theories

    CERN Document Server

    Henneaux, Marc; Vasiliev, Mikhail A

    2017-01-01

    Symmetries play a fundamental role in physics. Non-Abelian gauge symmetries are the symmetries behind theories for massless spin-1 particles, while the reparametrization symmetry is behind Einstein's gravity theory for massless spin-2 particles. In supersymmetric theories these particles can be connected also to massless fermionic particles. Does Nature stop at spin-2 or can there also be massless higher spin theories. In the past strong indications have been given that such theories do not exist. However, in recent times ways to evade those constraints have been found and higher spin gauge theories have been constructed. With the advent of the AdS/CFT duality correspondence even stronger indications have been given that higher spin gauge theories play an important role in fundamental physics. All these issues were discussed at an international workshop in Singapore in November 2015 where the leading scientists in the field participated. This volume presents an up-to-date, detailed overview of the theories i...

  7. Notes on gauge theory and gravitation

    International Nuclear Information System (INIS)

    Wallner, R.P.

    1981-01-01

    In order to investigate whether Einstein's general relativity theory (GRT) fits into the general scheme of a gauge theory, first the concept of a (classical) gauge theory is outlined in an introductionary spacetime approach. Having thus fixed the notation and the main properties of gauge fields, GRT is examined to find out what the gauge potentials and the corresponding gauge group might be. In this way the possibility of interpreting GRT as a gauge theory of the 4-dimensional translation group T(4) = (R 4 , +), and where the gauge potentials are incorporated in a T(4)-invariant way via orthonormal anholonomic basis 1-forms is considered. To include also the spin aspect a natural extension of GRT is given by gauging also the Lorentz group, whereby a Riemann-Cartan spacetime (U 4 -spacetime) comes into play. (Auth.)

  8. The renaissance of gauge theory

    International Nuclear Information System (INIS)

    Moriyasu, K.

    1982-01-01

    Gauge theory is a classic example of a good idea proposed before its time. A brief historical review of gauge theory is presented to see why it required over 50 years for gauge invariance to be rediscovered as the basic principle governing the fundamental forces of Nature. (author)

  9. Gauge theories in particle physics

    International Nuclear Information System (INIS)

    Aitchison, I.J.R.; Hey, A.J.G.

    1982-01-01

    The first theory, quantum electrodynamics (QED) is known to give a successful account of electromagnetic interactions. Weak and strong interactions are described by gauge theories which are generalisations of QED. The electro-weak gauge theory of Glashow Salam and Weinberg unites electromagnetic and weak interactions. Quantum chromodynamics (QCD) is the gauge theory of strong interactions. This approach to these theories, designed for the non-specialist, is based on a straightforward generalisation of non-relativistic quantum-mechanical perturbation theory to the relativistic case, leading to an intuitive introduction to Feynman graphs. Spontaneously broken-or 'hidden'-symmetries are given particular attention, with the physics of hidden gauge invariance and the role of the vacuum (essential to the unified theories) being illustrated by an extended but elementary discussion of the non-relativistic example of superconductivity. Throughout, emphasis is placed both on realistic calculations and on physical understanding. (author)

  10. Effective potential for spontaneously broken gauge theories and gauge hierarchies

    International Nuclear Information System (INIS)

    Hagiwara, T.; Ovrut, B.

    1979-01-01

    The Appelquist-Carazzone effective-field-theory method, where one uses effective light-field coupling constants dependent on the heavy-field sector, is explicitly shown to be valid for the discussion of the gauge-hierarchy problem in grand unified gauge models. Using the method of functionals we derive an expression for the one-loop approximation to the scalar-field effective potential for spontaneously broken theories in an arbitrary R/sub xi/ gauge. We argue that this potential generates, through its derivatives, valid zero-momentum, one-particle-irreducible vertices for any value of xi (not just the xi→infinity Landau gauge). The equation that the one-loop vacuum correction must satisfy is presented, and we solve this equation for a number of spontaneously broken theories including gauge theories with gauge groups U(1) and SO(3). We find that a one-loop vacuum shift in a massless, non-Goldstone direction occurs via the Coleman-Weinberg mechanism with an effective coupling constant dependent on the heavy-field sector

  11. Enhanced gauge symmetry and winding modes in double field theory

    Energy Technology Data Exchange (ETDEWEB)

    Aldazabal, G. [Centro Atómico Bariloche,8400 S.C. de Bariloche (Argentina); Instituto Balseiro (CNEA-UNC) and CONICET,8400 S.C. de Bariloche (Argentina); Graña, M. [Institut de Physique Théorique, CEA/ Saclay,91191 Gif-sur-Yvette Cedex (France); Iguri, S. [Instituto de Astronomía y Física del Espacio (CONICET-UBA), Universidad de Buenos Aires,1428 Buenos Aires (Argentina); Mayo, M. [Centro Atómico Bariloche,8400 S.C. de Bariloche (Argentina); Instituto Balseiro (CNEA-UNC) and CONICET,8400 S.C. de Bariloche (Argentina); Nuñez, C. [Instituto de Astronomía y Física del Espacio (CONICET-UBA), Universidad de Buenos Aires,1428 Buenos Aires (Argentina); Departamento de Física, FCEN, Universidad de Buenos Aires,C.C. 67 - Suc. 28, 1428 Buenos Aires (Argentina); Rosabal, J.A. [Departamento de Física, FCEN, Universidad de Buenos Aires,C.C. 67 - Suc. 28, 1428 Buenos Aires (Argentina)

    2016-03-15

    We provide an explicit example of how the string winding modes can be incorporated in double field theory. Our guiding case is the closed bosonic string compactified on a circle of radius close to the self-dual point, where some modes with non-zero winding or discrete momentum number become massless and enhance the U(1)×U(1) symmetry to SU(2)×SU(2). We compute three-point string scattering amplitudes of massless and slightly massive states, and extract the corresponding effective low energy gauge field theory. The enhanced gauge symmetry at the self-dual point and the Higgs-like mechanism arising when changing the compactification radius are examined in detail. The extra massless fields associated to the enhancement are incorporated into a generalized frame with ((O(d+3,d+3))/(O(d+3)×O(d+3))) structure, where d is the number of non-compact dimensions. We devise a consistent double field theory action that reproduces the low energy string effective action with enhanced gauge symmetry. The construction requires a truly non-geometric frame which explicitly depends on both the compact coordinate along the circle and its dual.

  12. Zero energy gauge fields and the phases of a gauge theory

    International Nuclear Information System (INIS)

    Guendelman, E.I.

    1990-01-01

    A new approach to the definition of the phases of a Poincare invariant gauge theory is developed. It is based on the role of gauge transformations that change the asymptotic value of the gauge fields from zero to a constant. In the context of theories without Higgs fields, this symmetry can be spontaneously broken when the gauge fields are massless particles, explicitly broken when the gauge fields develop a mass. Finally, the vacuum can be invariant under this transformation, this last case can be achieved when the theory has a violent infrared behavior, which in some theories can be connected to a confinement mechanism

  13. M2-brane surface operators and gauge theory dualities in Toda

    International Nuclear Information System (INIS)

    Gomis, Jaume; Floch, Bruno Le

    2016-01-01

    We give a microscopic two dimensional N=(2,2) gauge theory description of arbitrary M2-branes ending on N _f M5-branes wrapping a punctured Riemann surface. These realize surface operators in four dimensional N=2 field theories. We show that the expectation value of these surface operators on the sphere is captured by a Toda CFT correlation function in the presence of an additional degenerate vertex operator labelled by a representation R of SU(N _f), which also labels M2-branes ending on M5-branes. We prove that symmetries of Toda CFT correlators provide a geometric realization of dualities between two dimensional gauge theories, including N=(2,2) analogues of Seiberg and Kutasov-Schwimmer dualities. As a bonus, we find new explicit conformal blocks, braiding matrices, and fusion rules in Toda CFT.

  14. Classical field theory on electrodynamics, non-abelian gauge theories and gravitation

    CERN Document Server

    Scheck, Florian

    2018-01-01

    Scheck’s successful textbook presents a comprehensive treatment, ideally suited for a one-semester course. The textbook describes Maxwell's equations first in their integral, directly testable form, then moves on to their local formulation. The first two chapters cover all essential properties of Maxwell's equations, including their symmetries and their covariance in a modern notation. Chapter 3 is devoted to Maxwell's theory as a classical field theory and to solutions of the wave equation. Chapter 4 deals with important applications of Maxwell's theory. It includes topical subjects such as metamaterials with negative refraction index and solutions of Helmholtz' equation in paraxial approximation relevant for the description of laser beams. Chapter 5 describes non-Abelian gauge theories from a classical, geometric point of view, in analogy to Maxwell's theory as a prototype, and culminates in an application to the U(2) theory relevant for electroweak interactions. The last chapter 6 gives a concise summary...

  15. Introduction to gauge field theory

    International Nuclear Information System (INIS)

    Bailin, David; Love, Alexander

    1986-01-01

    The book is intended as an introduction to gauge field theory for the postgraduate student of theoretical particle physics. The topics discussed in the book include: path integrals, classical and quantum field theory, scattering amplitudes, feynman rules, renormalisation, gauge field theories, spontaneous symmetry breaking, grand unified theory, and field theories at finite temperature. (UK)

  16. Anomalous gauge theories revisited

    International Nuclear Information System (INIS)

    Matsui, Kosuke; Suzuki, Hiroshi

    2005-01-01

    A possible formulation of chiral gauge theories with an anomalous fermion content is re-examined in light of the lattice framework based on the Ginsparg-Wilson relation. It is shown that the fermion sector of a wide class of anomalous non-abelian theories cannot consistently be formulated within this lattice framework. In particular, in 4 dimension, all anomalous non-abelian theories are included in this class. Anomalous abelian chiral gauge theories cannot be formulated with compact U(1) link variables, while a non-compact formulation is possible at least for the vacuum sector in the space of lattice gauge fields. Our conclusion is not applied to effective low-energy theories with an anomalous fermion content which are obtained from an underlying anomaly-free theory by sending the mass of some of fermions to infinity. For theories with an anomalous fermion content in which the anomaly is cancelled by the Green-Schwarz mechanism, a possibility of a consistent lattice formulation is not clear. (author)

  17. Supersymmetric gauge field theories

    International Nuclear Information System (INIS)

    Slavnov, A.A.

    1976-01-01

    The paper is dealing with the role of supersymmetric gauge theories in the quantum field theory. Methods of manipulating the theories as well as possibilities of their application in elementary particle physics are presented. In particular, the necessity is explained of a theory in which there is symmetry between Fermi and Bose fields, in other words, of the supersymmetric gauge theory for construction of a scheme for the Higgs particle connecting parameters of scalar mesons with those of the rest fields. The mechanism of supersymmetry breaking is discussed which makes it possible to remain the symmetric procedure of renormalization intact. The above mechanism of spontaneous symmetry breaking is applied to demonstrate possibilities of constructing models of weak and electromagnetic interactions which would be acceptable from the point of view of experiments. It is noted that the supersymmetric gauge theories represent a natural technique for description of vector-like models

  18. Gauged U(1) clockwork theory

    Science.gov (United States)

    Lee, Hyun Min

    2018-03-01

    We consider the gauged U (1) clockwork theory with a product of multiple gauge groups and discuss the continuum limit of the theory to a massless gauged U (1) with linear dilaton background in five dimensions. The localization of the lightest state of gauge fields on a site in the theory space naturally leads to exponentially small effective couplings of external matter fields localized away from the site. We discuss the implications of our general discussion with some examples, such as mediators of dark matter interactions, flavor-changing B-meson decays as well as D-term SUSY breaking.

  19. Gauge theories and their superspace quantization

    International Nuclear Information System (INIS)

    Falck, N.K.

    1984-01-01

    In this thesis the mathematical formalism for gauge theory is treated together with its extensions to supersymmetry. After a description of the differential calculus in superspace, gauge theories at the classical level are considered. Then the superspace quantization of gauge theories is described. (HSI)

  20. Continuum gauge theories

    International Nuclear Information System (INIS)

    Stora, R.

    1976-09-01

    The mathematics of gauge fields and some related concepts are discussed: some corrections on the principal fiber bundles emphasize the idea that the present formulation of continuum theories is incomplete. The main ingredients used through the construction of the renormalized perturbation series are then described: the Faddeev Popov argument, and the Faddeev Popov Lagrangian; the Slavnov symmetry and the nature of the Faddeev Popov ghost fields; the Slavnov identity, with an obstruction: the Adler Bardeen anomaly, and its generalization to the local cohomology of the gauge Lie algebra. Some smooth classical configurations of gauge fields which ought to play a prominent role in the evaluation of the functional integral describing the theory are also reviewed

  1. Topologically massive gauge theories and their dual factorized gauge-invariant formulation

    International Nuclear Information System (INIS)

    Bertrand, Bruno; Govaerts, Jan

    2007-01-01

    There exists a well-known duality between the Maxwell-Chern-Simons theory and the 'self-dual' massive model in (2 + 1) dimensions. This dual description may be extended to topologically massive gauge theories (TMGT) for forms of arbitrary rank and in any dimension. This communication introduces the construction of this type of duality through a reparametrization of the 'master' theory action. The dual action thereby obtained preserves the full gauge symmetry structure of the original theory. Furthermore, the dual action is factorized into a propagating sector of massive gauge-invariant variables and a decoupled sector of gauge-variant variables defining a pure topological field theory. Combining the results obtained within the Lagrangian and Hamiltonian formulations, a completed structure for a gauge-invariant dual factorization of TMGT is thus achieved. (fast track communication)

  2. Two potentials, one gauge group: A possible geometrical motivation

    International Nuclear Information System (INIS)

    Doria, R.M.; Pombo, C.

    1985-01-01

    By studying the purely gravitational sector of a higher dimensional matter-gravity coupled theory, one can see that in the case of non-vanishing torsion the effective 4-dimensional theory exhibits two gauge potentials that transform under the action of a single gauge group. (Author) [pt

  3. Gauge-invariant variational methods for Hamiltonian lattice gauge theories

    International Nuclear Information System (INIS)

    Horn, D.; Weinstein, M.

    1982-01-01

    This paper develops variational methods for calculating the ground-state and excited-state spectrum of Hamiltonian lattice gauge theories defined in the A 0 = 0 gauge. The scheme introduced in this paper has the advantage of allowing one to convert more familiar tools such as mean-field, Hartree-Fock, and real-space renormalization-group approximation, which are by their very nature gauge-noninvariant methods, into fully gauge-invariant techniques. We show that these methods apply in the same way to both Abelian and non-Abelian theories, and that they are at least powerful enough to describe correctly the physics of periodic quantum electrodynamics (PQED) in (2+1) and (3+1) space-time dimensions. This paper formulates the problem for both Abelian and non-Abelian theories and shows how to reduce the Rayleigh-Ritz problem to that of computing the partition function of a classical spin system. We discuss the evaluation of the effective spin problem which one derives the PQED and then discuss ways of carrying out the evaluation of the partition function for the system equivalent to a non-Abelian theory. The explicit form of the effective partition function for the non-Abelian theory is derived, but because the evaluation of this function is considerably more complicated than the one derived in the Abelian theory no explicit evaluation of this function is presented. However, by comparing the gauge-projected Hartree-Fock wave function for PQED with that of the pure SU(2) gauge theory, we are able to show that extremely interesting differences emerge between these theories even at this simple level. We close with a discussion of fermions and a discussion of how one can extend these ideas to allow the computation of the glueball and hadron spectrum

  4. On geometrized gravitation theories

    International Nuclear Information System (INIS)

    Logunov, A.A.; Folomeshkin, V.N.

    1977-01-01

    General properties of the geometrized gravitation theories have been considered. Geometrization of the theory is realized only to the extent that by necessity follows from an experiment (geometrization of the density of the matter Lagrangian only). Aor a general case the gravitation field equations and the equations of motion for matter are formulated in the different Riemann spaces. A covariant formulation of the energy-momentum conservation laws is given in an arbitrary geometrized theory. The noncovariant notion of ''pseudotensor'' is not required in formulating the conservation laws. It is shown that in the general case (i.e., when there is an explicit dependence of the matter Lagrangian density on the covariant derivatives) a symmetric energy-momentum tensor of the matter is explicitly dependent on the curvature tensor. There are enlisted different geometrized theories that describe a known set of the experimental facts. The properties of one of the versions of the quasilinear geometrized theory that describes the experimental facts are considered. In such a theory the fundamental static spherically symmetrical solution has a singularity only in the coordinate origin. The theory permits to create a satisfactory model of the homogeneous nonstationary Universe

  5. Gauge fixing conditions for the SU(3) gauge theory

    International Nuclear Information System (INIS)

    Ragiadakos, Ch.; Viswanathan, K.S.

    1979-01-01

    SU(3) gauge theory is quantized in the temporal gauge A 0 =0. Gauge fixing conditions are imposed completely on the electric field components, conjugate to the vector potential Ssub(i) that belongs to the subalgebra SO(3) of SU(3). The generating functional in terms of the independent variables is derived. It is ghost-free and may be regarded as a theory of (non-relativistic) spin-0, 1, 2, and 3 fields. (Auth.)

  6. Physics from multidimensional gauge theories

    International Nuclear Information System (INIS)

    Forgacs, P.; Lust, D.; Zoupanos, G.

    1986-01-01

    The authors motivate high dimensional theories by recalling the original Kaluza-Klein proposal. They review the dimensional reduction of symmetric gauge theories and they present the results of the attempts to obtain realistic description of elementary particles interactions starting from symmetric gauge theories in high dimensions

  7. Gauge field theory

    International Nuclear Information System (INIS)

    Aref'eva, I.Ya.; Slavnov, A.A.

    1981-01-01

    This lecture is devoted to the discussion of gauge field theory permitting from the single point of view to describe all the interactions of elementary particles. The authors used electrodynamics and the Einstein theory of gravity to search for a renormgroup fixing a form of Lagrangian. It is shown that the gauge invariance added with the requirement of the minimum number of arbitraries in Lagrangian fixes unambigously the form of the electromagnetic interaction. The generalization of this construction for more complicate charge spaces results in the Yang-Mills theory. The interaction form in this theory is fixed with the relativity principle in the charge space. A quantum scheme of the Yang-Mills fields through the explicit separation of true dynamic variables is suggested. A comfortable relativistically invariant diagram technique for the calculation of a producing potential for the Green functions is described. The Ward generalized identities have been obtained and a procedure of the elimination of ultraviolet and infrared divergencies has been accomplished. Within the framework of QCD (quantum-chromodynamic) the phenomenon of the asymptotic freedom being the most successful prediction of the gauge theory of strong interactions was described. Working methods with QCD outside the framework of the perturbation theory have been described from a coupling constant. QCD is represented as a single theory possessing both the asymptotical freedom and the freedom retaining quarks [ru

  8. Gauge-invariant cosmological density perturbations

    International Nuclear Information System (INIS)

    Sasaki, Misao.

    1986-06-01

    Gauge-invariant formulation of cosmological density perturbation theory is reviewed with special emphasis on its geometrical aspects. Then the gauge-invariant measure of the magnitude of a given perturbation is presented. (author)

  9. Renormalization of gauge theories

    International Nuclear Information System (INIS)

    Becchi, C.; Rouet, A.; Stora, R.

    1975-04-01

    Gauge theories are characterized by the Slavnov identities which express their invariance under a family of transformations of the supergauge type which involve the Faddeev Popov ghosts. These identities are proved to all orders of renormalized perturbation theory, within the BPHZ framework, when the underlying Lie algebra is semi-simple and the gauge function is chosen to be linear in the fields in such a way that all fields are massive. An example, the SU2 Higgs Kibble model is analyzed in detail: the asymptotic theory is formulated in the perturbative sense, and shown to be reasonable, namely, the physical S operator is unitary and independant from the parameters which define the gauge function [fr

  10. Gauging hidden symmetries in two dimensions

    International Nuclear Information System (INIS)

    Samtleben, Henning; Weidner, Martin

    2007-01-01

    We initiate the systematic construction of gauged matter-coupled supergravity theories in two dimensions. Subgroups of the affine global symmetry group of toroidally compactified supergravity can be gauged by coupling vector fields with minimal couplings and a particular topological term. The gauge groups typically include hidden symmetries that are not among the target-space isometries of the ungauged theory. The gaugings constructed in this paper are described group-theoretically in terms of a constant embedding tensor subject to a number of constraints which parametrizes the different theories and entirely encodes the gauged Lagrangian. The prime example is the bosonic sector of the maximally supersymmetric theory whose ungauged version admits an affine e 9 global symmetry algebra. The various parameters (related to higher-dimensional p-form fluxes, geometric and non-geometric fluxes, etc.) which characterize the possible gaugings, combine into an embedding tensor transforming in the basic representation of e 9 . This yields an infinite-dimensional class of maximally supersymmetric theories in two dimensions. We work out and discuss several examples of higher-dimensional origin which can be systematically analyzed using the different gradings of e 9

  11. String field theory

    International Nuclear Information System (INIS)

    Kaku, M.

    1987-01-01

    In this article, the authors summarize the rapid progress in constructing string field theory actions, such as the development of the covariant BRST theory. They also present the newer geometric formulation of string field theory, from which the BRST theory and the older light cone theory can be derived from first principles. This geometric formulation allows us to derive the complete field theory of strings from two geometric principles, in the same way that general relativity and Yang-Mills theory can be derived from two principles based on global and local symmetry. The geometric formalism therefore reduces string field theory to a problem of finding an invariant under a new local gauge group they call the universal string group (USG). Thus, string field theory is the gauge theory of the universal string group in much the same way that Yang-Mills theory is the gauge theory of SU(N). The geometric formulation places superstring theory on the same rigorous group theoretical level as general relativity and gauge theory

  12. Higgs phase in non-Abelian gauge theories

    International Nuclear Information System (INIS)

    Kaymakcalan, O.S.

    1981-06-01

    A non-Abelian gauge theory involving scalar fields with non-tachyonic mass terms in the Lagrangian is considered, in order to construct a finite energy density trial vacuum for this theory. The usual scalar potential arguments suggest that the vacuum of such a theory would be in the perturbative phase. However, the obvious choices for a vacuum in this phase, the Axial gauge and the Coulomb gauge bare vacua, do not have finite energy densities even with an ultraviolet cutoff. Indeed, it is a non-trivial problem to construct finite energy density vacua for non-Abelian gauge theories and this is intimately connected with the gauge fixing degeneracies of these theories. Since the gauge fixing is achieved in the Unitary gauge, this suggests that the Unitary gauge bare vacuum might be a finite energy trial vacuum and, despite the form of the scalar potential, the vacuum of this theory might be in a Higgs phase rather than the perturbative phase

  13. Particle structure of gauge theories

    International Nuclear Information System (INIS)

    Fredenhagen, K.

    1985-11-01

    The implications of the principles of quantum field theory for the particle structure of gauge theories are discussed. The general structure which emerges is compared with that of the Z 2 Higgs model on a lattice. The discussion leads to several confinement criteria for gauge theories with matter fields. (orig.)

  14. Gauge Theories in the Twentieth Century

    CERN Document Server

    2001-01-01

    By the end of the 1970s, it was clear that all the known forces of nature (including, in a sense, gravity) were examples of gauge theories , characterized by invariance under symmetry transformations chosen independently at each position and each time. These ideas culminated with the finding of the W and Z gauge bosons (and perhaps also the Higgs boson). This important book brings together the key papers in the history of gauge theories, including the discoveries of: the role of gauge transformations in the quantum theory of electrically charged particles in the 1920s; nonabelian gauge groups

  15. Noncommutative induced gauge theories on Moyal spaces

    International Nuclear Information System (INIS)

    Wallet, J-C

    2008-01-01

    Noncommutative field theories on Moyal spaces can be conveniently handled within a framework of noncommutative geometry. Several renormalisable matter field theories that are now identified are briefly reviewed. The construction of renormalisable gauge theories on these noncommutative Moyal spaces, which remains so far a challenging problem, is then closely examined. The computation in 4-D of the one-loop effective gauge theory generated from the integration over a scalar field appearing in a renormalisable theory minimally coupled to an external gauge potential is presented. The gauge invariant effective action is found to involve, beyond the expected noncommutative version of the pure Yang-Mills action, additional terms that may be interpreted as the gauge theory counterpart of the harmonic term, which for the noncommutative ψ 4 -theory on Moyal space ensures renormalisability. A class of possible candidates for renormalisable gauge theory actions defined on Moyal space is presented and discussed

  16. Viscous conformal gauge theories

    DEFF Research Database (Denmark)

    Toniato, Arianna; Sannino, Francesco; Rischke, Dirk H.

    2017-01-01

    We present the conformal behavior of the shear viscosity-to-entropy density ratio and the fermion-number diffusion coefficient within the perturbative regime of the conformal window for gauge-fermion theories.......We present the conformal behavior of the shear viscosity-to-entropy density ratio and the fermion-number diffusion coefficient within the perturbative regime of the conformal window for gauge-fermion theories....

  17. Loop averages and partition functions in U(N) gauge theory on two-dimensional manifolds

    International Nuclear Information System (INIS)

    Rusokov, B.Y.

    1990-01-01

    Loop averages and partition functions in the U(N) gauge theory are calculated for loops without intersections on arbitrary two-dimensional manifolds including non-orientable one. The physical quantities are directly expressed through geometrical characteristics of a manifold (areas enclosed by loops and the genus) and gauge group parameters (Casimir eigenvalues and dimensions of the irreducible representations). It is shown that, from the physical quantities' point of view, non-orientability of the manifold is equivalent to its non-compactness

  18. Fourier acceleration in lattice gauge theories. I. Landau gauge fixing

    International Nuclear Information System (INIS)

    Davies, C.T.H.; Batrouni, G.G.; Katz, G.R.; Kronfeld, A.S.; Lepage, G.P.; Wilson, K.G.; Rossi, P.; Svetitsky, B.

    1988-01-01

    Fourier acceleration is a useful technique which can be applied to many different numerical algorithms in order to alleviate the problem of critical slowing down. Here we describe its application to an optimization problem in the simulation of lattice gauge theories, that of gauge fixing a configuration of link fields to the Landau gauge (partial/sub μ/A/sup μ/ = 0). We find that a steepest-descents method of gauge fixing link fields at β = 5.8 on an 8 4 lattice can be made 5 times faster using Fourier acceleration. This factor will grow as the volume of the lattice is increased. We also discuss other gauges that are useful to lattice-gauge-theory simulations, among them one that is a combination of the axial and Landau gauges. This seems to be the optimal gauge to impose for the Fourier acceleration of two other important algorithms, the inversion of the fermion matrix and the updating of gauge field configurations

  19. Hidden QCD in Chiral Gauge Theories

    DEFF Research Database (Denmark)

    Ryttov, Thomas; Sannino, Francesco

    2005-01-01

    The 't Hooft and Corrigan-Ramond limits of massless one-flavor QCD consider the two Weyl fermions to be respectively in the fundamental representation or the two index antisymmetric representation of the gauge group. We introduce a limit in which one of the two Weyl fermions is in the fundamental...... representation and the other in the two index antisymmetric representation of a generic SU(N) gauge group. This theory is chiral and to avoid gauge anomalies a more complicated chiral theory is needed. This is the generalized Georgi-Glashow model with one vector like fermion. We show that there is an interesting...... phase in which the considered chiral gauge theory, for any N, Higgses via a bilinear condensate: The gauge interactions break spontaneously to ordinary massless one-flavor SU(3) QCD. The additional elementary fermionic matter is uncharged under this SU(3) gauge theory. It is also seen that when...

  20. Gyrocenter-gauge kinetic theory

    International Nuclear Information System (INIS)

    Qin, H.; Tang, W.M.; Lee, W.W.

    2000-01-01

    Gyrocenter-gauge kinetic theory is developed as an extension of the existing gyrokinetic theories. In essence, the formalism introduced here is a kinetic description of magnetized plasmas in the gyrocenter coordinates which is fully equivalent to the Vlasov-Maxwell system in the particle coordinates. In particular, provided the gyroradius is smaller than the scale-length of the magnetic field, it can treat high frequency range as well as the usual low frequency range normally associated with gyrokinetic approaches. A significant advantage of this formalism is that it enables the direct particle-in-cell simulations of compressional Alfven waves for MHD applications and of RF waves relevant to plasma heating in space and laboratory plasmas. The gyrocenter-gauge kinetic susceptibility for arbitrary wavelength and arbitrary frequency electromagnetic perturbations in a homogeneous magnetized plasma is shown to recover exactly the classical result obtained by integrating the Vlasov-Maxwell system in the particle coordinates. This demonstrates that all the waves supported by the Vlasov-Maxwell system can be studied using the gyrocenter-gauge kinetic model in the gyrocenter coordinates. This theoretical approach is so named to distinguish it from the existing gyrokinetic theory, which has been successfully developed and applied to many important low-frequency and long parallel wavelength problems, where the conventional meaning of gyrokinetic has been standardized. Besides the usual gyrokinetic distribution function, the gyrocenter-gauge kinetic theory emphasizes as well the gyrocenter-gauge distribution function, which sometimes contains all the physics of the problems being studied, and whose importance has not been realized previously. The gyrocenter-gauge distribution function enters Maxwell's equations through the pull-back transformation of the gyrocenter transformation, which depends on the perturbed fields. The efficacy of the gyrocenter-gauge kinetic approach is

  1. SU(2) gauge theory in the maximally Abelian gauge without monopoles

    International Nuclear Information System (INIS)

    Shmakov, S.Yu.; Zadorozhnyj, A.M.

    1995-01-01

    We present an algorithm for simulation of SU(2) lattice gauge theory under the maximally Abelian (MA) gauge and first numerical results for the theory without Abelian monopoles. The results support the idea that nonperturbative interaction arises between monopoles and residual Abelian field and the other interactions are perturbative. It is shown that the Gribov region for the theory with the MA gauge fixed is non-connected. 12 refs., 1 tab

  2. Gauge theory description of compactified pp-waves

    International Nuclear Information System (INIS)

    Bertolini, Matteo; Boer, Jan de; Harmark, Troels; Imeroni, Emiliano; Obers, Niels A.

    2003-01-01

    We find a new Penrose limit of AdS 5 xS 5 that gives the maximally symmetric pp-wave background of type-IIB string theory in a coordinate system that has a manifest space-like isometry. This induces a new pp-wave/gauge-theory duality which on the gauge theory side involves a novel scaling limit of N=4 SYM theory. The new Penrose limit, when applied to AdS 5 xS 5 /Z M , yields a pp-wave with a space-like circle. The dual gauge theory description involves a triple scaling limit of an N=2 quiver gauge theory. We present in detail the map between gauge theory operators and string theory states including winding states, and verify agreement between the energy eigenvalues obtained from string theory and those computed in gauge theory, at least to one-loop order in the planar limit. We furthermore consider other related new Penrose limits and explain how these limits can be understood as part of a more general framework. (author)

  3. Five-dimensional gauge theory and compactification on a torus

    Science.gov (United States)

    Haghighat, Babak; Vandoren, Stefan

    2011-09-01

    We study five-dimensional minimally supersymmetric gauge theory compactified on a torus down to three dimensions, and its embedding into string/M-theory using geometric engineering. The moduli space on the Coulomb branch is hyperkähler equipped with a metric with modular transformation properties. We determine the one-loop corrections to the metric and show that they can be interpreted as worldsheet and D1-brane instantons in type IIB string theory. Furthermore, we analyze instanton corrections coming from the solitonic BPS magnetic string wrapped over the torus. In particular, we show how to compute the path-integral for the zero-modes from the partition function of the M5 brane, or, using a 2d/4d correspondence, from the partition function of N=4 SYM theory on a Hirzebruch surface.

  4. Amorphous gauge glass theory

    International Nuclear Information System (INIS)

    Nielsen, H.B.; Bennett, D.L.

    1987-08-01

    Assuming that a lattice gauge theory describes a fundamental attribute of Nature, it should be pointed out that such a theory in the form of a gauge glass is a weaker assumption than a regular lattice model in as much as it is not constrained by the imposition of translational invariance; translational invariance is, however, recovered approximately in the long wavelength or continuum limit. (orig./WL)

  5. Extended pure Yang-Mills gauge theories with scalar and tensor gauge fields

    International Nuclear Information System (INIS)

    Gabrielli, E.

    1991-01-01

    The usual abelian gauge theory is extended to an interacting Yang-Mills-like theory containing vector, scalar and tensor gauge fields. These gauge fields are seen as components along the Clifford algebra basis of a gauge vector-spinorial field. Scalar fields φ naturally coupled to vector and tensor fields have been found, leading to a natural φ 4 coupling in the lagrangian. The full expression of the lagrangian for the euclidean version of the theory is given. (orig.)

  6. Gauge theory of amorphous magnets

    International Nuclear Information System (INIS)

    Nesterov, A.I.; Ovchinnikov, S.G.

    1989-01-01

    A gauge theory of disordered magnets as a field theory in the principal fiber bundle with structure group SL(3, R) is constructed. The gauge field interacting with a vector field (the magnetization) is responsible for the disorder. A complete system of equations, valid for arbitrary disordered magnets, is obtained. In the limiting case of a free gauge field the proposed approach leads to the well-known Volovik-Dzyaloshinskii theory, which describes isotropic spin glasses. In the other limiting case when the curvature is zero the results of Ignatchenko and Iskhakov for weakly disordered ferromagnets are reproduced

  7. Noncommutative o*(N) and usp*(2N) algebras and the corresponding gauge field theories

    International Nuclear Information System (INIS)

    Bars, I.; Sheikh-Jabbari, M.M.; Vasiliev, M.A.

    2001-03-01

    The extension of the noncommutative u * (N) Lie algebra to noncommutative orthogonal and symplectic Lie algebras is studied. Using an anti-automorphism of the star-matrix algebra, we show that the u * (N) can consistently be restricted to o * (N) and usp * (N) algebras that have new mathematical structures. We give explicit fundamental matrix representations of these algebras, through which the formulation for the corresponding noncommutative gauge field theories are obtained. In addition, we present a D-brane configuration with an orientifold which realizes geometrically our algebraic construction, thus embedding the new noncommutative gauge theories in superstring theory in the presence of a constant background magnetic field. Some algebraic generalizations that may have applications in other areas of physics are also discussed. (author)

  8. Digital lattice gauge theories

    Science.gov (United States)

    Zohar, Erez; Farace, Alessandro; Reznik, Benni; Cirac, J. Ignacio

    2017-02-01

    We propose a general scheme for a digital construction of lattice gauge theories with dynamical fermions. In this method, the four-body interactions arising in models with 2 +1 dimensions and higher are obtained stroboscopically, through a sequence of two-body interactions with ancillary degrees of freedom. This yields stronger interactions than the ones obtained through perturbative methods, as typically done in previous proposals, and removes an important bottleneck in the road towards experimental realizations. The scheme applies to generic gauge theories with Lie or finite symmetry groups, both Abelian and non-Abelian. As a concrete example, we present the construction of a digital quantum simulator for a Z3 lattice gauge theory with dynamical fermionic matter in 2 +1 dimensions, using ultracold atoms in optical lattices, involving three atomic species, representing the matter, gauge, and auxiliary degrees of freedom, that are separated in three different layers. By moving the ancilla atoms with a proper sequence of steps, we show how we can obtain the desired evolution in a clean, controlled way.

  9. Geometric group theory

    CERN Document Server

    Druţu, Cornelia

    2018-01-01

    The key idea in geometric group theory is to study infinite groups by endowing them with a metric and treating them as geometric spaces. This applies to many groups naturally appearing in topology, geometry, and algebra, such as fundamental groups of manifolds, groups of matrices with integer coefficients, etc. The primary focus of this book is to cover the foundations of geometric group theory, including coarse topology, ultralimits and asymptotic cones, hyperbolic groups, isoperimetric inequalities, growth of groups, amenability, Kazhdan's Property (T) and the Haagerup property, as well as their characterizations in terms of group actions on median spaces and spaces with walls. The book contains proofs of several fundamental results of geometric group theory, such as Gromov's theorem on groups of polynomial growth, Tits's alternative, Stallings's theorem on ends of groups, Dunwoody's accessibility theorem, the Mostow Rigidity Theorem, and quasiisometric rigidity theorems of Tukia and Schwartz. This is the f...

  10. Geometric Lagrangian approach to the physical degree of freedom count in field theory

    Science.gov (United States)

    Díaz, Bogar; Montesinos, Merced

    2018-05-01

    To circumvent some technical difficulties faced by the geometric Lagrangian approach to the physical degree of freedom count presented in the work of Díaz, Higuita, and Montesinos [J. Math. Phys. 55, 122901 (2014)] that prevent its direct implementation to field theory, in this paper, we slightly modify the geometric Lagrangian approach in such a way that its resulting version works perfectly for field theory (and for particle systems, of course). As in previous work, the current approach also allows us to directly get the Lagrangian constraints, a new Lagrangian formula for the counting of the number of physical degrees of freedom, the gauge transformations, and the number of first- and second-class constraints for any action principle based on a Lagrangian depending on the fields and their first derivatives without performing any Dirac's canonical analysis. An advantage of this approach over the previous work is that it also allows us to handle the reducibility of the constraints and to get the off-shell gauge transformations. The theoretical framework is illustrated in 3-dimensional generalized general relativity (Palatini and Witten's exotic actions), Chern-Simons theory, 4-dimensional BF theory, and 4-dimensional general relativity given by Palatini's action with a cosmological constant.

  11. Gauge theories as theories of spontaneous breakdown

    International Nuclear Information System (INIS)

    Ivanov, E.A.; Ogievetsky, V.I.

    1976-01-01

    Any gauge theory is proved to arise from spontaneous breakdown of symmetry under certain infinite parameter group, the corresponding gauge field being the Goldstone field by which this breakdown is accompanied

  12. Principle-theoretic approach of kondo and construction-theoretic formalism of gauge theories

    International Nuclear Information System (INIS)

    Jain, L.C.

    1986-01-01

    Einstein classified various theories in physics as principle-theories and constructive-theories. In this lecture Kondo's approach to microscopic and macroscopic phenomena is analysed for its principle theoretic pursuit as followed by construction. The fundamentals of his theory may be recalled as Tristimulus principle, Observation principle, Kawaguchi spaces, empirical information, epistemological point of view, unitarity, intrinsicality, and dimensional analysis subject to logical and geometrical achievement. On the other hand, various physicists have evolved constructive gauge theories through the phenomenological point of view, often a collective one. Their synthetic method involves fibre bundles and connections, path integrals as well as other hypothetical structures. They lead towards clarity, completeness and adaptability

  13. Chern-Simons gauge theory: Ten years after

    International Nuclear Information System (INIS)

    Labastida, J. M. F.

    1999-01-01

    A brief review on the progress made in the study of Chern-Simons gauge theory since its relation to knot theory was discovered ten years ago is presented. Emphasis is made on the analysis of the perturbative study of the theory and its connection to the theory of Vassiliev invariants. It is described how the study of the quantum field theory for three different gauge fixings leads to three different representations for Vassiliev invariants. Two of these gauge fixings lead to well known representations: the covariant Landau gauge corresponds to the configuration space integrals while the non-covariant light-cone gauge to the Kontsevich integral. The progress made in the analysis of the third gauge fixing, the non-covariant temporal gauge, is described in detail. In this case one obtains combinatorial expressions, instead of integral ones, for Vassiliev invariants. The approach based on this last gauge fixing seems very promising to obtain a full combinatorial formula. We collect the combinatorial expressions for all the Vassiliev invariants up to order four which have been obtained in this approach

  14. A lattice formulation of chiral gauge theories

    International Nuclear Information System (INIS)

    Bodwin, G.T.

    1995-12-01

    The authors present a method for formulating gauge theories of chiral fermions in lattice field theory. The method makes use of a Wilson mass to remove doublers. Gauge invariance is then restored by modifying the theory in two ways: the magnitude of the fermion determinant is replaced with the square root of the determinant for a fermion with vector-like couplings to the gauge field; a double limit is taken in which the lattice spacing associated with the fermion field is taken to zero before the lattice spacing associated with the gauge field. The method applies only to theories whose fermions are in an anomaly-free representation of the gauge group. They also present a related technique for computing matrix elements of operators involving fermion fields. Although the analyses of these methods are couched in weak-coupling perturbation theory, it is argued that computational prescriptions are gauge invariant in the presence of a nonperturbative gauge-field configuration

  15. Renormalization of gauge theories of weak interactions

    International Nuclear Information System (INIS)

    Lee, B.W.

    1973-01-01

    The renormalizability of spontaneously broken gauge theories is discussed. A brief outline of the motivation for such an investigation is given, and the manner in which the renormalizability of such theories is proven is described. The renormalizability question of the unbroken gauge theory is considered, and the formulation of a renormalizable perturbation theory of Higgs phenomena (spontaneously broken gauge theories) is considered. (U.S.)

  16. Residual gauge invariance of Hamiltonian lattice gauge theories

    International Nuclear Information System (INIS)

    Ryang, S.; Saito, T.; Shigemoto, K.

    1984-01-01

    The time-independent residual gauge invariance of Hamiltonian lattice gauge theories is considered. Eigenvalues and eigenfunctions of the unperturbed Hamiltonian are found in terms of Gegengauer's polynomials. Physical states which satisfy the subsidiary condition corresponding to Gauss' law are constructed systematically. (orig.)

  17. Supertwistor orbifolds: gauge theory amplitudes and topological strings

    International Nuclear Information System (INIS)

    Park, Jaemo; Rey, Soojong

    2004-01-01

    Witten established correspondence between multiparton amplitudes in four-dimensional maximally supersymmetric gauge theory and topological string theory on supertwistor space CP 3verticalbar4 . We extend Witten's correspondence to gauge theories with lower supersymmetries, product gauge groups, and fermions and scalars in complex representations. Such gauge theories arise in high-energy limit of the Standard Model of strong and electroweak interactions. We construct such theories by orbifolding prescription. Much like gauge and string theories, such prescription is applicable equally well to topological string theories on supertwistor space. We work out several examples of orbifolds of CP 3verticalbar4 that are dual to N=2,1,0 quiver gauge theories. We study gauged sigma model describing topological B-model on the superorbifolds, and explore mirror pairs with particular attention to the parity symmetry. We check the orbifold construction by studying multiparton amplitudes in these theories with particular attention to those involving fermions in bifundamental representations and interactions involving U(1) subgroups. (author)

  18. String theory duals of Lifshitz–Chern–Simons gauge theories

    International Nuclear Information System (INIS)

    Balasubramanian, Koushik; McGreevy, John

    2012-01-01

    We propose candidate gravity duals for a class of non-Abelian z = 2 Lifshitz Chern–Simons (LCS) gauge theories studied by Mulligan, Kachru and Nayak. These are nonrelativistic gauge theories in 2+1 dimensions in which parity and time-reversal symmetries are explicitly broken by the presence of a Chern–Simons term. We show that these field theories can be realized as deformations of DLCQ N=4 super Yang–Mills theory. Using the holographic dictionary, we identify the bulk fields of type IIB supergravity that are dual to these deformations. The geometries describing the groundstates of the non-Abelian LCS gauge theories realized here exhibit a mass gap. (paper)

  19. Local gauge coupling running in supersymmetric gauge theories on orbifolds

    International Nuclear Information System (INIS)

    Hillenbach, M.

    2007-01-01

    By extending Feynman's path integral calculus to fields which respect orbifold boundary conditions we provide a straightforward and convenient framework for loop calculations on orbifolds. We take advantage of this general method to investigate supersymmetric Abelian and non-Abelian gauge theories in five, six and ten dimensions where the extra dimensions are compactified on an orbifold. We consider hyper and gauge multiplets in the bulk and calculate the renormalization of the gauge kinetic term which in particular allows us to determine the gauge coupling running. The renormalization of the higher dimensional theories in orbifold spacetimes exhibits a rich structure with three principal effects: Besides the ordinary renormalization of the bulk gauge kinetic term the loop effects may require the introduction of both localized gauge kinetic terms at the fixed points/planes of the orbifold and higher dimensional operators. (orig.)

  20. Local gauge coupling running in supersymmetric gauge theories on orbifolds

    Energy Technology Data Exchange (ETDEWEB)

    Hillenbach, M.

    2007-11-21

    By extending Feynman's path integral calculus to fields which respect orbifold boundary conditions we provide a straightforward and convenient framework for loop calculations on orbifolds. We take advantage of this general method to investigate supersymmetric Abelian and non-Abelian gauge theories in five, six and ten dimensions where the extra dimensions are compactified on an orbifold. We consider hyper and gauge multiplets in the bulk and calculate the renormalization of the gauge kinetic term which in particular allows us to determine the gauge coupling running. The renormalization of the higher dimensional theories in orbifold spacetimes exhibits a rich structure with three principal effects: Besides the ordinary renormalization of the bulk gauge kinetic term the loop effects may require the introduction of both localized gauge kinetic terms at the fixed points/planes of the orbifold and higher dimensional operators. (orig.)

  1. Stochastic quantization and gauge theories

    International Nuclear Information System (INIS)

    Kolck, U. van.

    1987-01-01

    Stochastic quantization is presented taking the Flutuation-Dissipation Theorem as a guide. It is shown that the original approach of Parisi and Wu to gauge theories fails to give the right results to gauge invariant quantities when dimensional regularization is used. Although there is a simple solution in an abelian theory, in the non-abelian case it is probably necessary to start from a BRST invariant action instead of a gauge invariant one. Stochastic regularizations are also discussed. (author) [pt

  2. Gauge theories of gravity

    International Nuclear Information System (INIS)

    Ne'eman, Y.

    1998-01-01

    The relatively simple Fibre-Bundle geometry of a Yang-Mills gauge theory - mainly the clear distinction between base and fibre - made it possible, between 1953 and 1971, to construct a fully quantized version and prove that theory's renormalizability; moreover, nonperturbative (topological) solutions were subsequently found in both the fully symmetric and the spontaneously broken modes (instantons, monopoles). Though originally constructed as a model formalism, it became in 1974 the mathematical mold holding the entire Standard Model (i.e. QCD and the Electroweak theory). On the other hand, between 1974 and 1984, Einstein's theory was shown to be perturbatively nonrenormalizable. Since 1974, the search for Quantum Gravity has therefore provided the main motivation for the construction of Gauge Theories of Gravity. Earlier, however, in 1958-76 several such attempts were initiated, for aesthetic or heuristic reasons, to provide a better understanding of the algebraic structure of GR. A third motivation has come from the interest in Unification, making it necessary to bring GR into a form compatible with an enlargement of the Standard Model. Models can be classified according to the relevant structure group in the fibre. Within the Poincare group, this has been either the R 4 translations, or the Lorentz group SL(2, C) - or the entire Poincare SL(2, C) x R 4 . Enlarging the group has involved the use of the Conformal SU(2, 2), the special Affine SA(4, R) = SL(4, R) x R 4 or Affine A(4, R) groups. Supergroups have included supersymmetry, i.e. the graded-Poincare group (n =1...8 m its extensions) or the superconformal SU(2, 2/n). These supergravity theories have exploited the lessons of the aesthetic-heuristic models - Einstein-Cartan etc. - and also achieved the Unification target. Although perturbative renormalizability has been achieved in some models, whether they satisfy unitarity is not known. The nonperturbative Ashtekar program has exploited the understanding of

  3. Noncommutative gauge theories and Kontsevich's formality theorem

    International Nuclear Information System (INIS)

    Jurco, B.; Schupp, P.; Wess, J.

    2001-01-01

    The equivalence of star products that arise from the background field with and without fluctuations and Kontsevich's formality theorem allow an explicitly construction of a map that relates ordinary gauge theory and noncommutative gauge theory (Seiberg-Witten map.) Using noncommutative extra dimensions the construction is extended to noncommutative nonabelian gauge theory for arbitrary gauge groups; as a byproduct we obtain a 'Mini Seiberg-Witten map' that explicitly relates ordinary abelian and nonabelian gauge fields. All constructions are also valid for non-constant B-field, and even more generally for any Poisson tensor

  4. Nonperturbative quantization of nonabelian gauge theories

    International Nuclear Information System (INIS)

    Slavnov, A.

    2011-01-01

    Full text: (author)On the basis of the equivalence theorems proven earlier, a new formulation of nonabelian gauge theories is proposed. Contrary to the usual scheme this formulation allows the quantization of gauge theories beyond perturbation theory. The method is applicable both to the Yang-Mills theory and to nonabelian models with spontaneously broken symmetries

  5. Hard amplitudes in gauge theories

    International Nuclear Information System (INIS)

    Parke, S.J.

    1991-03-01

    In this lecture series 1 presents recent developments in perturbation theory methods for gauge theories for processes with many partons. These techniques and results are useful in the calculation of cross sections for processes with many final state partons which have applications in the study of multi-jet phenomena in high-energy colliders. The results illuminate many important and interesting properties of non-abelian gauge theories. 30 refs., 9 figs

  6. The light-cone gauge in Polyakov's theory of strings and its relation to the conformal gauge

    International Nuclear Information System (INIS)

    Tzani, R.

    1989-01-01

    The author studies the string theory as a gauge theory. The analysis includes the formulation of the interacting bosonic string by fixing the Gervais-Sakita light-cone gauge in Polyakov's path-integral formulation of the theory and the study of the problem of changing gauge in string theory in the context of the functional formulation of the theory. The main results are the following: Mandelstam's picture is obtained from the light-cone gauge fixed Polyakov's theory. Due to the off-diagonal nature of the gauge, the calculation of the determinants differs from the usual (conformal gauge) case. The regularization of the functional integrals associated with these determinants is done by using the conformal-invariance principle. He then shows that the conformal anomaly associated with this new gauge fixing is canceled at dimensions of space-time d = 26. Studying the problem of changing gauge in string theory, he shows the equivalence between the light-cone and conformal gauge in the path-integral formulation of the theory. In particular, by performing a proper change of variables in the commuting and ghost fields in the Polyakov path-integral, the string theory in the conformal gauge is obtained from the light-cone gauge fixed expression. Finally, the problem of changing gauge is generalized to the higher genus surfaces. It is shown that the string theory in the conformal gauge is equivalent to the light-cone gauge fixed theory for surface with arbitrary number of handles

  7. CP violation in gauge theories

    International Nuclear Information System (INIS)

    Escobar, C.O.

    Some aspects of CP violation in gauge theories are reviewed. The topics covered include a discussion of the Kobayashi-Maskawa six-quarks model, models of soft- CP violation (extended Higgs sector), the strong CP problem and finally some speculations relating CP violation and magnetic charges in non-abelian gauge theories. (Author) [pt

  8. Hot Conformal Gauge Theories

    DEFF Research Database (Denmark)

    Mojaza, Matin; Pica, Claudio; Sannino, Francesco

    2010-01-01

    of flavors. Surprisingly this number, if computed to the order g^2, agrees with previous predictions for the lower boundary of the conformal window for nonsupersymmetric gauge theories. The higher order results tend to predict a higher number of critical flavors. These are universal properties, i......We compute the nonzero temperature free energy up to the order g^6 \\ln(1/g) in the coupling constant for vector like SU(N) gauge theories featuring matter transforming according to different representations of the underlying gauge group. The number of matter fields, i.e. flavors, is arranged...... in such a way that the theory develops a perturbative stable infrared fixed point at zero temperature. Due to large distance conformality we trade the coupling constant with its fixed point value and define a reduced free energy which depends only on the number of flavors, colors and matter representation. We...

  9. What's wrong with anomalous chiral gauge theory?

    International Nuclear Information System (INIS)

    Kieu, T.D.

    1994-05-01

    It is argued on general ground and demonstrated in the particular example of the Chiral Schwinger Model that there is nothing wrong with apparently anomalous chiral gauge theory. If quantised correctly, there should be no gauge anomaly and chiral gauge theory should be renormalisable and unitary, even in higher dimensions and with non-Abelian gauge groups. Furthermore, it is claimed that mass terms for gauge bosons and chiral fermions can be generated without spoiling the gauge invariance. 19 refs

  10. Gauge Theories of Vector Particles

    Science.gov (United States)

    Glashow, S. L.; Gell-Mann, M.

    1961-04-24

    The possibility of generalizing the Yang-Mills trick is examined. Thus we seek theories of vector bosons invariant under continuous groups of coordinate-dependent linear transformations. All such theories may be expressed as superpositions of certain "simple" theories; we show that each "simple theory is associated with a simple Lie algebra. We may introduce mass terms for the vector bosons at the price of destroying the gauge-invariance for coordinate-dependent gauge functions. The theories corresponding to three particular simple Lie algebras - those which admit precisely two commuting quantum numbers - are examined in some detail as examples. One of them might play a role in the physics of the strong interactions if there is an underlying super-symmetry, transcending charge independence, that is badly broken. The intermediate vector boson theory of weak interactions is discussed also. The so-called "schizon" model cannot be made to conform to the requirements of partial gauge-invariance.

  11. Symmetry gauge theory for paraparticles

    International Nuclear Information System (INIS)

    Kursawe, U.

    1986-01-01

    In the present thesis it was shown that for identical particles the wave function of which has a more complicated symmetry than it is the case at the known kinds of particles, the bosons and fermions, a gauge theory can be formulated, the so-called 'symmetry gauge theory'. This theory has its origin alone in the symmetry of the particle wave functions and becomes first relevant when more than two particles are considered. It was shown that for particles with mixed-symmetrical wave functions, so-called 'paraparticles', the quantum mechanical state is no more described by one Hilbert-space element but by a many-dimensional subspace of this Hilbert space. The gauge freedom consists then just in the freedom of the choice of the basis in this subspace, the corresponding gauge group is the group of the unitary basis transformation in this subspace. (orig./HSI) [de

  12. Four-dimensional Ashkin-Teller gauge theory

    International Nuclear Information System (INIS)

    Alcaraz, F.C.; Jacobs, L.

    1983-01-01

    The authors construct and analyze a lattice field theory of two Z 2 gauge fields which interact in a minimal gauge-invariant fashion. Although the theory presented here, a generalization of the two-dimensional Ashkin-Teller spin system, has no formal continuum limit, it is found that it has an electrodynamicslike phase similar to that observed in general Z/sub N/ theories for N> or =4. This model is probably the simplest generalization of the conventional Z 2 pure gauge theory which has a massless phase separated from the strong- and weak-coupling regions by lines of second-order phase transitions

  13. Gauge symmetry breaking in gauge theories -- in search of clarification

    NARCIS (Netherlands)

    Friederich, Simon

    2013-01-01

    The paper investigates the spontaneous breaking of gauge symmetries in gauge theories from a philosophical angle, taking into account the fact that the notion of a spontaneously broken local gauge symmetry, though widely employed in textbook expositions of the Higgs mechanism, is not supported by

  14. Abelian 2-form gauge theory: special features

    International Nuclear Information System (INIS)

    Malik, R P

    2003-01-01

    It is shown that the four (3 + 1)-dimensional (4D) free Abelian 2-form gauge theory provides an example of (i) a class of field theoretical models for the Hodge theory, and (ii) a possible candidate for the quasi-topological field theory (q-TFT). Despite many striking similarities with some of the key topological features of the two (1 + 1)-dimensional (2D) free Abelian (and self-interacting non-Abelian) gauge theories, it turns out that the 4D free Abelian 2-form gauge theory is not an exact TFT. To corroborate this conclusion, some of the key issues are discussed. In particular, it is shown that the (anti-)BRST and (anti-)co-BRST invariant quantities of the 4D 2-form Abelian gauge theory obey recursion relations that are reminiscent of the exact TFTs but the Lagrangian density of this theory is not found to be able to be expressed as the sum of (anti-)BRST and (anti-)co-BRST exact quantities as is the case with the topological 2D free Abelian (and self-interacting non-Abelian) gauge theories

  15. Theorems for asymptotic safety of gauge theories

    Energy Technology Data Exchange (ETDEWEB)

    Bond, Andrew D.; Litim, Daniel F. [University of Sussex, Department of Physics and Astronomy, Brighton (United Kingdom)

    2017-06-15

    We classify the weakly interacting fixed points of general gauge theories coupled to matter and explain how the competition between gauge and matter fluctuations gives rise to a rich spectrum of high- and low-energy fixed points. The pivotal role played by Yukawa couplings is emphasised. Necessary and sufficient conditions for asymptotic safety of gauge theories are also derived, in conjunction with strict no go theorems. Implications for phase diagrams of gauge theories and physics beyond the Standard Model are indicated. (orig.)

  16. Generally covariant gauge theories

    International Nuclear Information System (INIS)

    Capovilla, R.

    1992-01-01

    A new class of generally covariant gauge theories in four space-time dimensions is investigated. The field variables are taken to be a Lie algebra valued connection 1-form and a scalar density. Modulo an important degeneracy, complex [euclidean] vacuum general relativity corresponds to a special case in this class. A canonical analysis of the generally covariant gauge theories with the same gauge group as general relativity shows that they describe two degrees of freedom per space point, qualifying therefore as a new set of neighbors of general relativity. The modification of the algebra of the constraints with respect to the general relativity case is computed; this is used in addressing the question of how general relativity stands out from its neighbors. (orig.)

  17. Gauge theory for finite-dimensional dynamical systems

    International Nuclear Information System (INIS)

    Gurfil, Pini

    2007-01-01

    Gauge theory is a well-established concept in quantum physics, electrodynamics, and cosmology. This concept has recently proliferated into new areas, such as mechanics and astrodynamics. In this paper, we discuss a few applications of gauge theory in finite-dimensional dynamical systems. We focus on the concept of rescriptive gauge symmetry, which is, in essence, rescaling of an independent variable. We show that a simple gauge transformation of multiple harmonic oscillators driven by chaotic processes can render an apparently ''disordered'' flow into a regular dynamical process, and that there exists a strong connection between gauge transformations and reduction theory of ordinary differential equations. Throughout the discussion, we demonstrate the main ideas by considering examples from diverse fields, including quantum mechanics, chemistry, rigid-body dynamics, and information theory

  18. Decoupling, effective Lagrangian, and gauge hierarchy in spontaneously broken non-Abelian gauge theories

    International Nuclear Information System (INIS)

    Kazama, Y.; Yao, Y.

    1982-01-01

    In spontaneously broken non-Abelian gauge theories which admit gauge hierarchy at the tree level, we show, to all orders in perturbation theory, that (i) the superheavy particles decouple from the light sector at low energies, (ii) an effective low-energy renormalizable theory emerges together with appropriate counterterms, and (iii) the gauge hierarchy can be consistently maintained in the presence of radiative corrections. These assertions are explicitly demonstrated for O(3) gauge theory with two triplets of Higgs particles in a manner easily applicable to more realistic grand unified theories. Furthermore, as a by-product of our analysis, we obtain a systematic method of computing the parameters of the effective low-energy theory via renormalization-group equations to any desired accuracy

  19. Nonabelian noncommutative gauge theory via noncommutative extra dimensions

    Energy Technology Data Exchange (ETDEWEB)

    Jurco, Branislav E-mail: jurco@theorie.physik.uni-muenchen.de; Schupp, Peter E-mail: schupp@theorie.physik.uni-muenchen.de; Wess, Julius E-mail: wess@theorie.physik.uni-muenchen.de

    2001-06-18

    The concept of covariant coordinates on noncommutative spaces leads directly to gauge theories with generalized noncommutative gauge fields of the type that arises in string theory with background B-fields. The theory is naturally expressed in terms of cochains in an appropriate cohomology; we discuss how it fits into the framework of projective modules. The equivalence of star products that arise from the background field with and without fluctuations and Kontsevich's formality theorem allow an explicitly construction of a map that relates ordinary gauge theory and noncommutative gauge theory (Seiberg-Witten map). As application we show the exact equality of the Dirac-Born-Infeld action with B-field in the commutative setting and its semi-noncommutative cousin in the intermediate picture. Using noncommutative extra dimensions the construction is extended to noncommutative nonabelian gauge theory for arbitrary gauge groups; an explicit map between abelian and nonabelian gauge fields is given. All constructions are also valid for non-constant B-field, Poisson structure and metric.

  20. Nonabelian noncommutative gauge theory via noncommutative extra dimensions

    International Nuclear Information System (INIS)

    Jurco, Branislav; Schupp, Peter; Wess, Julius

    2001-01-01

    The concept of covariant coordinates on noncommutative spaces leads directly to gauge theories with generalized noncommutative gauge fields of the type that arises in string theory with background B-fields. The theory is naturally expressed in terms of cochains in an appropriate cohomology; we discuss how it fits into the framework of projective modules. The equivalence of star products that arise from the background field with and without fluctuations and Kontsevich's formality theorem allow an explicitly construction of a map that relates ordinary gauge theory and noncommutative gauge theory (Seiberg-Witten map). As application we show the exact equality of the Dirac-Born-Infeld action with B-field in the commutative setting and its semi-noncommutative cousin in the intermediate picture. Using noncommutative extra dimensions the construction is extended to noncommutative nonabelian gauge theory for arbitrary gauge groups; an explicit map between abelian and nonabelian gauge fields is given. All constructions are also valid for non-constant B-field, Poisson structure and metric

  1. Bianchi-identities for supersymmetric gauge-theories

    International Nuclear Information System (INIS)

    Sohnius, M.F.

    1978-01-01

    The Bianchi-identities for gauge-theories in an extended flat superspace are evaluated. They permitbetter understanding of possible constraint equations, and can serve as a starting point for further constructions of gauge-theories with extended supersymmetry. (orig.) [de

  2. Octonionic gauge theory from spontaneously broken SO(8)

    International Nuclear Information System (INIS)

    Lassig, C.C.; Joshi, G.C.

    1995-01-01

    An attempt is made to construct a gauge theory based on a bimodular representation of the octonion algebra, the non associativity of which is manifested as a non-closure of the bimodule algebra. It is found that this fact leads to gauge-noninvariance of the theory. However, the bimodule algebra can be embedded in SO(8), the gauge theory of which can be broken down to give a massless SO(7) theory together with a massive octonionic gauge theory. 7 refs

  3. Supersymmetric gauge theories with classical groups via M theory fivebrane

    International Nuclear Information System (INIS)

    Terashima, S.

    1998-01-01

    We study the moduli space of vacua of four-dimensional N=1 and N=2 supersymmetric gauge theories with the gauge groups Sp(2N c ), SO(2N c ) and SO(2N c +1) using the M theory fivebrane. Higgs branches of the N=2 supersymmetric gauge theories are interpreted in terms of the M theory fivebrane and the type IIA s-rule is realized in it. In particular, we construct the fivebrane configuration which corresponds to a special Higgs branch root. This root is analogous to the baryonic branch root in the SU(N c ) theory which remains as a vacuum after the adjoint mass perturbation to break N=2 to N=1. Furthermore, we obtain the monopole condensations and the meson vacuum expectation values in the confining phase of N=1 supersymmetric gauge theories using the fivebrane technique. These are in complete agreement with the field theory results for the vacua in the phase with a single confined photon. (orig.)

  4. Monopole charges in unified gauge theories

    CERN Document Server

    Chan Hong Mo

    1981-01-01

    Monopole charges, being global quantities, depend on the gauge group of a theory, which in turn is determined by the representations of all its fields. For example, chromodynamics in its present form when combined with electrodynamics has as its gauge group not SU(3)*U(1) but a 'smaller' group U(3). The specification of monopole charges for a theory can thus be quite intricate. The authors report the result of an investigation in several current gauge theories. Of particular interest is the possible existence in some theories of monopoles carrying multiplicative charges. As a by-product, some earlier assertions seem to be incorrect, are clarified. (16 refs).

  5. Quantizing non-Lagrangian gauge theories: an augmentation method

    International Nuclear Information System (INIS)

    Lyakhovich, Simon L.; Sharapov, Alexei A.

    2007-01-01

    We discuss a recently proposed method of quantizing general non-Lagrangian gauge theories. The method can be implemented in many different ways, in particular, it can employ a conversion procedure that turns an original non-Lagrangian field theory in d dimensions into an equivalent Lagrangian, topological field theory in d+1 dimensions. The method involves, besides the classical equations of motion, one more geometric ingredient called the Lagrange anchor. Different Lagrange anchors result in different quantizations of one and the same classical theory. Given the classical equations of motion and Lagrange anchor as input data, a new procedure, called the augmentation, is proposed to quantize non-Lagrangian dynamics. Within the augmentation procedure, the originally non-Lagrangian theory is absorbed by a wider Lagrangian theory on the same space-time manifold. The augmented theory is not generally equivalent to the original one as it has more physical degrees of freedom than the original theory. However, the extra degrees of freedom are factorized out in a certain regular way both at classical and quantum levels. The general techniques are exemplified by quantizing two non-Lagrangian models of physical interest

  6. Dualiy for Z(N) gauge theories

    International Nuclear Information System (INIS)

    Korthals Altes, C.P.

    1978-04-01

    The duality properties of simple Z(N) gauge theories are discussed. For N 4 these systems are not self dual. Also the order parameter is discussed. The general Z(N) gauge theory is found to be self dual for all N

  7. Duality for Z(N) gauge theories

    International Nuclear Information System (INIS)

    Korthals Altes, C.P.

    1978-01-01

    The duality properties of simple Z(N) gauge theories are discussed. For N 4 these systems are not self dual. Also, the order parameter is discussed. The general Z(N) gauge theory is found to be self dual for all N. (Auth.)

  8. Instantons in gauge theories

    CERN Document Server

    1994-01-01

    This volume is a compilation of works which, taken together, give a complete and consistent presentation of instanton calculus in non-Abelian gauge theories, as it exists now. Some of the papers reproduced are instanton classics. Among other things, they show from a historical perspective how the instanton solution has been found, the motivation behind it and how the physical meaning of instantons has been revealed. Other papers are devoted to different aspects of instanton formalism including instantons in supersymmetric gauge theories. A few unsolved problems associated with instantons are d

  9. Gauge/string duality in confining theories

    International Nuclear Information System (INIS)

    Edelstein, J.D.; Portugues, R.

    2006-01-01

    This is the content of a set of lectures given at the ''XIII Jorge Andre Swieca Summer School on Particles and Fields'', Campos do Jordao, Brazil in January 2005. They intend to be a basic introduction to the topic of gauge/gravity duality in confining theories. We start by reviewing some key aspects of the low energy physics of non-Abelian gauge theories. Then, we present the basics of the AdS/CFT correspondence and its extension both to gauge theories in different spacetime dimensions with sixteen supercharges and to more realistic situations with less supersymmetry. We discuss the different options of interest: placing D-branes at singularities and wrapping D-branes in calibrated cycles of special holonomy manifolds. We finally present an outline of a number of non-perturbative phenomena in non-Abelian gauge theories as seen from supergravity. (Abstract Copyright [2006], Wiley Periodicals, Inc.)

  10. Gauge/string duality in confining theories

    Energy Technology Data Exchange (ETDEWEB)

    Edelstein, J.D. [Departamento de Fi sica de Particulas, Universidade de Santiago de Compostela and Instituto Galego de Fisica de Altas Enerxias (IGFAE), 15782 Santiago de Compostela (Spain); Instituto de Fisica de La Plata (IFLP), Universidad Nacional de La Plata, La Plata (Argentina); Centro de Estudios Cientificos (CECS), Casilla 1469, Valdivia (Chile); Portugues, R. [Centro de Estudios Cientificos (CECS), Casilla 1469, Valdivia (Chile)

    2006-07-03

    This is the content of a set of lectures given at the ''XIII Jorge Andre Swieca Summer School on Particles and Fields'', Campos do Jordao, Brazil in January 2005. They intend to be a basic introduction to the topic of gauge/gravity duality in confining theories. We start by reviewing some key aspects of the low energy physics of non-Abelian gauge theories. Then, we present the basics of the AdS/CFT correspondence and its extension both to gauge theories in different spacetime dimensions with sixteen supercharges and to more realistic situations with less supersymmetry. We discuss the different options of interest: placing D-branes at singularities and wrapping D-branes in calibrated cycles of special holonomy manifolds. We finally present an outline of a number of non-perturbative phenomena in non-Abelian gauge theories as seen from supergravity. (Abstract Copyright [2006], Wiley Periodicals, Inc.)

  11. Holism and structuralism in U(1) gauge theory

    Science.gov (United States)

    Lyre, Holger

    After decades of neglect philosophers of physics have discovered gauge theories-arguably the paradigm of modern field physics-as a genuine topic for foundational and philosophical research. Incidentally, in the last couple of years interest from the philosophy of physics in structural realism-in the eyes of its proponents the best suited realist position towards modern physics-has also raised. This paper tries to connect both topics and aims to show that structural realism gains further credence from an ontological analysis of gauge theories-in particular U (1) gauge theory. In the first part of the paper the framework of fiber bundle gauge theories is briefly presented and the interpretation of local gauge symmetry will be examined. In the second part, an ontological underdetermination of gauge theories is carved out by considering the various kinds of non-locality involved in such typical effects as the Aharonov-Bohm effect. The analysis shows that the peculiar form of non-separability figuring in gauge theories is a variant of spatiotemporal holism and can be distinguished from quantum theoretic holism. In the last part of the paper the arguments for a gauge theoretic support of structural realism are laid out and discussed.

  12. Relating double field theory to the scalar potential of N=2 gauged supergravity

    Energy Technology Data Exchange (ETDEWEB)

    Blumenhagen, Ralph [Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), Föhringer Ring 6, München, 80805 (Germany); Font, Anamaria [Max-Planck-Institut für Physik (Werner-Heisenberg-Institut), Föhringer Ring 6, München, 80805 (Germany); Arnold Sommerfeld Center for Theoretical Physics, LMU,Theresienstr. 37, München, 80333 (Germany); Plauschinn, Erik [Arnold Sommerfeld Center for Theoretical Physics, LMU,Theresienstr. 37, München, 80333 (Germany)

    2015-12-18

    The double field theory action in the flux formulation is dimensionally reduced on a Calabi-Yau three-fold equipped with non-vanishing type IIB geometric and non-geometric fluxes. First, we rewrite the metric-dependent reduced DFT action in terms of quantities that can be evaluated without explicitly knowing the metric on the Calabi-Yau manifold. Second, using properties of special geometry we obtain the scalar potential of N=2 gauged supergravity. After an orientifold projection, this potential is consistent with the scalar potential arising from the flux-induced superpotential, plus an additional D-term contribution.

  13. An octonionic gauge theory

    International Nuclear Information System (INIS)

    Lassig, C.C.; Joshi, G.C.

    1995-01-01

    The nonassociativity of the octonion algebra makes necessitates a bimodule representation, in which each element is represented by a left and a right multiplier. This representation can then be used to generate gauge transformations for the purpose of constructing a field theory symmetric under a gauged octonion algebra, the nonassociativity of which appears as a failure of the representation to close, and hence produces new interactions in the gauge field kinetic term of the symmetric Lagrangian. 5 refs., 1 tab

  14. Lattice Gauge Theories Have Gravitational Duals

    International Nuclear Information System (INIS)

    Hellerman, Simeon

    2002-01-01

    In this paper we examine a certain threebrane solution of type IIB string theory whose long-wavelength dynamics are those of a supersymmetric gauge theory in 2+1 continuous and 1 discrete dimension, all of infinite extent. Low-energy processes in this background are described by dimensional deconstruction, a strict limit in which gravity decouples but the lattice spacing stays finite. Relating this limit to the near-horizon limit of our solution we obtain an exact, continuum gravitational dual of a lattice gauge theory with nonzero lattice spacing. H-flux in this translationally invariant background encodes the spatial discreteness of the gauge theory, and we relate the cutoff on allowed momenta to a giant graviton effect in the bulk

  15. Introduction to gauge theories of electroweak interactions

    International Nuclear Information System (INIS)

    Ecker, G.

    1982-01-01

    Intended as a lecture for physicists who are not familiar with the sophisticated theoretical models in particle physics. Starting with the standard gauge model of electromagnetic, weak and strong interactions the recent developments of a unified gauge theory of electroweak interactions are shown. Shortcomings in the unitarity problem of the V-A fermi theory of charged intermediate vector bosons. Presented are the spontaneous symmetry breaking in quantum mechanics, the abelian higgs model as an example of a spontaneously broken gauge field theory, the minimal gauge group of electroweak interactions, the fermion mass generation. Further on the anomalies in quantum field theory are discussed and the radiative corrections to the vector boson masses are considered. (H.B.)

  16. Introduction to gauge field theory

    International Nuclear Information System (INIS)

    Bailin, D.; Love, A.

    1986-01-01

    This book provides a postgraduate level introduction to gauge field theory entirely from a path integral standpoint without any reliance on the more traditional method of canonical quantisation. The ideas are developed by quantising the self-interacting scalar field theory, and are then used to deal with all the gauge field theories relevant to particle physics, quantum electrodynamics, quantum chromodynamics, electroweak theory, grand unified theories, and field theories at non-zero temperature. The use of these theories to make precise experimental predictions requires the development of the renormalised theories. This book provides a knowledge of relativistic quantum mechanics, but not of quantum field theory. The topics covered form a foundation for a knowledge of modern relativistic quantum field theory, providing a comprehensive coverage with emphasis on the details of actual calculations rather than the phenomenology of the applications

  17. Dielectric lattice gauge theory

    International Nuclear Information System (INIS)

    Mack, G.

    1983-06-01

    Dielectric lattice gauge theory models are introduced. They involve variables PHI(b)epsilong that are attached to the links b = (x+esub(μ),x) of the lattice and take their values in the linear space g which consists of real linear combinations of matrices in the gauge group G. The polar decomposition PHI(b)=U(b)osub(μ)(x) specifies an ordinary lattice gauge field U(b) and a kind of dielectric field epsilonsub(ij)proportionalosub(i)osub(j)sup(*)deltasub(ij). A gauge invariant positive semidefinite kinetic term for the PHI-field is found, and it is shown how to incorporate Wilson fermions in a way which preserves Osterwalder Schrader positivity. Theories with G = SU(2) and without matter fields are studied in some detail. It is proved that confinement holds, in the sense that Wilson loop expectation values show an area law decay, if the Euclidean action has certain qualitative features which imply that PHI = 0 (i.e. dielectric field identical 0) is the unique maximum of the action. (orig.)

  18. Dielectric lattice gauge theory

    International Nuclear Information System (INIS)

    Mack, G.

    1984-01-01

    Dielectric lattice gauge theory models are introduced. They involve variables PHI(b)element ofG that are attached to the links b = (x+esub(μ), x) of the lattice and take their values in the linear space G which consists of real linear combinations of matrices in the gauge group G. The polar decomposition PHI(b)=U(b)sigmasub(μ)(x) specifies an ordinary lattice gauge field U(b) and a kind of dielectric field epsilonsub(ij)proportional sigmasub(i)sigmasub(j)sup(*)deltasub(ij). A gauge invariant positive semidefinite kinetic term for the PHI-field is found, and it is shown how to incorporate Wilson fermions in a way which preserves Osterwalder-Schrader positivity. Theories with G = SU(2) and without matter fields are studied in some detail. It is proved that confinement holds, in the sense that Wilson-loop expectation values show an area law decay, if the euclidean action has certain qualitative features which imply that PHI=0 (i.e. dielectric field identical 0) is the unique maximum of the action. (orig.)

  19. Higher spin gauge theories in any dimension

    International Nuclear Information System (INIS)

    Vasiliev, M.A.

    2004-01-01

    Some general properties of higher spin (HS) gauge theories are summarized, with the emphasize on the nonlinear theories in any dimension. The main conclusion is that nonlinear HS theories exist in any dimension. Note that HS gauge symmetries in the nonlinear HS theory differ from the Yang-Mills gauging of the global HS symmetry of a free theory one starts with by HS field strength dependent nonlinear corrections resulting from the partial gauge fixing of spontaneously broken HS symmetries in the extended non-commutative space. The HS geometry is that of the fuzzy hyperboloid in the auxiliary (fiber) non-commutative space. Its radius depends on the Weyl 0-forms which take values in the infinitive-dimensional module dual to the space of single-particle states in the system

  20. Investigations in gauge theories, topological solitons and string theories

    International Nuclear Information System (INIS)

    1993-01-01

    This is the Final Report on a supported research project on theoretical particle physics entitled ''Investigations in Gauge Theories, Topological Solitons and String Theories.'' The major theme of particle theory pursued has been within the rubric of the standard model, particularly on the interplay between symmetries and dynamics. Thus, the research has been carried out primarily in the context of gauge with or without chiral fermions and in effective chiral lagrangian field theories. The topics studied include the physical implications of abelian and non-abelian anomalies on the spectrum and possible dynamical symmetry breaking in a wide range of theories. A wide range of techniques of group theory, differential geometry and function theory have been applied to probe topological and conformal properties of quantum field theories in two and higher dimensions, the breaking of global chiral symmetries by vector-like gauge theories such as QCD,the phenomenology of a possibly strongly interacting Higgs sector within the minimal standard model, and the relevance of solitonic ideas to non-perturbative phenomena at SSC energies

  1. General relativity and gauge gravity theories of higher order

    International Nuclear Information System (INIS)

    Konopleva, N.P.

    1998-01-01

    It is a short review of today's gauge gravity theories and their relations with Einstein General Relativity. The conceptions of construction of the gauge gravity theories with higher derivatives are analyzed. GR is regarded as the gauge gravity theory corresponding to the choice of G ∞4 as the local gauge symmetry group and the symmetrical tensor of rank two g μν as the field variable. Using the mathematical technique, single for all fundamental interactions (namely variational formalism for infinite Lie groups), we can obtain Einstein's theory as the gauge theory without any changes. All other gauge approaches lead to non-Einstein theories of gravity. But above-mentioned mathematical technique permits us to construct the gauge gravity theory of higher order (for instance SO (3,1)-gravity) so that all vacuum solutions of Einstein equations are the solutions of the SO (3,1)-gravity theory. The structure of equations of SO(3,1)-gravity becomes analogous to Weeler-Misner geometrodynamics one

  2. Chiral gauged Wess-Zumino-Witten theories and coset models in conformal field theory

    International Nuclear Information System (INIS)

    Chung, S.; Tye, S.H.

    1993-01-01

    The Wess-Zumino-Witten (WZW) theory has a global symmetry denoted by G L direct-product G R . In the standard gauged WZW theory, vector gauge fields (i.e., with vector gauge couplings) are in the adjoint representation of the subgroup H contained-in G. In this paper, we show that, in the conformal limit in two dimensions, there is a gauged WZW theory where the gauge fields are chiral and belong to the subgroups H L and H R where H L and H R can be different groups. In the special case where H L =H R , the theory is equivalent to vector gauged WZW theory. For general groups H L and H R , an examination of the correlation functions (or more precisely, conformal blocks) shows that the chiral gauged WZW theory is equivalent to (G/H L ) L direct-product(G/H R ) R coset models in conformal field theory

  3. An infinite-dimensional calculus for gauge theories

    OpenAIRE

    Mendes, Rui Vilela

    2010-01-01

    A space for gauge theories is defined, using projective limits as subsets of Cartesian products of homomorphisms from a lattice on the structure group. In this space, non-interacting and interacting measures are defined as well as functions and operators. From projective limits of test functions and distributions on products of compact groups, a projective gauge triplet is obtained, which provides a framework for the infinite-dimensional calculus in gauge theories. The gauge measure behavior ...

  4. Unified gauge theories with spontaneous symmetry breaking

    International Nuclear Information System (INIS)

    MacDowell, S.W.

    1975-01-01

    Unified gauge theories with spontaneous symmetry breaking are studied with a view to renormalize quantum field theory. Georgi-Glashow and Weinberg-Salam models to unify weak and electromagnetic interactions are discussed in detail. Gauge theories of strong interactions are also considered [pt

  5. Machines for lattice gauge theory

    International Nuclear Information System (INIS)

    Mackenzie, P.B.

    1989-05-01

    The most promising approach to the solution of the theory of strong interactions is large scale numerical simulation using the techniques of lattice gauge theory. At the present time, computing requirements for convincing calculations of the properties of hadrons exceed the capabilities of even the most powerful commercial supercomputers. This has led to the development of massively parallel computers dedicated to lattice gauge theory. This talk will discuss the computing requirements behind these machines, and general features of the components and architectures of the half dozen major projects now in existence. 20 refs., 1 fig

  6. Some aspects of non-Abelian gauge theories

    International Nuclear Information System (INIS)

    Tyburski, L.J.

    1976-01-01

    Two aspects of the theory of non-Abelian gauge fields are considered. In the first part, the fermion-fermion scattering amplitude is calculated for a non-Abelian gauge theory with SU(N) gauge symmetry in the limit of high energy with fixed momentum transfer through sixth order in the coupling constant. Only the leading logarithmic terms in each order of perturbation theory are kept. To avoid the infrared problem, the Higgs mechanism is invoked to give masses to the vector bosons of the theory. It is found that the scattering amplitude exponentiates to a Regge form. This result is qualitatively different from an earlier published calculation. In the second part of the thesis, we consider fermion-fermion scattering in a non-Abelian gauge theory with massless vector bosons, and demonstrate that for physically measurable cross sections the infrared divergences of the theory cancel out to lowest nontrivial order

  7. String theory considered as a local gauge theory of an extended object

    International Nuclear Information System (INIS)

    Chan Hongmo; Tsou Sheungtsun.

    1986-11-01

    In attempting to understand more about the physical origin of the so-called 'chordal gauge symmetry' in string field theory it is found that one can, at least formally, consider the theory as a generalised local gauge theory. However, the fundamental object is no longer a point, as in ordinary gauge theory, but a point with a tail, and it is the motion of this tail which represents the internal gauge degree of freedom. Moreover, the differential geometry is based on the non-abelian conformal group instead of the usual translation group. (author)

  8. A gauge-invariant reorganization of thermal gauge theory

    International Nuclear Information System (INIS)

    Su, Nan

    2010-01-01

    This dissertation is devoted to the study of thermodynamics for quantum gauge theories. The poor convergence of quantum field theory at finite temperature has been the main obstacle in the practical applications of thermal QCD for decades. In this dissertation I apply hard-thermal-loop perturbation theory, which is a gauge-invariant reorganization of the conventional perturbative expansion for quantum gauge theories to the thermodynamics of QED and Yang-Mills theory to three-loop order. For the Abelian case, I present a calculation of the free energy of a hot gas of electrons and photons by expanding in a power series in m D /T, m f /T and e 2 , where m D and m f are the photon and electron thermal masses, respectively, and e is the coupling constant. I demonstrate that the hard-thermal-loop perturbation reorganization improves the convergence of the successive approximations to the QED free energy at large coupling, e ∝ 2. For the non-Abelian case, I present a calculation of the free energy of a hot gas of gluons by expanding in a power series in m D /T and g 2 , where m D is the gluon thermal mass and g is the coupling constant. I show that at three-loop order hard-thermal-loop perturbation theory is compatible with lattice results for the pressure, energy density, and entropy down to temperatures T ∝ 2 - 3 T c . The results suggest that HTLpt provides a systematic framework that can be used to calculate static and dynamic quantities for temperatures relevant at LHC. (orig.)

  9. Relativity and equivalence principles in the gauge theory of gravitation

    International Nuclear Information System (INIS)

    Ivanenko, D.; Sardanashvili, G.

    1981-01-01

    Roles of relativity (RP) and equivalence principles (EP) in the gauge theory of gravity are shown. RP in the gravitational theory in formalism of laminations can be formulated as requirement of covariance of equations relative to the GL + (4, R)(X) gauge group. In such case RP turns out to be identical to the gauge principle in the gauge theory of a group of outer symmetries, and the gravitational theory can be directly constructed as the gauge theory. In general relativity theory the equivalence theory adds RP and is intended for description of transition to a special relativity theory in some system of reference. The approach described takes into account that in the gauge theory, besides gauge fields under conditions of spontaneous symmetry breaking, the Goldstone and Higgs fields can also arise, to which the gravitational metric field is related, what is the sequence of taking account of RP in the gauge theory of gravitation [ru

  10. Fundamental problems of gauge field theory

    International Nuclear Information System (INIS)

    Velo, G.; Wightman, A.S.

    1986-01-01

    As a result of the experimental and theoretical developments of the last two decades, gauge field theory, in one form or another, now provides the standard language for the description of Nature; QCD and the standard model of the electroweak interactions illustrate this point. It is a basic task of mathematical physics to provide a solid foundation for these developments by putting the theory in a physically transparent and mathematically rigorous form. The lecture notes collected in this volume concentrate on the many unsolved problems which arise here, and on the general ideas and methods which have been proposed for their solution. In particular, the use of rigorous renormalization group methods to obtain control over the continuum limit of lattice gauge field theories, the exploration of the extraordinary enigmatic connections between Kac-Moody-Virasoro algebras and string theory, and the systematic use of the theory of local algebras and indefinite metric spaces to classify the charged C* states in gauge field theories are mentioned

  11. Canonical transformation path to gauge theories of gravity

    Science.gov (United States)

    Struckmeier, J.; Muench, J.; Vasak, D.; Kirsch, J.; Hanauske, M.; Stoecker, H.

    2017-06-01

    In this paper, the generic part of the gauge theory of gravity is derived, based merely on the action principle and on the general principle of relativity. We apply the canonical transformation framework to formulate geometrodynamics as a gauge theory. The starting point of our paper is constituted by the general De Donder-Weyl Hamiltonian of a system of scalar and vector fields, which is supposed to be form-invariant under (global) Lorentz transformations. Following the reasoning of gauge theories, the corresponding locally form-invariant system is worked out by means of canonical transformations. The canonical transformation approach ensures by construction that the form of the action functional is maintained. We thus encounter amended Hamiltonian systems which are form-invariant under arbitrary spacetime transformations. This amended system complies with the general principle of relativity and describes both, the dynamics of the given physical system's fields and their coupling to those quantities which describe the dynamics of the spacetime geometry. In this way, it is unambiguously determined how spin-0 and spin-1 fields couple to the dynamics of spacetime. A term that describes the dynamics of the "free" gauge fields must finally be added to the amended Hamiltonian, as common to all gauge theories, to allow for a dynamic spacetime geometry. The choice of this "dynamics" Hamiltonian is outside of the scope of gauge theory as presented in this paper. It accounts for the remaining indefiniteness of any gauge theory of gravity and must be chosen "by hand" on the basis of physical reasoning. The final Hamiltonian of the gauge theory of gravity is shown to be at least quadratic in the conjugate momenta of the gauge fields—this is beyond the Einstein-Hilbert theory of general relativity.

  12. Introduction to gauge theories of electroweak interactions

    International Nuclear Information System (INIS)

    Ecker, G.

    1982-01-01

    The author presents an introduction to electroweak gauge theories. Emphasis is placed on the properties of a general gauge theory. The standard model is discussed as the simplest example to illustrate these properties. (G.T.H.)

  13. Perturbative Quantum Gravity from Gauge Theory

    Science.gov (United States)

    Carrasco, John Joseph

    In this dissertation we present the graphical techniques recently developed in the construction of multi-loop scattering amplitudes using the method of generalized unitarity. We construct the three-loop and four-loop four-point amplitudes of N = 8 supergravity using these methods and the Kawaii, Lewellen and Tye tree-level relations which map tree-level gauge theory amplitudes to tree-level gravity theory amplitudes. We conclude by extending a tree-level duality between color and kinematics, generic to gauge theories, to a loop level conjecture, allowing the easy relation between loop-level gauge and gravity kinematics. We provide non-trivial evidence for this conjecture at three-loops in the particular case of maximal supersymmetry.

  14. Renormalization of gauge theories without cohomology

    International Nuclear Information System (INIS)

    Anselmi, Damiano

    2013-01-01

    We investigate the renormalization of gauge theories without assuming cohomological properties. We define a renormalization algorithm that preserves the Batalin-Vilkovisky master equation at each step and automatically extends the classical action till it contains sufficiently many independent parameters to reabsorb all divergences into parameter-redefinitions and canonical transformations. The construction is then generalized to the master functional and the field-covariant proper formalism for gauge theories. Our results hold in all manifestly anomaly-free gauge theories, power-counting renormalizable or not. The extension algorithm allows us to solve a quadratic problem, such as finding a sufficiently general solution of the master equation, even when it is not possible to reduce it to a linear (cohomological) problem. (orig.)

  15. From topological quantum field theories to supersymmetric gauge theories; Des theories quantiques de champ topologiques aux theories de jauge supersymetriques

    Energy Technology Data Exchange (ETDEWEB)

    Bossard, G

    2007-10-15

    This thesis contains 2 parts based on scientific contributions that have led to 2 series of publications. The first one concerns the introduction of vector symmetry in cohomological theories, through a generalization of the so-called Baulieu-Singer equation. Together with the topological BRST (Becchi-Rouet-Stora-Tyutin) operator, this symmetry gives an off-shell closed sub-sector of supersymmetry that permits to determine the action uniquely. The second part proposes a methodology for re-normalizing supersymmetric Yang-Mills theory without assuming a regularization scheme which is both supersymmetry and gauge invariance preserving. The renormalization prescription is derived thanks to the definition of 2 consistent Slavnov-Taylor operators for supersymmetry and gauge invariance, whose construction requires the introduction of the so-called shadow fields. We demonstrate the renormalizability of supersymmetric Yang-Mills theories. We give a fully consistent, regularization scheme independent, proof of the vanishing of the {beta} function and of the anomalous dimensions of the one half BPS operators in maximally supersymmetric Yang-Mills theory. After a short introduction, in chapter two, we give a review of the cohomological Yang-Mills theory in eight dimensions. We then study its dimensional reductions in seven and six dimensions. The last chapter gives quite independent results, about a geometrical interpretation of the shadow fields, an unpublished work about topological gravity in four dimensions, an extension of the shadow formalism to superconformal invariance, and finally the solution of the constraints in a twisted superspace. (author)

  16. Gauge theory and renormalization

    NARCIS (Netherlands)

    Hooft, G. 't

    1996-01-01

    Early developments leading to renormalizable non-Abelian gauge theories for the weak, electromagnetic and strong interactions, are discussed from a personal viewpoint. They drastically improved our view of the role of field theory, symmetry and topology, as well as other branches of mathematics, in

  17. Lattice gauge theories

    International Nuclear Information System (INIS)

    Petronzio, R.

    1992-01-01

    Lattice gauge theories are about fifteen years old and I will report on the present status of the field without making the elementary introduction that can be found in the proceedings of the last two conferences. The talk covers briefly the following subjects: the determination of α s , the status of spectroscopy, heavy quark physics and in particular the calculation of their hadronic weak matrix elements, high temperature QCD, non perturbative Higgs bounds, chiral theories on the lattice and induced theories

  18. Determination of covariant Schwinger terms in anomalous gauge theories

    International Nuclear Information System (INIS)

    Kelnhofer, G.

    1991-01-01

    A functional integral method is used to determine equal time commutators between the covariant currents and the covariant Gauss-law operators in theories which are affected by an anomaly. By using a differential geometrical setup we show how the derivation of consistent- and covariant Schwinger terms can be understood on an equal footing. We find a modified consistency condition for the covariant anomaly. As a by-product the Bardeen-Zumino functional, which relates consistent and covariant anomalies, can be interpreted as connection on a certain line bundle over all gauge potentials. Finally the commutator anomalies are calculated for the two- and four dimensional case. (Author) 13 refs

  19. Determination of covariant Schwinger terms in anomalous gauge theories

    International Nuclear Information System (INIS)

    Kelnhofer, G.

    1991-01-01

    A functional integral method is used to determine equal time commutators between the covariant currents and the covariant Gauss-law operators in theories which are affected by an anomaly. By using a differential geometrical setup we show how the derivation of consistent- and covariant Schwinger terms can be understood on an equal footing. We find a modified consistency condition for the covariant anomaly. As a by-product the Bardeen-Zumino functional, which relates consistent and covariant anomalies, can be interpreted as connection on a certain line bundle over all gauge potentials. Finally the covariant commutator anomalies are calculated for the two- and four dimensional case. (orig.)

  20. Abelian gauge theories on homogeneous spaces

    International Nuclear Information System (INIS)

    Vassilevich, D.V.

    1992-07-01

    An algebraic technique of separation of gauge modes in Abelian gauge theories on homogeneous spaces is proposed. An effective potential for the Maxwell-Chern-Simons theory on S 3 is calculated. A generalization of the Chern-Simons action is suggested and analysed with the example of SU(3)/U(1) x U(1). (author). 11 refs

  1. A gauge-invariant reorganization of thermal gauge theory

    Energy Technology Data Exchange (ETDEWEB)

    Su, Nan

    2010-07-01

    This dissertation is devoted to the study of thermodynamics for quantum gauge theories. The poor convergence of quantum field theory at finite temperature has been the main obstacle in the practical applications of thermal QCD for decades. In this dissertation I apply hard-thermal-loop perturbation theory, which is a gauge-invariant reorganization of the conventional perturbative expansion for quantum gauge theories to the thermodynamics of QED and Yang-Mills theory to three-loop order. For the Abelian case, I present a calculation of the free energy of a hot gas of electrons and photons by expanding in a power series in m{sub D}/T, m{sub f}/T and e{sup 2}, where m{sub D} and m{sub f} are the photon and electron thermal masses, respectively, and e is the coupling constant. I demonstrate that the hard-thermal-loop perturbation reorganization improves the convergence of the successive approximations to the QED free energy at large coupling, e {proportional_to} 2. For the non-Abelian case, I present a calculation of the free energy of a hot gas of gluons by expanding in a power series in m{sub D}/T and g{sup 2}, where m{sub D} is the gluon thermal mass and g is the coupling constant. I show that at three-loop order hard-thermal-loop perturbation theory is compatible with lattice results for the pressure, energy density, and entropy down to temperatures T {proportional_to} 2 - 3 T{sub c}. The results suggest that HTLpt provides a systematic framework that can be used to calculate static and dynamic quantities for temperatures relevant at LHC. (orig.)

  2. Unity from duality: gravity, gauge theory and strings

    International Nuclear Information System (INIS)

    Bachas, C.; Bilal, A.; Douglas, M.; Nekrasov, N.; David, F.

    2002-01-01

    The 76. session of the summer school in theoretical physics was devoted to recent developments in string theory, gauge theories and quantum gravity. Superstring theory is the leading candidate for a unified theory of all fundamental physical forces and elementary particles. The discovery of dualities and of important tools such as D-branes, has greatly reinforced this point of view. This document gathers the papers of 9 lectures: 1) supergravity, 2) supersymmetric gauge theories, 3) an introduction to duality symmetries, 4) large N field theories and gravity, 5) D-branes on the conifold and N = 1 gauge/gravity dualities, 6) de Sitter space, 7) string compactification with N = 1 supersymmetry, 8) open strings and non-commutative gauge theories, and 9) condensates near the Argyres-Douglas point in SU(2) gauge theory with broken N = 2 supersymmetry, and of 8 seminars: 1) quantum field theory with extra dimensions, 2) special holonomy spaces and M-theory, 3) four dimensional non-critical strings, 4) U-opportunities: why ten equal to ten?, 5) exact answers to approximate questions - non-commutative dipoles, open Wilson lines and UV-IR duality, 6) open-string models with broken supersymmetry, 7) on a field theory of open strings, tachyon condensation and closed strings, and 8) exceptional magic. (A.C.)

  3. F-theory and 2d (0,2) theories

    Energy Technology Data Exchange (ETDEWEB)

    Schäfer-Nameki, Sakura [Department of Mathematics, King’s College London, The Strand, London WC2R 2LS (United Kingdom); Weigand, Timo [Institut für Theoretische Physik, Ruprecht-Karls-Universität,Philosophenweg 19, 69120 Heidelberg (Germany)

    2016-05-11

    F-theory compactified on singular, elliptically fibered Calabi-Yau five-folds gives rise to two-dimensional gauge theories preserving N=(0,2) supersymmetry. In this paper we initiate the study of such compactifications and determine the dictionary between the geometric data of the elliptic fibration and the 2d gauge theory such as the matter content in terms of (0,2) superfields and their supersymmetric couplings. We study this setup both from a gauge-theoretic point of view, in terms of the partially twisted 7-brane theory, and provide a global geometric description based on the structure of the elliptic fibration and its singularities. Global consistency conditions are determined and checked against the dual M-theory compactification to one dimension. This includes a discussion of gauge anomalies, the structure of the Green-Schwarz terms and the Chern-Simons couplings in the dual M-theory supersymmetric quantum mechanics. Furthermore, by interpreting the resulting 2d (0,2) theories as heterotic worldsheet theories, we propose a correspondence between the geometric data of elliptically fibered Calabi-Yau five-folds and the target space of a heterotic gauged linear sigma-model (GLSM). In particular the correspondence between the Landau-Ginsburg and sigma-model phase of a 2d (0,2) GLSM is realized via different T-branes or gluing data in F-theory.

  4. Duality transformation of a spontaneously broken gauge theory

    International Nuclear Information System (INIS)

    Mizrachi, L.

    1981-04-01

    Duality transformation for a spontaneously broken gauge theory is constructed in the CDS gauge (xsub(μ)Asub(μ)sup(a)=0). The dual theory is expressed in terms of dual potentials which satisfy the same gauge condition, but with g→ 1 /g. Generally the theory is not self dual but in the weak coupling region (small g), self duality is found for the subgroup which is not spontaneously broken or in regions where monopoles and vortices are concentrated (in agreement with t'Hooft's ideas that monopoles and vortices in the Georgi-Glashow model make it self dual). In the strong coupling regime a systematic strong coupling expansion can be written. For this region the dual theory is generally not local gauge invariant, but it is invariant under global gauge transformations. (author)

  5. SO(2N) and SU(N) gauge theories

    OpenAIRE

    Lau, Richard; Teper, Michael

    2013-01-01

    We present our preliminary results of SO(2N) gauge theories, approaching the large-N limit. SO(2N) theories may help us to understand QCD at finite chemical potential since there is an orbifold equivalence between SO(2N) and SU(N) gauge theories at large-N and SO(2N) theories do not have the sign problem present in QCD. We consider the string tensions, mass spectra, and deconfinement temperatures in the SO(2N) pure gauge theories in 2+1 dimensions, comparing them to their corresponding SU(N) ...

  6. Introduction to lattice gauge theories

    International Nuclear Information System (INIS)

    La Cock, P.

    1988-03-01

    A general introduction to Lattice Gauge Theory (LGT) is given. The theory is discussed from first principles to facilitate an understanding of the techniques used in LGT. These include lattice formalism, gauge invariance, fermions on the lattice, group theory and integration, strong coupling methods and mean field techniques. A review of quantum chromodynamics on the lattice at finite temperature and density is also given. Monte Carlo results and analytical methods are discussed. An attempt has been made to include most relevant data up to the end of 1987, and to update some earlier reviews existing on the subject. 224 refs., 33 figs., 14 tabs

  7. SU(N) chiral gauge theories on the lattice

    International Nuclear Information System (INIS)

    Golterman, Maarten; Shamir, Yigal

    2004-01-01

    We extend the construction of lattice chiral gauge theories based on non-perturbative gauge fixing to the non-Abelian case. A key ingredient is that fermion doublers can be avoided at a novel type of critical point which is only accessible through gauge fixing, as we have shown before in the Abelian case. The new ingredient allowing us to deal with the non-Abelian case as well is the use of equivariant gauge fixing, which handles Gribov copies correctly, and avoids Neuberger's no-go theorem. We use this method in order to gauge fix the non-Abelian group (which we will take to be SU(N)) down to its maximal Abelian subgroup. Obtaining an undoubled, chiral fermion content requires us to gauge-fix also the remaining Abelian gauge symmetry. This modifies the equivariant Becchi-Rouet-Stora-Tyutin (BRST) identities, but their use in proving unitarity remains intact, as we show in perturbation theory. On the lattice, equivariant BRST symmetry as well as the Abelian gauge invariance are broken, and a judiciously chosen irrelevant term must be added to the lattice gauge-fixing action in order to have access to the desired critical point in the phase diagram. We argue that gauge invariance is restored in the continuum limit by adjusting a finite number of counter terms. We emphasize that weak-coupling perturbation theory applies at the critical point which defines the continuum limit of our lattice chiral gauge theory

  8. Topological higher gauge theory: From BF to BFCG theory

    International Nuclear Information System (INIS)

    Girelli, F.; Pfeiffer, H.; Popescu, E. M.

    2008-01-01

    We study generalizations of three- and four-dimensional BF theories in the context of higher gauge theory. First, we construct topological higher gauge theories as discrete state sum models and explain how they are related to the state sums of Yetter, Mackaay, and Porter. Under certain conditions, we can present their corresponding continuum counterparts in terms of classical Lagrangians. We then explain that two of these models are already familiar from the literature: the ΣΦEA model of three-dimensional gravity coupled to topological matter and also a four-dimensional model of BF theory coupled to topological matter

  9. Exact renormalization group for gauge theories

    International Nuclear Information System (INIS)

    Balaban, T.; Imbrie, J.; Jaffe, A.

    1984-01-01

    Renormalization group ideas have been extremely important to progress in our understanding of gauge field theory. Particularly the idea of asymptotic freedom leads us to hope that nonabelian gauge theories exist in four dimensions and yet are capable of producing the physics we observe-quarks confined in meson and baryon states. For a thorough understanding of the ultraviolet behavior of gauge theories, we need to go beyond the approximation of the theory at some momentum scale by theories with one or a small number of coupling constants. In other words, we need a method of performing exact renormalization group transformations, keeping control of higher order effects, nonlocal effects, and large field effects that are usually ignored. Rigorous renormalization group methods have been described or proposed in the lectures of Gawedzki, Kupiainen, Mack, and Mitter. Earlier work of Glimm and Jaffe and Gallavotti et al. on the /phi/ model in three dimensions were quite important to later developments in this area. We present here a block spin procedure which works for gauge theories, at least in the superrenormalizable case. It should be enlightening for the reader to compare the various methods described in these proceedings-especially from the point of view of how each method is suited to the physics of the problem it is used to study

  10. Once more about the topologically massive gauge theory

    International Nuclear Information System (INIS)

    Kogan, Ya.I.

    1989-01-01

    The general properties of the three-dimensional gauge theory with the topological mass is discussed namely the long-range interaction of the Aharonov-Bohm type. It is argued that Chern-Simons gauge theories must be considered as the infrared limit of the topologically massive theories. The analogy between the Landau problem of a charged particle in a magnetic field and quantization of this gauge theory is considered, as well as the quantization condition for the Abelian Chern-Simons term. 38 refs.; 5 figs

  11. Geometrical interpretation of extended supergravity

    International Nuclear Information System (INIS)

    Townsend, P.K.; Nieuwenhuizen, P.van

    1977-01-01

    SO 2 extended supergravity is shown to be a geometrical theory, whose underlying gauge group is OSp(4,2). The couplings which gauge the SO 2 symmetry as well as the accompanying cosmological and masslike terms are directly obtained, and the usual SO 2 model is obtained after a Wigner-Inoenue group contraction. (Auth.)

  12. Dynamic conservation of anomalous current in gauge theories

    International Nuclear Information System (INIS)

    Kulikov, A.V.

    1986-01-01

    The symmetry of classical Lagrangian of gauge fields is shown to lead in quantum theory to certain limitations for the fields interacting with gauge ones. Due to this property, additional terms appear in the effective action in the theories with anomalous currents and its gauge invariance is ensured

  13. Weyl gravity as a gauge theory

    Science.gov (United States)

    Trujillo, Juan Teancum

    In 1920, Rudolf Bach proposed an action based on the square of the Weyl tensor or CabcdCabcd where the Weyl tensor is an invariant under a scaling of the metric. A variation of the metric leads to the field equation known as the Bach equation. In this dissertation, the same action is analyzed, but as a conformal gauge theory. It is shown that this action is a result of a particular gauging of this group. By treating it as a gauge theory, it is natural to vary all of the gauge fields independently, rather than performing the usual fourth-order metric variation only. We show that solutions of the resulting vacuum field equations are all solutions to the vacuum Einstein equation, up to a conformal factor---a result consistent with local scale freedom. We also show how solutions for the gauge fields imply there is no gravitational self energy.

  14. One-loop renormalization of Lee-Wick gauge theory

    International Nuclear Information System (INIS)

    Grinstein, Benjamin; O'Connell, Donal

    2008-01-01

    We examine the renormalization of Lee-Wick gauge theory to one-loop order. We show that only knowledge of the wave function renormalization is necessary to determine the running couplings, anomalous dimensions, and vector boson masses. In particular, the logarithmic running of the Lee-Wick vector boson mass is exactly related to the running of the coupling. In the case of an asymptotically free theory, the vector boson mass runs to infinity in the ultraviolet. Thus, the UV fixed point of the pure gauge theory is an ordinary quantum field theory. We find that the coupling runs more quickly in Lee-Wick gauge theory than in ordinary gauge theory, so the Lee-Wick standard model does not naturally unify at any scale. Finally, we present results on the beta function of more general theories containing dimension six operators which differ from previous results in the literature.

  15. Gauge theories and integrable lattice models

    International Nuclear Information System (INIS)

    Witten, E.

    1989-01-01

    Investigations of new knot polynomials discovered in the last few years have shown them to be intimately connected with soluble models of two dimensional lattice statistical mechanics. In this paper, these results, which in time may illuminate the whole question of why integrable lattice models exist, are reconsidered from the point of view of three dimensional gauge theory. Expectation values of Wilson lines in three dimensional Chern-Simons gauge theories can be computed by evaluating the partition functions of certain lattice models on finite graphs obtained by projecting the Wilson lines to the plane. The models in question - previously considered in both the knot theory and statistical mechanics literature - are IRF models in which the local Boltzmann weights are the matrix elements of braiding matrices in rational conformal field theories. These matrix elements, in turn, can be represented in three dimensional gauge theory in terms of the expectation value of a certain tetrahedral configuration of Wilson lines. This representation makes manifest a surprising symmetry of the braiding matrix elements in conformal field theory. (orig.)

  16. Jet quenching parameters in strongly coupled nonconformal gauge theories

    International Nuclear Information System (INIS)

    Buchel, Alex

    2006-01-01

    Recently Liu, Rajagopal, and Wiedemann (LRW) [H. Liu, K. Rajagopal, and U. A. Wiedemann, hep-ph/0605178.] proposed a first principle, nonperturbative quantum field theoretic definition of 'jet quenching parameter' q-circumflex used in models of medium-induced radiative parton energy loss in nucleus-nucleus collisions at RHIC. Relating q-circumflex to a short-distance behavior of a certain lightlike Wilson loop, they used gauge theory-string theory correspondence to evaluate q-circumflex for the strongly coupled N=4 SU(N c ) gauge theory plasma. We generalize analysis of LRW to strongly coupled nonconformal gauge theory plasma. We find that a jet quenching parameter is gauge theory specific (not universal). Furthermore, it appears its value increases as the number of effective adjoint degrees of freedom of a gauge theory plasma increases

  17. Dynamics of Strings in Noncommutative Gauge Theory

    International Nuclear Information System (INIS)

    Gross, David J.; Nekrasov, Nikia A.

    2000-01-01

    We continue our study of solitons in noncommutative gauge theories and present an extremely simple BPS solution of N=4 U(1) noncommutative gauge theory in 4 dimensions, which describes N infinite D1 strings that pierce a D3 brane at various points, in the presence of a background B-field in the Seiberg-Witten limit. We call this solution the N-fluxon. For N=1 we calculate the complete spectrum of small fluctuations about the fluxon and find three kinds of modes: the fluctuations of the superstring in 10 dimensions arising from fundamental strings attached to the D1 strings, the ordinary particles of the gauge theory in 4 dimensions and a set of states with discrete spectrum, localized at the intersection point - corresponding to fundamental strings stretched between the D1 string and the D3 brane. We discuss the fluctuations about the N-fluxon as well and derive explicit expressions for the amplitudes of interactions between these various modes. We show that translations in noncommutative gauge theories are equivalent to gauge transformations (plus a constant shift of the gauge field) and discuss the implications for the translational zeromodes of our solitons. We also find the dyonic versions of N-fluxon, as well as of our previous string-monopole solution. (author)

  18. Renormalizable Abelian-projected effective gauge theory derived from quantum chromodynamics

    International Nuclear Information System (INIS)

    Kondo, Kei-ichi; Shinohara, Toru

    2001-01-01

    We show that an effective Abelian gauge theory can be obtained as a renormalizable theory from QCD in the maximal Abelian gauge. The derivation improves in a systematic manner the previous version that was obtained by one of the authors and was referred to as the Abelian-projected effective gauge theory. This result supports the view that we can construct an effective Abelian gauge theory from QCD without losing characteristic features of the original non-Abelian gauge theory. In fact, it is shown that the effective coupling constant in the resulting renormalizable theory has a renormalization-scale dependence governed by the β-function that is exactly the same as that of the original Yang-Mills theory, irrespective of the choice of gauge fixing parameters of the maximal Abelian gauge and the parameters used for identifying the dual variables. Moreover, we evaluate the anomalous dimensions of the fields and parameters in the resultant theory. By choosing the renormalized parameters appropriately, we can switch the theory into an electric or a magnetic theory. (author)

  19. Cohomological gauge theory, quiver matrix models and Donaldson-Thomas theoryCohomological gauge theory, quiver matrix models and Donaldson-Thomas theory

    NARCIS (Netherlands)

    Cirafici, M.; Sinkovics, A.; Szabo, R.J.

    2009-01-01

    We study the relation between Donaldson–Thomas theory of Calabi–Yau threefolds and a six-dimensional topological Yang–Mills theory. Our main example is the topological U(N) gauge theory on flat space in its Coulomb branch. To evaluate its partition function we use equivariant localization techniques

  20. Group theory and lattice gauge fields

    International Nuclear Information System (INIS)

    Creutz, M.

    1988-09-01

    Lattice gauge theory, formulated in terms of invariant integrals over group elements on lattice bonds, benefits from many group theoretical notions. Gauge invariance provides an enormous symmetry and powerful constraints on expectation values. Strong coupling expansions require invariant integrals over polynomials in group elements, all of which can be evaluated by symmetry considerations. Numerical simulations involve random walks over the group. These walks automatically generate the invariant group measure, avoiding explicit parameterization. A recently proposed overrelaxation algorithm is particularly efficient at exploring the group manifold. These and other applications of group theory to lattice gauge fields are reviewed in this talk. 17 refs

  1. Gauge theories under incorporation of a generalized uncertainty principle

    International Nuclear Information System (INIS)

    Kober, Martin

    2010-01-01

    There is considered an extension of gauge theories according to the assumption of a generalized uncertainty principle which implies a minimal length scale. A modification of the usual uncertainty principle implies an extended shape of matter field equations like the Dirac equation. If there is postulated invariance of such a generalized field equation under local gauge transformations, the usual covariant derivative containing the gauge potential has to be replaced by a generalized covariant derivative. This leads to a generalized interaction between the matter field and the gauge field as well as to an additional self-interaction of the gauge field. Since the existence of a minimal length scale seems to be a necessary assumption of any consistent quantum theory of gravity, the gauge principle is a constitutive ingredient of the standard model, and even gravity can be described as gauge theory of local translations or Lorentz transformations, the presented extension of gauge theories appears as a very important consideration.

  2. Hidden simplicity of gauge theory amplitudes

    Energy Technology Data Exchange (ETDEWEB)

    Drummond, J M, E-mail: drummond@lapp.in2p3.f [LAPTH, Universite de Savoie, CNRS, B.P. 110, F-74941 Annecy-le-Vieux, Cedex (France)

    2010-11-07

    These notes were given as lectures at the CERN Winter School on Supergravity, Strings and Gauge Theory 2010. We describe the structure of scattering amplitudes in gauge theories, focussing on the maximally supersymmetric theory to highlight the hidden symmetries which appear. Using the Britto, Cachzo, Feng and Witten (BCFW) recursion relations we solve the tree-level S-matrix in N=4 super Yang-Mills theory and describe how it produces a sum of invariants of a large symmetry algebra. We review amplitudes in the planar theory beyond tree level, describing the connection between amplitudes and Wilson loops, and discuss the implications of the hidden symmetries.

  3. Problem of ''global color'' in gauge theories

    International Nuclear Information System (INIS)

    Horvathy, P.A.; Rawnsley, J.H.; UER de Mathematique, Universite de Provence, Marseille, France)

    1986-01-01

    The problem of ''global color'' (which arose recently in monopole theory) is generalized to arbitrary gauge theories: a subgroup K of the ''unbroken'' gauge group G is implementable iff the gauge bundle reduces to the centralizer of K in G. Equivalent implementations correspond to equivalent reductions. Such an action is an internal symmetry for a given configuration iff the Yang-Mills field reduces also. The case of monopoles is worked out in detail

  4. Theory and application of a gauge invariant effective action to the multi-loop renormalization of non-Abelian gauge theories

    International Nuclear Information System (INIS)

    Hart, C.F.

    1981-01-01

    A gauge invariant effective action which generalizes the usual background field method is applied to quantum non-Abelian gauge theories. The gauge properties of the theory as well as its equivalence to the conventional theory are presented. Solutions to the new effective field equations are found to be physical and it is shown how S-matrix elements may be computed in terms of this new effective action. Feynman rules are given and the renormalization theory is discussed using minimal subtraction and dimensional regularization. The resulting computation of counterterms is found to be simpler than that of the usual method. A complete two-loop calculation of the β function for pure Yang-Mills theory is given as a specific example of this approach

  5. Estimation of Dynamic Errors in Laser Optoelectronic Dimension Gauges for Geometric Measurement of Details

    Directory of Open Access Journals (Sweden)

    Khasanov Zimfir

    2018-01-01

    Full Text Available The article reviews the capabilities and particularities of the approach to the improvement of metrological characteristics of fiber-optic pressure sensors (FOPS based on estimation estimation of dynamic errors in laser optoelectronic dimension gauges for geometric measurement of details. It is shown that the proposed criteria render new methods for conjugation of optoelectronic converters in the dimension gauge for geometric measurements in order to reduce the speed and volume requirements for the Random Access Memory (RAM of the video controller which process the signal. It is found that the lower relative error, the higher the interrogetion speed of the CCD array. It is shown that thus, the maximum achievable dynamic accuracy characteristics of the optoelectronic gauge are determined by the following conditions: the parameter stability of the electronic circuits in the CCD array and the microprocessor calculator; linearity of characteristics; error dynamics and noise in all electronic circuits of the CCD array and microprocessor calculator.

  6. Geometric group theory an introduction

    CERN Document Server

    Löh, Clara

    2017-01-01

    Inspired by classical geometry, geometric group theory has in turn provided a variety of applications to geometry, topology, group theory, number theory and graph theory. This carefully written textbook provides a rigorous introduction to this rapidly evolving field whose methods have proven to be powerful tools in neighbouring fields such as geometric topology. Geometric group theory is the study of finitely generated groups via the geometry of their associated Cayley graphs. It turns out that the essence of the geometry of such groups is captured in the key notion of quasi-isometry, a large-scale version of isometry whose invariants include growth types, curvature conditions, boundary constructions, and amenability. This book covers the foundations of quasi-geometry of groups at an advanced undergraduate level. The subject is illustrated by many elementary examples, outlooks on applications, as well as an extensive collection of exercises.

  7. Topological methods in gauge theory

    International Nuclear Information System (INIS)

    Sarukkai, S.R.

    1992-01-01

    The author begins with an overview of the important topological methods used in gauge theory. In the first chapter, the author discusses the general structure of fiber bundles and associated mathematical concepts and briefly discuss their application in gauge theory. The second chapter deals with the study of instantons in both gauge and gravity theories. These self-dual solutions are presented. This chapter is also a broad introduction to certain topics in gravitational physics. Gravity and gauge theory are unified in Kaluza-Klein theory as discussed in the third chapter. Of particular interest is the physics of the U(1) bundles over non-trivial manifolds. The radius of the fifth dimension is undetermined classically in the Kaluza-Klein theory. A mechanism is described using topological information to derive the functional form of the radius of the fifth dimension and show that it is possible classically to derive expressions for the radius as a consequence of topology. The behavior of the radius is dependent on the information present in the base metric. Results are computed for three gravitational instantons. Consequences of this mechanism are discussed. The description is studied of instantons in terms of projector valued fields and universal bundles. The results of the previous chapter and this are connected via the study of universal bundles. Projector valued transformations are defined and their consequences discussed. With the solutions of instantons in this formalism, it is shown explicitly that there can be solutions which allow for a Sp(n) instanton to be transformed to a Sp(k) instanton, thus showing that there can be interpolations which carry one instanton with a rank n to another characterized by rank k with different topological numbers

  8. Revisiting entanglement entropy of lattice gauge theories

    Energy Technology Data Exchange (ETDEWEB)

    Hung, Ling-Yan [Department of Physics and Center for Field Theory and Particle Physics, Fudan University,220 Handan Lu, Shanghai 200433 (China); Collaborative Innovation Center of Advanced Microstructures, Fudan University,220 Handan Lu, Shanghai 200433 (China); Wan, Yidun [Perimeter Institute for Theoretical Physics,31 Caroline Street, Waterloo, ON N2L 2Y5 (Canada)

    2015-04-22

    It is realized recently that the entanglement entropy in gauge theories is ambiguous because the Hilbert space cannot be expressed as a simple direct product of Hilbert spaces defined on the two regions; different ways of dividing the Hilbert spaces near the boundary leads to significantly different result, to the extreme that it could annihilate the otherwise finite topological entanglement entropy between two regions altogether. In this article, we first show that the topological entanglement entropy in the Kitaev model http://dx.doi.org/10.1016/S0003-4916(02)00018-0 which is not a true gauge theory, is free of ambiguity. Then, we give a physical interpretation, from the perspectives of what can be measured in an experiment, to the purported ambiguity of true gauge theories, where the topological entanglement arises as redundancy in counting the degrees of freedom along the boundary separating two regions. We generalize these discussions to non-Abelian gauge theories.

  9. Antisymmetric tensor Zp gauge symmetries in field theory and string theory

    International Nuclear Information System (INIS)

    Berasaluce-González, Mikel; Ramírez, Guillermo; Uranga, Angel M.

    2014-01-01

    We consider discrete gauge symmetries in D dimensions arising as remnants of broken continuous gauge symmetries carried by general antisymmetric tensor fields, rather than by standard 1-forms. The lagrangian for such a general Z p gauge theory can be described in terms of a r-form gauge field made massive by a (r−1)-form, or other dual realizations, that we also discuss. The theory contains charged topological defects of different dimensionalities, generalizing the familiar charged particles and strings in D=4. We describe realizations in string theory compactifications with torsion cycles, or with background field strength fluxes. We also provide examples of non-abelian discrete groups, for which the group elements are associated with charged objects of different dimensionality

  10. Lattice gauge theory approach to quantum chromodynamics

    International Nuclear Information System (INIS)

    Kogut, J.B.

    1983-01-01

    The author reviews in a pedagogical fashion some of the recent developments in lattice quantum chromodynamics. This review emphasizes explicit examples and illustrations rather than general proofs and analyses. It begins with a discussion of the heavy-quark potential in continuum quantum chromodynamics. Asymptotic freedom and renormalization-group improved perturbation theory are discussed. A simple dielectric model of confinement is considered as an intuitive guide to the vacuum of non-Abelian gauge theories. Next, the Euclidean form of lattice gauge theory is introduced, and an assortment of calculational methods are reviewed. These include high-temperature expansions, duality, Monte Carlo computer simulations, and weak coupling expansions. A #betta#-parameter calculation for asymptotically free-spin models is presented. The Hamiltonian formulation of lattice gauge theory is presented and is illustrated in the context of flux tube dynamics. Roughening transitions, Casimir forces, and the restoration of rotational symmetry are discussed. Mechanisms of confinement in lattice theories are illustrated in the two-dimensional electrodynamics of the planar model and the U(1) gauge theory in four dimensions. Generalized actions for SU(2) gauge theories and the relevance of monopoles and strings to crossover phenomena are considered. A brief discussion of the continuity of fields and topologial charge in asymptotically free lattice models is presented. The final major topic of this review concerns lattice fermions. The species doubling problem and its relation to chiral symmetry are illustrated. Staggered Euclidean fermion methods are discussed in detail, with an emphasis on species counting, remnants of chiral symmetry, Block spin variables, and the axial anomaly. Numerical methods for including fermions in computer simulations are considered. Jacobi and Gauss-Siedel inversion methods to obtain the fermion propagator in a background gauge field are reviewed

  11. Finite N=1 SUSY gauge field theories

    International Nuclear Information System (INIS)

    Kazakov, D.I.

    1986-01-01

    The authors give a detailed description of the method to construct finite N=1 SUSY gauge field theories in the framework of N=1 superfields within dimensional regularization. The finiteness of all Green functions is based on supersymmetry and gauge invariance and is achieved by a proper choice of matter content of the theory and Yukawa couplings in the form Y i =f i (ε)g, where g is the gauge coupling, and the function f i (ε) is regular at ε=0 and is calculated in perturbation theory. Necessary and sufficient conditions for finiteness are determined already in the one-loop approximation. The correspondence with an earlier proposed approach to construct finite theories based on aigenvalue solutions of renormalization-group equations is established

  12. Internal space decimation for lattice gauge theories

    International Nuclear Information System (INIS)

    Flyvbjerg, H.

    1984-01-01

    By a systematic decimation of internal space lattice gauge theories with continuous symmetry groups are mapped into effective lattice gauge theories with finite symmetry groups. The decimation of internal space makes a larger lattice tractable with the same computational resources. In this sense the method is an alternative to Wilson's and Symanzik's programs of improved actions. As an illustrative test of the method U(1) is decimated to Z(N) and the results compared with Monte Carlo data for Z(4)- and Z(5)-invariant lattice gauge theories. The result of decimating SU(3) to its 1080-element crystal-group-like subgroup is given and discussed. (orig.)

  13. Extended Nambu models: Their relation to gauge theories

    Science.gov (United States)

    Escobar, C. A.; Urrutia, L. F.

    2017-05-01

    Yang-Mills theories supplemented by an additional coordinate constraint, which is solved and substituted in the original Lagrangian, provide examples of the so-called Nambu models, in the case where such constraints arise from spontaneous Lorentz symmetry breaking. Some explicit calculations have shown that, after additional conditions are imposed, Nambu models are capable of reproducing the original gauge theories, thus making Lorentz violation unobservable and allowing the interpretation of the corresponding massless gauge bosons as the Goldstone bosons arising from the spontaneous symmetry breaking. A natural question posed by this approach in the realm of gauge theories is to determine under which conditions the recovery of an arbitrary gauge theory from the corresponding Nambu model, defined by a general constraint over the coordinates, becomes possible. We refer to these theories as extended Nambu models (ENM) and emphasize the fact that the defining coordinate constraint is not treated as a standard gauge fixing term. At this level, the mechanism for generating the constraint is irrelevant and the case of spontaneous Lorentz symmetry breaking is taken only as a motivation, which naturally bring this problem under consideration. Using a nonperturbative Hamiltonian analysis we prove that the ENM yields the original gauge theory after we demand current conservation for all time, together with the imposition of the Gauss laws constraints as initial conditions upon the dynamics of the ENM. The Nambu models yielding electrodynamics, Yang-Mills theories and linearized gravity are particular examples of our general approach.

  14. Gauge invariant actions for string models

    International Nuclear Information System (INIS)

    Banks, T.

    1986-06-01

    String models of unified interactions are elegant sets of Feynman rules for the scattering of gravitons, gauge bosons, and a host of massive excitations. The purpose of these lectures is to describe the progress towards a nonperturbative formulation of the theory. Such a formulation should make the geometrical meaning of string theory manifest and explain the many ''miracles'' exhibited by the string Feynman rules. There are some new results on gauge invariant observables, on the cosmological constant, and on the symmetries of interacting string field theory. 49 refs

  15. Introduction to gauge theories and unification

    International Nuclear Information System (INIS)

    Das, A.

    1990-01-01

    This paper contains the following lectures on gauge theories: basic notations; dimensional regularization; complex scalar field theory; scalar field theory; self-interacting scalar field theory; Noether's theorem; spontaneous symmetry breaking; dirac field theories; local symmetry; quantum electrodynamics; Higgs mechanism; non-Abelian symmetries; and Weinberg-Salam-Glashow theory

  16. Topological resolution of gauge theory singularities

    Science.gov (United States)

    Saracco, Fabio; Tomasiello, Alessandro; Torroba, Gonzalo

    2013-08-01

    Some gauge theories with Coulomb branches exhibit singularities in perturbation theory, which are usually resolved by nonperturbative physics. In string theory this corresponds to the resolution of timelike singularities near the core of orientifold planes by effects from F or M theory. We propose a new mechanism for resolving Coulomb branch singularities in three-dimensional gauge theories, based on Chern-Simons interactions. This is illustrated in a supersymmetric SU(2) Yang-Mills-Chern-Simons theory. We calculate the one-loop corrections to the Coulomb branch of this theory and find a result that interpolates smoothly between the high-energy metric (that would exhibit the singularity) and a regular singularity-free low-energy result. We suggest possible applications to singularity resolution in string theory and speculate a relationship to a similar phenomenon for the orientifold six-plane in massive IIA supergravity.

  17. Topological resolution of gauge theory singularities

    Energy Technology Data Exchange (ETDEWEB)

    Saracco, Fabio; Tomasiello, Alessandro; Torroba, Gonzalo

    2013-08-21

    Some gauge theories with Coulomb branches exhibit singularities in perturbation theory, which are usually resolved by nonperturbative physics. In string theory this corresponds to the resolution of timelike singularities near the core of orientifold planes by effects from F or M theory. We propose a new mechanism for resolving Coulomb branch singularities in three-dimensional gauge theories, based on Chern-Simons interactions. This is illustrated in a supersymmetric S U ( 2 ) Yang-Mills-Chern-Simons theory. We calculate the one-loop corrections to the Coulomb branch of this theory and find a result that interpolates smoothly between the high-energy metric (that would exhibit the singularity) and a regular singularity-free low-energy result. We suggest possible applications to singularity resolution in string theory and speculate a relationship to a similar phenomenon for the orientifold six-plane in massive IIA supergravity.

  18. Gauge field theories

    International Nuclear Information System (INIS)

    Pokorski, S.

    1987-01-01

    Quantum field theory forms the present theoretical framework for the understanding of the fundamental interactions of particle physics. This book examines gauge theories and their symmetries with an emphasis on their physical and technical aspects. The author discusses field-theoretical techniques and encourages the reader to perform many of the calculations presented. This book includes a brief introduction to perturbation theory, the renormalization programme, and the use of the renormalization group equation. Several topics of current research interest are covered, including chiral symmetry and its breaking, anomalies, and low energy effective lagrangians and some basics of supersymmetry

  19. M-theory and U-duality on Td with gauge backgrounds

    International Nuclear Information System (INIS)

    Obers, N.A.; Pioline, B.; Rabinovici, E.

    1998-01-01

    The full U-duality symmetry of toroidally compactified M-theory can only be displayed by allowing non-rectangular tori with expectation values of the gauge fields. We construct an E d (Z) U-duality invariant mass formula incorporating non-vanishing gauge backgrounds of the M-theory three-form C. We interpret this mass formula from the point of view of the matrix gauge theory, and identify the coupling of the three-form to the gauge theory as a topological theta term, in agreement with earlier conjectures. We give a derivation of this fact from D-brane analysis, and obtain the matrix gauge theory description of other gauge backgrounds allowed by the discrete light-cone quantization. We further show that the conjectured extended U-duality symmetry of matrix theory on T d in the discrete light-cone quantization has an implementation as an action of E d+1 (Z) on the BPS spectrum. Some implications for the proper interpretation of the rank N of the matrix gauge theory are discussed. (orig.)

  20. Topological charge in non-abelian lattice gauge theory

    International Nuclear Information System (INIS)

    Lisboa, P.

    1983-01-01

    We report on a numerical calculation of topological charge densities in non-abelian gauge theory with gauge groups SU(2) and SU(3). The group manifold is represented by a discrete subset thereof which lies outside its finite subgroups. The results shed light on the usefulness of these representations in Monte Carlo evaluations of non-abelian lattice gauge theory. (orig.)

  1. On the structure of translational gauge theories of gravitation

    International Nuclear Information System (INIS)

    Wallner, R.P.

    1982-01-01

    Guided by decoupling processes in general gauge theories, we examine the translation limit in U 4 -theories. It is shown that this leads to Einstein's gravity theory as the appropriate choice for a translational gauge theory of gravitation. (Author)

  2. Geometric function theory in higher dimension

    CERN Document Server

    2017-01-01

    The book collects the most relevant outcomes from the INdAM Workshop “Geometric Function Theory in Higher Dimension” held in Cortona on September 5-9, 2016. The Workshop was mainly devoted to discussions of basic open problems in the area, and this volume follows the same line. In particular, it offers a selection of original contributions on Loewner theory in one and higher dimensions, semigroups theory, iteration theory and related topics. Written by experts in geometric function theory in one and several complex variables, it focuses on new research frontiers in this area and on challenging open problems. The book is intended for graduate students and researchers working in complex analysis, several complex variables and geometric function theory.

  3. Non-Abelian Gauge Theory in the Lorentz Violating Background

    Science.gov (United States)

    Ganai, Prince A.; Shah, Mushtaq B.; Syed, Masood; Ahmad, Owais

    2018-03-01

    In this paper, we will discuss a simple non-Abelian gauge theory in the broken Lorentz spacetime background. We will study the partial breaking of Lorentz symmetry down to its sub-group. We will use the formalism of very special relativity for analysing this non-Abelian gauge theory. Moreover, we will discuss the quantisation of this theory using the BRST symmetry. Also, we will analyse this theory in the maximal Abelian gauge.

  4. Renormalization of a distorted gauge: invariant theory

    International Nuclear Information System (INIS)

    Hsu, J.P.; Underwood, J.A.

    1976-02-01

    A new type of renormalizable theory involving massive Yang-Mills fields whose mass is generated by an intrinsic breakdown of the usual local gauge symmetry is considered. However, the Lagrangian has a distorted gauge symmetry which leads to the Ward-Takahashi (W-T) identities. Also, the theory is independent of the gauge parameter xi. An explicit renormalization at the oneloop level is completely carried out by exhibiting counter terms, defining the physical parameters and computing all renormalization constants to check the W-T identities

  5. National Computational Infrastructure for Lattice Gauge Theory

    Energy Technology Data Exchange (ETDEWEB)

    Brower, Richard C.

    2014-04-15

    SciDAC-2 Project The Secret Life of Quarks: National Computational Infrastructure for Lattice Gauge Theory, from March 15, 2011 through March 14, 2012. The objective of this project is to construct the software needed to study quantum chromodynamics (QCD), the theory of the strong interactions of sub-atomic physics, and other strongly coupled gauge field theories anticipated to be of importance in the energy regime made accessible by the Large Hadron Collider (LHC). It builds upon the successful efforts of the SciDAC-1 project National Computational Infrastructure for Lattice Gauge Theory, in which a QCD Applications Programming Interface (QCD API) was developed that enables lattice gauge theorists to make effective use of a wide variety of massively parallel computers. This project serves the entire USQCD Collaboration, which consists of nearly all the high energy and nuclear physicists in the United States engaged in the numerical study of QCD and related strongly interacting quantum field theories. All software developed in it is publicly available, and can be downloaded from a link on the USQCD Collaboration web site, or directly from the github repositories with entrance linke http://usqcd-software.github.io

  6. An approach to higher dimensional theories based on lattice gauge theory

    International Nuclear Information System (INIS)

    Murata, M.; So, H.

    2004-01-01

    A higher dimensional lattice space can be decomposed into a number of four-dimensional lattices called as layers. The higher dimensional gauge theory on the lattice can be interpreted as four-dimensional gauge theories on the multi-layer with interactions between neighboring layers. We propose the new possibility to realize the continuum limit of a five-dimensional theory based on the property of the phase diagram

  7. Gauge field theories an introduction with applications

    CERN Document Server

    Guidry, Mike

    1991-01-01

    Acquaints readers with the main concepts and literature of elementary particle physics and quantum field theory. In particular, the book is concerned with the elaboration of gauge field theories in nuclear physics; the possibility of creating fundamental new states of matter such as an extended quark-gluon plasma in ultra-relativistic heavy ion collisions; and the relation of gauge theories to the creation and evolution of the universe. Divided into three parts, it opens with an introduction to the general principles of relativistic quantum field theory followed by the essential ingredients of gauge fields for weak and electromagnetic interactions, quantum chromodynamics and strong interactions. The third part is concerned with the interface between modern elementary particle physics and "applied disciplines" such as nuclear physics, astrophysics and cosmology. Includes references and numerous exercises

  8. Gauge-invariant charged, monopole and dyon fields in gauge theories

    International Nuclear Information System (INIS)

    Froehlich, J.; Marchetti, P.A.

    1999-01-01

    We propose explicit recipes to construct the Euclidean Green functions of gauge-invariant charged, monopole and dyon fields in four-dimensional gauge theories whose phase diagram contains phases with deconfined electric and/or magnetic charges. In theories with only either abelian electric or magnetic charges, our construction is an Euclidean version of Dirac's original proposal, the magnetic dual of his proposal, respectively. Rigorous mathematical control is achieved for a class of abelian lattice theories. In theories where electric and magnetic charges coexist, our construction of Green functions of electrically or magnetically charged fields involves taking an average over Mandelstam strings or the dual magnetic flux tubes, in accordance with Dirac's flux quantization condition. We apply our construction to 't Hooft-Polyakov monopoles and Julia-Zee dyons. Connections between our construction and the semiclassical approach are discussed

  9. Noncommutative SO(n) and Sp(n) gauge theories

    International Nuclear Information System (INIS)

    Bonora, L.; INFN, Sezione di Trieste, Trieste; Schnabl, M.; INFN, Sezione di Trieste, Trieste; Sheikh-Jabbari, M.M.; Tomasiello, A.

    2000-08-01

    We study the generalization of noncommutative gauge theories to the case of orthogonal and symplectic groups. We find out that this is possible, since we are allowed to define orthogonal and symplectic subgroups of noncommutative unitary gauge transformations even though the gauge potentials and gauge transformations are not valued in the orthogonal and symplectic subalgebras of the Lie algebra of antihermitean matrices. Our construction relies on an antiautomorphism of the basic noncommutative algebra of functions which generalizes the charge conjugation operator of ordinary field theory. We show that the corresponding noncommutative picture from low energy string theory is obtained via orientifold projection in the presence of a non-trivial NSNS B-field. (author)

  10. The holomorphicity of the gauge coupling constant in supersymmetric gauge theories

    International Nuclear Information System (INIS)

    Li, H.

    1993-01-01

    Holomorphicity is the analytical dependence of the gauge coupling function, f = 1/g 2 + Θ/8π 2 , on the chiral fields in supergravity and supersymmetric gauge theories. The holomorphic property of 1/g 2 in supersymmetric gauge theories is studied by calculating its dependence on the mass matrix. The general representations of the mass matrix allowed by the constraints of gauge invariance is considered, and calculate the one- and two-loop corrections to 1/g 2 for both super QED and super Yang-Mills theories. For the massive mass matrix it is shown that one- and two-loop corrections to the gauge coupling constant are holomorphic. The reason for two-loop holomorphicity is that the second order logarithmic terms cancel out. For the mass matrix with at least one zero mode, it is recognized that there are two distinct cases which we call pseudo massive and intrinsically massless. For the case of pseudo mass matrix, the reducible representation of the gauge group is (i) complex with equal numbers of irreducible representations and their conjugates, (ii) real, or (iii) pseudo-real. Even though there are massless modes, it is found that the dependence of the gauge coupling constant on the mass matrix is holomorphic. This holomorphicity follows because the mass matrix can be perturbed to regularize the infrared divergence. For the case of intrinsically massless mass matrix, a reducible complex representation with unequal numbers of irreducible representations and their conjugates. The author shows that loop corrections to the gauge coupling constant are non-holomorphic. The reason is an infrared momentum cutoff is used which spins holomorphicity. The results show that, for the pseudo massive case, even though there is an infrared divergence, the one- and two-loop corrections are still holomorphic. Hence, it is concluded that non-holomorphicity is caused by the unbalanced numbers of families and antifamilies in the complex representation

  11. CERN Winter School on Supergravity, Strings, and Gauge Theory 2010

    CERN Multimedia

    CERN. Geneva

    2010-01-01

    The CERN Winter School on Supergravity, Strings, and Gauge Theory is the analytic continuation of the yearly training school of the former EC-RTN string network "Constituents, Fundamental Forces and Symmetries of the Universe". The 2010 edition of the school is supported and organized by the CERN Theory Divison, and will take place from Monday January 25 to Friday January 29, at CERN. As its predecessors, this school is meant primarily for training of doctoral students and young postdoctoral researchers in recent developments in theoretical high-energy physics and string theory. The programme of the school will consist of five series of pedagogical lectures, complemented by tutorial discussion sessions in the afternoons. Previous schools in this series were organized in 2005 at SISSA in Trieste, and in 2006, 2007, 2008, and 2009 at CERN, Geneva. Other similar schools have been organized in the past by the former related RTN network "The Quantum Structure of Spacetime and the Geometric Nature of Fundamenta...

  12. Construction of non-Abelian gauge theories on noncommutative spaces

    International Nuclear Information System (INIS)

    Jurco, B.; Schupp, P.; Moeller, L.; Wess, J.; Max-Planck-Inst. fuer Physik, Muenchen; Humboldt-Univ., Berlin; Schraml, S.; Humboldt-Univ., Berlin

    2001-01-01

    We present a formalism to explicitly construct non-Abelian gauge theories on noncommutative spaces (induced via a star product with a constant Poisson tensor) from a consistency relation. This results in an expansion of the gauge parameter, the noncommutative gauge potential and fields in the fundamental representation, in powers of a parameter of the noncommutativity. This allows the explicit construction of actions for these gauge theories. (orig.)

  13. Construction of non-Abelian gauge theories on noncommutative spaces

    Energy Technology Data Exchange (ETDEWEB)

    Jurco, B.; Schupp, P. [Sektion Physik, Muenchen Univ. (Germany); Moeller, L.; Wess, J. [Sektion Physik, Muenchen Univ. (Germany); Max-Planck-Inst. fuer Physik, Muenchen (Germany); Humboldt-Univ., Berlin (Germany). Inst. fuer Physik; Schraml, S. [Sektion Physik, Muenchen Univ. (Germany)

    2001-06-01

    We present a formalism to explicitly construct non-Abelian gauge theories on noncommutative spaces (induced via a star product with a constant Poisson tensor) from a consistency relation. This results in an expansion of the gauge parameter, the noncommutative gauge potential and fields in the fundamental representation, in powers of a parameter of the noncommutativity. This allows the explicit construction of actions for these gauge theories. (orig.)

  14. Light-Front Quantization of Gauge Theories

    Energy Technology Data Exchange (ETDEWEB)

    Brodsky, Stanley J.

    2003-03-25

    Light-front wavefunctions provide a frame-independent representation of hadrons in terms of their physical quark and gluon degrees of freedom. The light-front Hamiltonian formalism provides new nonperturbative methods for obtaining the QCD spectrum and eigensolutions, including resolvant methods, variational techniques, and discretized light-front quantization. A new method for quantizing gauge theories in light-cone gauge using Dirac brackets to implement constraints is presented. In the case of the electroweak theory, this method of light-front quantization leads to a unitary and renormalizable theory of massive gauge particles, automatically incorporating the Lorentz and 't Hooft conditions as well as the Goldstone boson equivalence theorem. Spontaneous symmetry breaking is represented by the appearance of zero modes of the Higgs field leaving the light-front vacuum equal to the perturbative vacuum. I also discuss an ''event amplitude generator'' for automatically computing renormalized amplitudes in perturbation theory. The importance of final-state interactions for the interpretation of diffraction, shadowing, and single-spin asymmetries in inclusive reactions such as deep inelastic lepton-hadron scattering is emphasized.

  15. Light-Front Quantization of Gauge Theories

    Energy Technology Data Exchange (ETDEWEB)

    Brodskey, Stanley

    2002-12-01

    Light-front wavefunctions provide a frame-independent representation of hadrons in terms of their physical quark and gluon degrees of freedom. The light-front Hamiltonian formalism provides new nonperturbative methods for obtaining the QCD spectrum and eigensolutions, including resolvant methods, variational techniques, and discretized light-front quantization. A new method for quantizing gauge theories in light-cone gauge using Dirac brackets to implement constraints is presented. In the case of the electroweak theory, this method of light-front quantization leads to a unitary and renormalizable theory of massive gauge particles, automatically incorporating the Lorentz and 't Hooft conditions as well as the Goldstone boson equivalence theorem. Spontaneous symmetry breaking is represented by the appearance of zero modes of the Higgs field leaving the light-front vacuum equal to the perturbative vacuum. I also discuss an ''event amplitude generator'' for automatically computing renormalized amplitudes in perturbation theory. The importance of final-state interactions for the interpretation of diffraction, shadowing, and single-spin asymmetries in inclusive reactions such as deep inelastic lepton-hadron scattering is emphasized.

  16. Mean field with corrections in lattice gauge theory

    International Nuclear Information System (INIS)

    Flyvbjerg, H.; Zuber, J.B.; Lautrup, B.

    1981-12-01

    A systematic expansion of the path integral for lattice gauge theory is performed around the mean field solution. In this letter the authors present the results for the pure gauge groups Z(2), SU(2) and SO(3). The agreement with Monte Carlo calculations is excellent. For the discrete group the calculation is performed with and without gauge fixing, whereas for the continuous groups gauge fixing is mandatory. In the case of SU(2) the absence of a phase transition is correctly signalled by mean field theory. (Auth.)

  17. Gauge bridges in classical field theory

    International Nuclear Information System (INIS)

    Jakobs, S.

    2009-03-01

    In this thesis Poisson structures of two classical gauge field theories (Maxwell-Klein-Gordon- and Maxwell-Dirac-system) are constructed using the parametrix construction of Green's functions. Parametrices for the Maxwell-Klein-Gordon- and Maxwell-Dirac-system are constructed in Minkowski space and this construction is later generalized to curved space times for the Maxwell-Klein-Gordon-system. With these Green's functions Poisson brackets will be defined as Peierls brackets. Finally non-local, gauge invariant observables, the so-called ''gauge bridges''are constructed. Gauge bridges are the matrix elements of holonomy operators. It is shown, that these emerge from Poisson brackets of local, gauge invariant observables. (orig.)

  18. Gauge-free gyrokinetic theory

    Science.gov (United States)

    Burby, Joshua; Brizard, Alain

    2017-10-01

    Test-particle gyrocenter equations of motion play an essential role in the diagnosis of turbulent strongly-magnetized plasmas, and are playing an increasingly-important role in the formulation of kinetic-gyrokinetic hybrid models. Previous gyrocenter models required the knowledge of the perturbed electromagnetic potentials, which are not directly observable quantities (since they are gauge-dependent). A new gauge-free formulation of gyrocenter motion is presented, which enables gyrocenter trajectories to be determined using only measured values of the directly-observable electromagnetic field. Our gauge-free gyrokinetic theory is general enough to allow for gyroradius-scale fluctuations in both the electric and magnetic field. In addition, we provide gauge-free expressions for the charge and current densities produced by a distribution of gyrocenters, which explicitly include guiding-center and gyrocenter polarization and magnetization effects. This research was supported by the U.S. DOE Contract Nos. DE-SC0014032 (AB) and DE-AC05-06OR23100 (JB).

  19. Anomaly-free gauges in superstring theory and double supersymmetric sigma-model

    International Nuclear Information System (INIS)

    Demichev, A.P.; Iofa, M.Z.

    1991-01-01

    Superharmonic gauge which is a nontrivial analog of the harmonic gauge in bosonic string theory is constructed for the fermionic superstrings. In contrast to the conformal gauge, the harmonic gauge in bosonic string and superharmonic gauge in superstring theory are shown to be free from previously discovered BRST anomaly (in critical dimension) in higher orders of string perturbation theory and thus provide the setup for consistent quantization of (super)string theory. Superharmonic gauge appears to be closely connected with the supersymmetric σ-model with the target space being also a supermanifold. 28 refs

  20. Axial-gauge formulation of a three-dimensional field theory

    International Nuclear Information System (INIS)

    Hagen, C.R.

    1985-01-01

    Since the non-Abelian version of a recently formulated gauge theory in two spatial dimensions gives rise to a nonlinear constraint upon the fields in the radiation-gauge approach, one is motivated to attempt a description in terms of the axial gauge. This is accomplished in the Abelian version of the model, with results similar to those encountered in the radiation gauge. The non-Abelian case is then formally solved in the same gauge, it being subsequently shown, however, that the theory is not covariant. It is argued on the basis of perturbation theory that such noncovariance is a real effect which is not readily circumvented by modification of the field transformation properties

  1. Quiver gauge theory and extended electric-magnetic duality

    International Nuclear Information System (INIS)

    Maruyoshi, Kazunobu

    2009-01-01

    We construct N = 1 A-D-E quiver gauge theory with the gauge kinetic term which depends on the adjoint chiral superfields, as a low energy effective theory on D5-branes wrapped on 2-cycles of Calabi-Yau 3-fold in IIB string theory. The field-dependent gauge kinetic term can be engineered by introducing B-field which holomorphically varies on the base space (complex plane) of Calabi-Yau. We consider Weyl reflection on A-D-E node, which acts non-trivially on the gauge kinetic term. It is known that Weyl reflection is related to N = 1 electric-magnetic duality. Therefore, the non-trivial action implies an extension of the electric-magnetic duality to the case with the field-dependent gauge kinetic term. We show that this extended duality is consistent from the field theoretical point of view. We also consider the duality map of the operators.

  2. A geometrical description of local and global anomalies

    International Nuclear Information System (INIS)

    Catenacci, R.; Pirola, G.P.

    1990-01-01

    The general topological framework for testing the possible occurrence of anomalies in gauge theories can be constructed in terms of the theory of group actions on line bundles through the introduction of a suitable group cohomology. In this Letter, we generalize this construction in such a way that it can be applied to a larger class of theories, allowing for a noncontractible configuration space and a nonconnected 'gauge' group. This construction find applications to the problem of the lifts of principal group actions. As a physical application, we compare the mechanisms of the anomalies cancelation in gauge and string theories, through a geometrical splitting of local and global anomalies. (orig.)

  3. Class of very simple gauge theories which remain renormalizable even in the limit of infinite gauge coupling constant

    International Nuclear Information System (INIS)

    Kaptanoglu, S.

    1983-01-01

    A class of local gauge theories based on compact semisimple Lie groups is studied in the limit of infinite gauge coupling constant (g = infinity). In general, in this limit, the gauge fields become auxiliary in all gauge theories, and the system develops a richer structure of constraints. Unfortunately for most gauge theories, this limit turns out to be too singular to quantize and the theory ceases to be renormalizable. For a special class of gauge theories, however, where there are no fermions and there is only one multiplet of scalars in the adjoint representation, we prove that a consistent renormalizable quantum theory exists even in this very singular limit. We trace this exceptional behavior to a new local translationlike symmetry in the functional space that this class of gauge models possesses in the limit of infinite gauge coupling constant. By carrying out the constraint analysis, evaluating the Faddeev-Popov-Senjanovic determinant, and doing the functional integrations over the canonical momenta, the gauge fields, and most of the components of the scalar fields, we obtain an extremely simple result with no non-Abelian structure left in it. For example, for the group SU(2), the final answer reduces to the theory of a one-component self-interacting real phi 4 scalar field theory. Throughout this paper, we use functional methods and make no approximations; our results are nonperturbative and exact. We also discuss some of the possible implications of our results

  4. RIKEN BNL RESEARCH CENTER WORKSHOP ON GAUGE-INVARIANT VARIABLES IN GAUGE THEORIES, VOLUME 20

    Energy Technology Data Exchange (ETDEWEB)

    VAN BAAL,P.; ORLAND,P.; PISARSKI,R.

    2000-06-01

    This four-day workshop focused on the wide variety of approaches to the non-perturbative physics of QCD. The main topic was the formulation of non-Abelian gauge theory in orbit space, but some other ideas were discussed, in particular the possible extension of the Maldacena conjecture to nonsupersymmetric gauge theories. The idea was to involve most of the participants in general discussions on the problem. Panel discussions were organized to further encourage debate and understanding. Most of the talks roughly fell into three categories: (1) Variational methods in field theory; (2) Anti-de Sitter space ideas; (3) The fundamental domain, gauge fixing, Gribov copies and topological objects (both in the continuum and on a lattice). In particular some remarkable progress in three-dimensional gauge theories was presented, from the analytic side by V.P. Nair and mostly from the numerical side by O. Philipsen. This work may ultimately have important implications for RHIC experiments on the high-temperature quark-gluon plasma.

  5. Geometric group theory

    CERN Document Server

    Bestvina, Mladen; Vogtmann, Karen

    2014-01-01

    Geometric group theory refers to the study of discrete groups using tools from topology, geometry, dynamics and analysis. The field is evolving very rapidly and the present volume provides an introduction to and overview of various topics which have played critical roles in this evolution. The book contains lecture notes from courses given at the Park City Math Institute on Geometric Group Theory. The institute consists of a set of intensive short courses offered by leaders in the field, designed to introduce students to exciting, current research in mathematics. These lectures do not duplicate standard courses available elsewhere. The courses begin at an introductory level suitable for graduate students and lead up to currently active topics of research. The articles in this volume include introductions to CAT(0) cube complexes and groups, to modern small cancellation theory, to isometry groups of general CAT(0) spaces, and a discussion of nilpotent genus in the context of mapping class groups and CAT(0) gro...

  6. Gauge fluxes in F-theory compactifications

    Energy Technology Data Exchange (ETDEWEB)

    Lin, Ling

    2016-07-13

    In this thesis, we study the geometry and physics of gauge fluxes in F-theory compactifications to four dimensions. Motivated by the phenomenological requirement of chiral matter in realistic model building scenarios, we develop methods for a systematic analysis of primary vertical G{sub 4}-fluxes on torus-fibred Calabi-Yau fourfolds. In particular, we extend the well-known description of fluxes on elliptic fibrations with sections to the more general set-up of genus-one fibrations with multi-sections. The latter are known to give rise to discrete abelian symmetries in F-theory. We test our proposal for constructing fluxes in such geometries on an explicit model with SU(5) x Z{sub 2} symmetry, which is connected to an ordinary elliptic fibration with SU(5) x U(1) symmetry by a conifold transition. With our methods we systematically verify anomaly cancellation and tadpole matching in both models. Along the way, we find a novel way of understanding anomaly cancellation in 4D F-theory in purely geometric terms. This observation is further strengthened by a similar analysis of an SU(3) x SU(2) x U(1){sup 2} model. The obvious connection of this particular model with the Standard Model is then investigated in a more phenomenologically motivated survey. There, we will first provide possible matchings of the geometric spectrum with the Standard Model states, which highlights the role of the additional U(1) factor as a selection rule. In a second step, we then utilise our novel methods on flux computations to set up a search algorithm for semi-realistic chiral spectra in our Standard- Model-like fibrations over specific base manifolds B. As a demonstration, we scan over three choices P{sup 3}, Bl{sub 1}P{sup 3} and Bl{sub 2}P{sup 3} for the base. As a result we find a consistent flux that gives the chiral Standard Model spectrum with a vector-like triplet exotic, which may be lifted by a Higgs mechanism.

  7. Numerical techniques for lattice gauge theories

    International Nuclear Information System (INIS)

    Creutz, M.

    1981-01-01

    The motivation for formulating gauge theories on a lattice is reviewed. Monte Carlo simulation techniques are then discussed for these systems. Finally, the Monte Carlo methods are combined with renormalization group analysis to give strong numerical evidence for confinement of quarks by non-Abelian gauge fields

  8. Superfield formulation of stochastic quantization for gauge theories

    International Nuclear Information System (INIS)

    Egoryan, Ed.Sh.; Manvelian, R.P.

    1990-01-01

    Using gauge symmetry localization relative to superspace coordinates an extended stochastic action for the Yang-Mills field possessing supergauge invariance is obtained. This allows to formulate correctly a mechanism of stochastic reduction for gauge theories beyond the framework of perturbation theory. 12 refs

  9. Infrared behaviors of SU(2 gauge theory

    Directory of Open Access Journals (Sweden)

    Tuominen Kimmo

    2017-01-01

    Full Text Available We will discuss some recent results in the determination of the location of the conformal window in SU(2 gauge theory with Nf fermions in the fundamental representation of the gauge group. In particular, we will demonstrate that the long distance behavior of the continuum theory with Nf = 6 is governed by an infrared stable fixed point.

  10. Gauge field theories. Part three. Renormalization

    International Nuclear Information System (INIS)

    Frampon, P.H.

    1978-01-01

    The renormalization of nonabelian gauge theories both with exact symmetry and with spontaneous symmetry breaking is discussed. The method of dimensional regularization is described and used in the ensuing discussion. Triangle anomalies and their implications and the method for cancellation of anomalies in an SU(2) x U(1) theory, introduction of the BRS form of local gauge transformation and its use for the iterative proof of renormalizability to all orders for pure Yang--Mills and with fermion and scalar matter fields are considered. Lastly for massive vectors arising from spontaneous breaking, the demonstration of renormalizability is given, using the 't Hooft gauges introduced first in 1971. While the treatment is not totally rigorous, all the principle steps are given. 108 references

  11. Restoration of the local gauge symmetry and color confinement in non-Abelian gauge theories

    International Nuclear Information System (INIS)

    Hata, Hiroyuki

    1982-01-01

    Restoration of the local gauge symmetry and its connection to color confinement is investigated in non-Abelian gauge theories with covariant gauge fixing. We consider the Noether current J sub(μ,#betta#)sup(a) of the local gauge transformation with transformation functions #betta#sup(b)(x) linear in x sub(μ); #betta#sup(b)(x) = delta sup(ab)x sub(#betta#). This current is conserved only in the physical subspace of the state vector space and in perturbation theory contains a massless pole communicating to the gauge field. We define the local gauge symmetry restoration as the disappearance of this massless ''Goldstone'' pole from J sub(μ,#betta#)sup(a). The restoration condition is obtained and it coincides exactly with the color confinement criterion proposed earlier by Kugo and Ojima. Quarks and other colored particles are shown to be confined in the local gauge symmetry restored phase by using the Ward identities of J sub(μ,#betta#)sup(a). (author)

  12. Strong dynamics and lattice gauge theory

    Science.gov (United States)

    Schaich, David

    In this dissertation I use lattice gauge theory to study models of electroweak symmetry breaking that involve new strong dynamics. Electroweak symmetry breaking (EWSB) is the process by which elementary particles acquire mass. First proposed in the 1960s, this process has been clearly established by experiments, and can now be considered a law of nature. However, the physics underlying EWSB is still unknown, and understanding it remains a central challenge in particle physics today. A natural possibility is that EWSB is driven by the dynamics of some new, strongly-interacting force. Strong interactions invalidate the standard analytical approach of perturbation theory, making these models difficult to study. Lattice gauge theory is the premier method for obtaining quantitatively-reliable, nonperturbative predictions from strongly-interacting theories. In this approach, we replace spacetime by a regular, finite grid of discrete sites connected by links. The fields and interactions described by the theory are likewise discretized, and defined on the lattice so that we recover the original theory in continuous spacetime on an infinitely large lattice with sites infinitesimally close together. The finite number of degrees of freedom in the discretized system lets us simulate the lattice theory using high-performance computing. Lattice gauge theory has long been applied to quantum chromodynamics, the theory of strong nuclear interactions. Using lattice gauge theory to study dynamical EWSB, as I do in this dissertation, is a new and exciting application of these methods. Of particular interest is non-perturbative lattice calculation of the electroweak S parameter. Experimentally S ≈ -0.15(10), which tightly constrains dynamical EWSB. On the lattice, I extract S from the momentum-dependence of vector and axial-vector current correlators. I created and applied computer programs to calculate these correlators and analyze them to determine S. I also calculated the masses

  13. The metric-affine gravitational theory as the gauge theory of the affine group

    International Nuclear Information System (INIS)

    Lord, E.A.

    1978-01-01

    The metric-affine gravitational theory is shown to be the gauge theory of the affine group, or equivalently, the gauge theory of the group GL(4,R) of tetrad deformations in a space-time with a locally Minkowskian metric. The identities of the metric-affine theory, and the relationship between them and those of general relativity and Sciama-Kibble theory, are derived. (Auth.)

  14. Nonlattice Simulation for Supersymmetric Gauge Theories in One Dimension

    International Nuclear Information System (INIS)

    Hanada, Masanori; Nishimura, Jun; Takeuchi, Shingo

    2007-01-01

    Lattice simulation of supersymmetric gauge theories is not straightforward. In some cases the lack of manifest supersymmetry just necessitates cumbersome fine-tuning, but in the worse cases the chiral and/or Majorana nature of fermions makes it difficult to even formulate an appropriate lattice theory. We propose circumventing all these problems inherent in the lattice approach by adopting a nonlattice approach for one-dimensional supersymmetric gauge theories, which are important in the string or M theory context. In particular, our method can be used to investigate the gauge-gravity duality from first principles, and to simulate M theory based on the matrix theory conjecture

  15. Classical solutions in lattice gauge theories

    International Nuclear Information System (INIS)

    Mitrjushkin, V.K.

    1996-08-01

    The solutions of the classical equations of motion on a periodic lattice are found which correspond to abelian single and double Dirac sheets. These solutions exist also in non-abelian theories. Possible applications of these solutions to the calculation of gauge dependent and gauge invariant observables are discussed. (orig.)

  16. On novel string theories from 4d gauge theories

    Directory of Open Access Journals (Sweden)

    Kiritsis Elias

    2014-04-01

    Full Text Available We investigate strings theories as defined from four dimensional gauge theories. It is argued that novel (superstring theories exist up to 26 dimensions. Some of them may support weakly curved geometries. A proposal is outlined to link their local conformal invariance to the dynamics of the bulk string theory.

  17. Gauge theory and elementary particles

    International Nuclear Information System (INIS)

    Zwirn, H.

    1982-01-01

    The present orientation of particle physics, founded on local gauge invariance theories and spontaneous symmetry breaking is described in a simple formalism. The application of these ideas to the latest theories describing electromagnetic and weak interactions (Glashow, Weinberg, Salam models) and strong interactions, quantum chromodynamics, is presented so as to give a general picture of the mechanisms subtending these theories [fr

  18. Nonequilibrium formulation of abelian gauge theories

    Energy Technology Data Exchange (ETDEWEB)

    Zoeller, Thorsten

    2013-09-01

    This work is about a formulation of abelian gauge theories out-of-equilibrium. In contrast to thermal equilibrium, systems out-of-equilibrium are not constant in time, and the interesting questions in such systems refer to time evolution problems. After a short introduction to quantum electrodynamics (QED), the two-particle irreducible (2PI) effective action is introduced as an essential technique for the study of quantum field theories out-of-equilibrium. The equations of motion (EOMs) for the propagators of the theory are then derived from it. It follows a discussion of the physical degrees of freedom (DOFs) of the theory, in particular with respect to the photons, since in covariant formulations of gauge theories unphysical DOFs are necessarily contained. After that the EOMs for the photon propagator are examined more closely. It turns out that they are structurally complicated, and a reformulation of the equations is presented which for the untruncated theory leads to an essential structural simplification of the EOMs. After providing the initial conditions which are necessary in order to solve the EOMs, the free photon EOMs are solved with the help of the reformulated equations. It turns out that the solutions diverge in time, i.e. they are secular. This is a manifestation of the fact that gauge theories contain unphysical DOFs. It is reasoned that these secularities exist only in the free case and are therefore ''artificial''. It is however emphasized that they may not be a problem in principle, but certainly are in practice, in particular for the numerical solution of the EOMs. Further, the origin of the secularities, for which there exists an illustrative explanation, is discussed in more detail. Another characteristic feature of 2PI formulations of gauge theories is the fact that quantities calculated from approximations of the 2PI effective action, which are gauge invariant in the exact theory as well as in an approximated theory at

  19. Analytic stochastic regularization: gauge and supersymmetry theories

    International Nuclear Information System (INIS)

    Abdalla, M.C.B.

    1988-01-01

    Analytic stochastic regularization for gauge and supersymmetric theories is considered. Gauge invariance in spinor and scalar QCD is verified to brak fown by an explicit one loop computation of the two, theree and four point vertex function of the gluon field. As a result, non gauge invariant counterterms must be added. However, in the supersymmetric multiplets there is a cancellation rendering the counterterms gauge invariant. The calculation is considered at one loop order. (author) [pt

  20. M-Theory and Maximally Supersymmetric Gauge Theories

    CERN Document Server

    Lambert, Neil

    2012-01-01

    In this informal review for non-specalists we discuss the construction of maximally supersymmetric gauge theories that arise on the worldvolumes branes in String Theory and M-Theory. Particular focus is made on the relatively recent construction of M2-brane worldvolume theories. In a formal sense, the existence of these quantum field theories can be viewed as predictions of M-Theory. Their construction is therefore a reinforcement of the ideas underlying String Theory and M-Theory. We also briefly discuss the six-dimensional conformal field theory that is expected to arise on M5-branes. The construction of this theory is not only an important open problem for M-Theory but also a significant challenge to our current understanding of quantum field theory more generally.

  1. The Arithmetic of Elliptic Fibrations in Gauge Theories on a Circle

    CERN Document Server

    Grimm, Thomas W.; Klevers, Denis

    2016-01-01

    The geometry of elliptic fibrations translates to the physics of gauge theories in F-theory. We systematically develop the dictionary between arithmetic structures on elliptic curves as well as desingularized elliptic fibrations and symmetries of gauge theories on a circle. We show that the Mordell-Weil group law matches integral large gauge transformations around the circle in Abelian gauge theories and explain the significance of Mordell-Weil torsion in this context. We also use Higgs transitions and circle large gauge transformations to introduce a group law for genus-one fibrations with multi-sections. Finally, we introduce a novel arithmetic structure on elliptic fibrations with non-Abelian gauge groups in F-theory. It is defined on the set of exceptional divisors resolving the singularities and divisor classes of sections of the fibration. This group structure can be matched with certain integral non-Abelian large gauge transformations around the circle when studying the theory on the lower-dimensional ...

  2. Introduction to lattice gauge theory

    International Nuclear Information System (INIS)

    Gupta, R.

    1987-01-01

    The lattice formulation of Quantum Field Theory (QFT) can be exploited in many ways. We can derive the lattice Feynman rules and carry out weak coupling perturbation expansions. The lattice then serves as a manifestly gauge invariant regularization scheme, albeit one that is more complicated than standard continuum schemes. Strong coupling expansions: these give us useful qualitative information, but unfortunately no hard numbers. The lattice theory is amenable to numerical simulations by which one calculates the long distance properties of a strongly interacting theory from first principles. The observables are measured as a function of the bare coupling g and a gauge invariant cut-off ≅ 1/α, where α is the lattice spacing. The continuum (physical) behavior is recovered in the limit α → 0, at which point the lattice artifacts go to zero. This is the more powerful use of lattice formulation, so in these lectures the author focuses on setting up the theory for the purpose of numerical simulations to get hard numbers. The numerical techniques used in Lattice Gauge Theories have their roots in statistical mechanics, so it is important to develop an intuition for the interconnection between quantum mechanics and statistical mechanics. This will be the emphasis of the first lecture. In the second lecture, the author reviews the essential ingredients of formulating QCD on the lattice and discusses scaling and the continuum limit. In the last lecture the author summarizes the status of some of the main results. He also mentions the bottlenecks and possible directions for research. 88 refs

  3. Statistical mechanics view of quantum chromodynamics: Lattice gauge theory

    International Nuclear Information System (INIS)

    Kogut, J.B.

    1984-01-01

    Recent developments in lattice gauge theory are discussed from a statistial mechanics viewpoint. The basic physics problems of quantum chromodynamics (QCD) are reviewed for an audience of critical phenomena theorists. The idea of local gauge symmetry and color, the connection between statistical mechanics and field theory, asymptotic freedom and the continuum limit of lattice gauge theories, and the order parameters (confinement and chiral symmetry) of QCD are reviewed. Then recent developments in the field are discussed. These include the proof of confinement in the lattice theory, numerical evidence for confinement in the continuum limit of lattice gauge theory, and perturbative improvement programs for lattice actions. Next, we turn to the new challenges facing the subject. These include the need for a better understanding of the lattice Dirac equation and recent progress in the development of numerical methods for fermions (the pseudofermion stochastic algorithm and the microcanonical, molecular dynamics equation of motion approach). Finally, some of the applications of lattice gauge theory to QCD spectrum calculations and the thermodynamics of QCD will be discussed and a few remarks concerning future directions of the field will be made

  4. Conformal Gauge-Yukawa Theories away From Four Dimensions

    DEFF Research Database (Denmark)

    Codello, Alessandro; Langaeble, Kasper; Litim, Daniel

    2016-01-01

    We present the phase diagram and associated fixed points for a wide class of Gauge-Yukawa theories in $d=4+\\epsilon$ dimensions. The theories we investigate involve non-abelian gauge fields, fermions and scalars in the Veneziano-Witten limit. The analysis is performed in steps, we start with QCD$...

  5. Exact partition functions for gauge theories on Rλ3

    Directory of Open Access Journals (Sweden)

    Jean-Christophe Wallet

    2016-11-01

    Full Text Available The noncommutative space Rλ3, a deformation of R3, supports a 3-parameter family of gauge theory models with gauge-invariant harmonic term, stable vacuum and which are perturbatively finite to all orders. Properties of this family are discussed. The partition function factorizes as an infinite product of reduced partition functions, each one corresponding to the reduced gauge theory on one of the fuzzy spheres entering the decomposition of Rλ3. For a particular sub-family of gauge theories, each reduced partition function is exactly expressible as a ratio of determinants. A relation with integrable 2-D Toda lattice hierarchy is indicated.

  6. Lattice calculations in gauge theory

    International Nuclear Information System (INIS)

    Rebbi, C.

    1985-01-01

    The lattice formulation of quantum gauge theories is discussed as a viable technique for quantitative studies of nonperturbative effects in QCD. Evidence is presented to ascertain that whole classes of lattice actions produce a universal continuum limit. Discrepancies between numerical results from Monto Carlo simulations for the pure gauge system and for the system with gauge and quark fields are discussed. Numerical calculations for QCD require very substantial computational resources. The use of powerful vector processors of special purpose machines, in extending the scope and magnitude or the calculations is considered, and one may reasonably expect that in the near future good quantitative predictions will be obtained for QCD

  7. Tumbling in two djmensional gauge theories

    International Nuclear Information System (INIS)

    Banks, T.; Yankielowicz, S.; Frishman, Y.

    1981-05-01

    The ideas of Tumbling and Most Attractive Channel condensation are confronted in two dimensional chiral gauge theories. The performance of a gauge invariant regularization is first demonstrated. Exact results about the spectra in both abelian and non abelian cases are then found. These conflict with the predictions of Tumbling and MAC. (author)

  8. Gauge-invariant factorization and canonical quantization of topologically massive gauge theories in any dimension

    International Nuclear Information System (INIS)

    Bertrand, Bruno; Govaerts, Jan

    2007-01-01

    Abelian topologically massive gauge theories (TMGT) provide a topological mechanism to generate mass for a bosonic p-tensor field in any spacetime dimension. These theories include the (2+1)-dimensional Maxwell-Chern-Simons and (3+1)-dimensional Cremmer-Scherk actions as particular cases. Within the Hamiltonian formulation, the embedded topological field theory (TFT) sector related to the topological mass term is not manifest in the original phase space. However, through an appropriate canonical transformation, a gauge-invariant factorization of phase space into two orthogonal sectors is feasible. The first of these sectors includes canonically conjugate gauge-invariant variables with free massive excitations. The second sector, which decouples from the total Hamiltonian, is equivalent to the phase-space description of the associated non-dynamical pure TFT. Within canonical quantization, a likewise factorization of quantum states thus arises for the full spectrum of TMGT in any dimension. This new factorization scheme also enables a definition of the usual projection from TMGT onto topological quantum field theories in a most natural and transparent way. None of these results rely on any gauge-fixing procedure whatsoever

  9. Gravity duals of supersymmetric gauge theories on three-manifolds

    International Nuclear Information System (INIS)

    Farquet, Daniel; Lorenzen, Jakob; Martelli, Dario; Sparks, James

    2016-01-01

    We study gravity duals to a broad class of N=2 supersymmetric gauge theories defined on a general class of three-manifold geometries. The gravity backgrounds are based on Euclidean self-dual solutions to four-dimensional gauged supergravity. As well as constructing new examples, we prove in general that for solutions defined on the four-ball the gravitational free energy depends only on the supersymmetric Killing vector, finding a simple closed formula when the solution has U(1)×U(1) symmetry. Our result agrees with the large N limit of the free energy of the dual gauge theory, computed using localization. This constitutes an exact check of the gauge/gravity correspondence for a very broad class of gauge theories with a large N limit, defined on a general class of background three-manifold geometries.

  10. Noncommutative Gauge Theory with Covariant Star Product

    International Nuclear Information System (INIS)

    Zet, G.

    2010-01-01

    We present a noncommutative gauge theory with covariant star product on a space-time with torsion. In order to obtain the covariant star product one imposes some restrictions on the connection of the space-time. Then, a noncommutative gauge theory is developed applying this product to the case of differential forms. Some comments on the advantages of using a space-time with torsion to describe the gravitational field are also given.

  11. Problems of an external field in non-Abelian gauge theory

    International Nuclear Information System (INIS)

    Gavrilov, S.P.; Gitman, D.M.

    1992-01-01

    In the Abelian gauge field theory QED the principal problems connected with an external field are the problems of exact keeping of an external field in a perturbation theory and appearing in this case the peculiarities of the theory such as the instability of the vacuum and so on. There is the problem of an external field introduction or its interpretation side by side with this problem in Non-Abelian gauge theory. The solution of both these problems in Non-Abelian theory can be considered by analogy with QED. In the present paper, the authors discuss on the example of the spontaneously broken SU(2) x U(1) electroweak theory both the problems of an external field introduction and the problem of exact keeping of this field in the perturbation theory. The Langrangian of this theory in covariant gauge is chosen in the BRST invariant form. In spite of concrete character of the theory studied, the method can be extended to any gauge theory

  12. Monte Carlo studies of non-Abelian gauge theories

    International Nuclear Information System (INIS)

    Creutz, M.

    1980-05-01

    After some general remarks on the efficiency of various Monte Carlo algorithms for gauge theories, the calculation of the asymptotic freedom scales of SU(2) and SU(3) gauge theories in the absence of quarks was discussed. There are large numerical factors between these scales when defined in terms of the bare coupling of the lattice theory or when defined in terms of the physical force between external sources

  13. Gauge invariance and radiative corrections in an extra dimensional theory

    International Nuclear Information System (INIS)

    Novales-Sanchez, H; Toscano, J J

    2011-01-01

    The gauge structure of the four dimensional effective theory originated in a pure five dimensional Yang-Mills theory compactified on the orbifold S 1 /Z 2 , is discussed on the basis of the BRST symmetry. If gauge parameters propagate in the bulk, the excited Kaluza-Klein (KK) modes are gauge fields and the four dimensional theory is gauge invariant only if the compactification is carried out by using curvatures as fundamental objects. The four dimensional theory is governed by two types of gauge transformations, one determined by the KK zero modes of the gauge parameters and the other by the excited ones. Within this context, a gauge-fixing procedure to quantize the KK modes that is covariant under the first type of gauge transformations is shown and the ghost sector induced by the gauge-fixing functions is presented. If the gauge parameters are confined to the usual four dimensional space-time, the known result in the literature is reproduced with some minor variants, although it is emphasized that the excited KK modes are not gauge fields, but matter fields transforming under the adjoint representation of SU 4 (N). A calculation of the one-loop contributions of the excited KK modes of the SU L (2) gauge group on the off-shell W + W - V, with V a photon or a Z boson, is exhibited. Such contributions are free of ultraviolet divergences and well-behaved at high energies.

  14. Frustration and dual superconductivity in lattice gauge theories

    International Nuclear Information System (INIS)

    Orland, P.

    1984-01-01

    Introducing plaquette fields in SU(N) gauge theories yields a mass gap and confinement by a dual Meisnner effect. Sources for the plaquette fields are electric strings. Similiar plaquette fields exist in pure compact lattice gauge theories. In principle they make it possible to expand in h while keeping the guage field compact

  15. Generalized string theory mapping relations between gravity and gauge theory

    International Nuclear Information System (INIS)

    Bjerrum-Bohr, N.E.J.

    2003-01-01

    A previous study of the Kawai, Lewellen and Tye (KLT) relations between gravity and gauge theories, imposed by the relationship of closed and open strings, are here extended in the light of general relativity and Yang-Mills theory as effective field theories. We discuss the possibility of generalizing the traditional KLT mapping in this effective setting. A generalized mapping between the effective Lagrangians of gravity and Yang-Mills theory is presented, and the corresponding operator relations between gauge and gravity theories at the tree level are further explored. From this generalized mapping remarkable diagrammatic relations are found, linking diagrams in gravity and Yang-Mills theory, as well as diagrams in pure effective Yang-Mills theory. Also the possibility of a gravitational coupling to an antisymmetric field in the gravity scattering amplitude is considered, and shown to allow for mixed open-closed string solutions, i.e., closed heterotic strings

  16. Supersymmetric gauge theories, quantization of Mflat, and conformal field theory

    International Nuclear Information System (INIS)

    Teschner, J.; Vartanov, G.S.

    2013-02-01

    We propose a derivation of the correspondence between certain gauge theories with N=2 supersymmetry and conformal field theory discovered by Alday, Gaiotto and Tachikawa in the spirit of Seiberg-Witten theory. Based on certain results from the literature we argue that the quantum theory of the moduli spaces of flat SL(2,R)-connections represents a nonperturbative ''skeleton'' of the gauge theory, protected by supersymmetry. It follows that instanton partition functions can be characterized as solutions to a Riemann-Hilbert type problem. In order to solve it, we describe the quantization of the moduli spaces of flat connections explicitly in terms of two natural sets of Darboux coordinates. The kernel describing the relation between the two pictures represents the solution to the Riemann Hilbert problem, and is naturally identified with the Liouville conformal blocks.

  17. Supersymmetry, quantum gauge anomalies and generalized Chern-Simons terms in chiral gauge theory

    International Nuclear Information System (INIS)

    Schmidt, Torsten

    2009-01-01

    The purpose of this thesis is to investigate the interplay of anomaly cancellation and generalized Chern-Simons terms in four-dimensional chiral gauge theory. We start with a detailed discussion of generalized Chern-Simons terms with the canellation of anomalies via the Green-Schwarz mechanism. With this at hand, we investigate the situation in general N=1 supersymmetric field theories with generalized Chern-Simons terms. Two simple consistency conditions are shown to encode strong constraints on the allowed anomalies for different types of gauge groups. In one major part of this thesis we are going to display to what extent one has to modify the existing formalism in order to allow for the cancellation of quantum gauge anomalies via the Green-Schwarz mechanism. At the end of this thesis we comment on a puzzle in the literature on supersymmetric field theories with massive tensor fields. The potential contains a term that does not arise from eliminating an auxiliary field. We clarify the origin of this term and display the relation to standard D-term potential. In an appendix it is explicitly shown how these low energy effective actions might be connected to the formulation of four-dimensional gauge theories discussed at earlier stages of this thesis. (orig.)

  18. Strong coupling in F-theory and geometrically non-Higgsable seven-branes

    Directory of Open Access Journals (Sweden)

    James Halverson

    2017-06-01

    Full Text Available Geometrically non-Higgsable seven-branes carry gauge sectors that cannot be broken by complex structure deformation, and there is growing evidence that such configurations are typical in F-theory. We study strongly coupled physics associated with these branes. Axiodilaton profiles are computed using Ramanujan's theories of elliptic functions to alternative bases, showing explicitly that the string coupling is O(1 in the vicinity of the brane; that it sources nilpotent SL(2,Z monodromy and therefore the associated brane charges are modular; and that essentially all F-theory compactifications have regions with order one string coupling. It is shown that non-perturbative SU(3 and SU(2 seven-branes are related to weakly coupled counterparts with D7-branes via deformation-induced Hanany–Witten moves on (p,q string junctions that turn them into fundamental open strings; only the former may exist for generic complex structure. D3-brane near these and the Kodaira type II seven-branes probe Argyres–Douglas theories. The BPS states of slightly deformed theories are shown to be dyonic string junctions.

  19. Geometrical aspects of operator ordering terms in gauge invariant quantum models

    International Nuclear Information System (INIS)

    Houston, P.J.

    1990-01-01

    Finite-dimensional quantum models with both boson and fermion degrees of freedom, and which have a gauge invariance, are studied here as simple versions of gauge invariant quantum field theories. The configuration space of these finite-dimensional models has the structure of a principal fibre bundle and has defined on it a metric which is invariant under the action of the bundle or gauge group. When the gauge-dependent degrees of freedom are removed, thereby defining the quantum models on the base of the principal fibre bundle, extra operator ordering terms arise. By making use of dimensional reduction methods in removing the gauge dependence, expressions are obtained here for the operator ordering terms which show clearly their dependence on the geometry of the principal fibre bundle structure. (author)

  20. Lattices for laymen: a non-specialist's introduction to lattice gauge theory

    International Nuclear Information System (INIS)

    Callaway, D.J.E.

    1985-01-01

    The review on lattice gauge theory is based upon a series of lectures given to the Materials Science and Technology Division at Argonne National Laboratory. Firstly the structure of gauge theories in the continuum is discussed. Then the lattice formulation of these theories is presented, including quantum electrodynamics and non-abelian lattice gauge theories. (U.K.)

  1. Н(1) Gauge theory as quantum hydrodynamics

    Indian Academy of Sciences (India)

    The Institute of Mathematical Sciences, Taramani, Chennai 600 113, India ... gauge fixing is needed in this approach that is closest to the spirit of the gauge principle. ...... C Itzykson and J B Zuber, Quantum field theory (McGraw Hill, Singapore, ...

  2. Chiral gauge theory on AdS domain wall

    International Nuclear Information System (INIS)

    Shirman, Yuri

    2005-01-01

    We describe a realization of chiral gauge theories based on the domaim wall fermion construction implemented on an interval in five dimensional AdS spacetime. At semi-classical level deconstructed description of the theory is given in terms of 4-dimensional Minkowski slices supporting chiral zero modes at the ends. Energy scales warp down along the fifth dimension. When the theory is augmented by 4-dimensional neutral Majorana spinors together with the Higgs mechanism at the low energy end, we can arrange for a theory where the lightest gauge boson mode as well as chiral zero mode at the high energy end are parametrically lighter than other states. Triangle anomalies and instanton effects are expected to make gauge bosons heavy if the resulting effective theory is anomalous. Due to the strong coupling effects at the quantum level, full non-perturbative calculation will be necessary to validate this construction

  3. Overview of lattice gauge theory at the CSSM

    International Nuclear Information System (INIS)

    Williams, A.G.

    2002-01-01

    Full text: I present an overview of the lattice gauge theory effort at the Special Research Centre for the Subatomic Structure of Matter (CSSM). The CSSM specializes in research into the strong interactions and into quantum chromodynamics (QCD), which is the fundamental quantum gauge field theory of the strong interactions. The primary mission of the CSSM is to attempt to solve QCD and hence test the implications of the theory against experimental evidence. The difficulty lies in the fact that the QCD is a highly nonlinear, strongly coupled theory. The only known first-principles means to solve it is to approximate space-time by a four-dimensional 'grid' or 'lattice' and to simulate this 'lattice QCD' on massively parallel supercomputers. A discussion of the Orion supercomputer of the National Computing Facility for Lattice Gauge Theory (NFCLGT) and the latest QCD predictions obtained from Orion by CSSM researchers will be presented

  4. High-energy behavior of non-Abelian gauge theories

    International Nuclear Information System (INIS)

    Nieh, H.T.; Yao, Y.

    1976-01-01

    This paper is a detailed account of a study in perturbation theory of the high-energy behavior of non-Abelian gauge theories. The fermion-fermion scattering amplitude is calculated up to sixth order in the coupling constant in the high-energy limit s → infinity with fixed t, in the approximation of keeping only the leading logarithmic terms. Results indicate that the high-energy behavior of non-Abelian gauge theories are complicated, and quite different from the known behaviors of other field theories studied so far

  5. Perturbation theory in light-cone gauge

    International Nuclear Information System (INIS)

    Vianello, Eliana

    2000-01-01

    Perturbation calculations are presented for the light-cone gauge Schwinger model. Eigenstates can be calculated perturbatively but the perturbation theory is nonstandard. We hope to extend the work to QCD 2 to resolve some outstanding issues in those theories

  6. Simulating plasma instabilities in SU(3) gauge theory

    International Nuclear Information System (INIS)

    Berges, Juergen; Gelfand, Daniil; Scheffler, Sebastian; Sexty, Denes

    2009-01-01

    We compute nonequilibrium dynamics of plasma instabilities in classical-statistical lattice gauge theory in 3+1 dimensions. The simulations are done for the first time for the SU(3) gauge group relevant for quantum chromodynamics. We find a qualitatively similar behavior as compared to earlier investigations in SU(2) gauge theory. The characteristic growth rates are about 25% lower for given energy density, such that the isotropization process is slower. Measured in units of the characteristic screening mass, the primary growth rate is independent of the number of colors.

  7. Investigation of spontaneously broken gauge theories

    International Nuclear Information System (INIS)

    Nagy, T.

    1978-01-01

    Spontaneously broken gauge theories (SBGT) with effects treated perturbatively are investigated. The general structure of SBGT is exhibited and gauge invariant renormalization program for practical calculations is set up. The proof of renormalizability of Lee and Zinn-Justin are extended to the problems of SBGT. A general semisimple compact gauge group is used. Arbitrary fermion and scalar multiplets are considered. The structure of the Lagrangian is discussed. The problem of quantization is described and the definition of the generating functionals of the Green functions and the Green functions themselves is given

  8. Muon number nonconservation in gauge theories

    International Nuclear Information System (INIS)

    Cheng, T.P.; Li, L.F.

    1977-01-01

    The question of separate conservation of muon and electron number is considered in the context of unified gauge theories of weak and electromagnetic interactions. Theories with heavy neutral leptons, Higgs scalars, and doubly charged heavy leptons are discussed. 28 references

  9. Yang-Mills theory in Coulomb gauge; Yang-Mills-theorie in Coulombeichung

    Energy Technology Data Exchange (ETDEWEB)

    Feuchter, C.

    2006-07-01

    In this thesis we study the Yang-Mills vacuum structure by using the functional Schroedinger picture in Coulomb gauge. In particular we discuss the scenario of colour confinement, which was originally formulated by Gribov. After a short introduction, we recall some basic aspects of Yang-Mills theories, its canonical quantization in the Weyl gauge and the functional Schroedinger picture. We then consider the minimal Coulomb gauge and the Gribov problem of the gauge theory. The gauge fixing of the Coulomb gauge is done by using the Faddeev-Popov method, which enables the resolution of the Gauss law - the constraint on physical states. In the third chapter, we variationally solve the stationary Yang-Mills Schroedinger equation in Coulomb gauge for the vacuum state. Therefor we use a vacuum wave functional, which is strongly peaked at the Gribov horizon. The vacuum energy functional is calculated and minimized resulting in a set of coupled Schwinger-Dyson equations for the gluon energy, the ghost and Coulomb form factors and the curvature in gauge orbit space. Using the angular approximation these integral equations have been solved analytically in both the infrared and the ultraviolet regime. The asymptotic analytic solutions in the infrared and ultraviolet regime are reasonably well reproduced by the full numerical solutions of the coupled Schwinger-Dyson equations. In the fourth chapter, we investigate the dependence of the Yang-Mills wave functional in Coulomb gauge on the Faddeev-Popov determinant. (orig.)

  10. Parity anomalies in gauge theories in 2 + 1 dimensions

    International Nuclear Information System (INIS)

    Rao, S.; Yahalom, R.

    1986-01-01

    We show that the introduction of massless fermions in an abelian gauge theory in 2+1 dimensions does not lead to any parity anomaly despite a non-commutativity of limits in the structure function of the odd part of the vacuum polarization tensor. However, parity anomaly does exist in non-abelian theories due to a conflict between gauge invariance under large gauge transformations and the parity symmetry. 6 refs

  11. Gauge theory and variational principles

    CERN Document Server

    Bleecker, David

    2005-01-01

    This text provides a framework for describing and organizing the basic forces of nature and the interactions of subatomic particles. A detailed and self-contained mathematical account of gauge theory, it is geared toward beginning graduate students and advanced undergraduates in mathematics and physics. This well-organized treatment supplements its rigor with intuitive ideas.Starting with an examination of principal fiber bundles and connections, the text explores curvature; particle fields, Lagrangians, and gauge invariance; Lagrange's equation for particle fields; and the inhomogeneous field

  12. An introduction to gauge theories

    CERN Document Server

    Cabibbo, Nicola; Benhar, Omar

    2017-01-01

    Written by three of the world's leading experts on particle physics and the standard model, including an award-winning former director general of CERN, this book provides a completely up-to-date account of gauge theories. Starting from Feynman’s path integrals, Feynman rules are derived, gauge fixing and Faddeev-Popov ghosts are discussed, and renormalization group equations are derived. Several important applications to quantum electrodynamics and quantum chromodynamics (QCD) are discussed, including the one-loop derivation of asymptotic freedom for QCD.

  13. On the entanglement entropy for gauge theories

    International Nuclear Information System (INIS)

    Ghosh, Sudip; Soni, Ronak M; Trivedi, Sandip P.

    2015-01-01

    We propose a definition for the entanglement entropy of a gauge theory on a spatial lattice. Our definition applies to any subset of links in the lattice, and is valid for both Abelian and Non-Abelian gauge theories. For ℤ_N and U(1) theories, without matter, our definition agrees with a particular case of the definition given by Casini, Huerta and Rosabal. We also argue that in general, both for Abelian and Non-Abelian theories, our definition agrees with the entanglement entropy calculated using a definition of the replica trick. Our definition, however, does not agree with some standard ways to measure entanglement, like the number of Bell pairs which can be produced by entanglement distillation.

  14. Equivariant Reduction of Gauge Theories over Fuzzy Extra Dimensions

    International Nuclear Information System (INIS)

    Kürkçüoglu, Seçkin

    2012-01-01

    In SU(N) Yang-Mills theories on a manifold M, which are suitably coupled to a set of scalars, fuzzy spheres may be generated as extra dimensions by spontaneous symmetry breaking. This process results in gauge theories over the product space of the manifold M and the fuzzy spheres with smaller gauge groups. Here we present the SU(2)– and SU(2) × SU(2)-equivariant parametrization of U(2) and U(4) gauge fields on S 2 F and S 2 F × S 2 F respectively and outline the dimensional reduction of these theories over the fuzzy extra dimensions. The emerging dimensionally reduced theories are Higgs type models. Some vortex type solutions of these theories are briefly discussed.

  15. Superspace gauge fixing of topological Yang-Mills theories

    Energy Technology Data Exchange (ETDEWEB)

    Constantinidis, Clisthenis P; Piguet, Olivier [Universidade Federal do Espirito Santo (UFES) (Brazil); Spalenza, Wesley [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro (Brazil)

    2004-03-01

    We revisit the construction of topological Yang-Mills theories of the Witten type with arbitrary space-time dimension and number of ''shift supersymmetry'' generators, using a superspace formalism. The super-BF structure of these theories is exploited in order to determine their actions uniquely, up to the ambiguities due to the fixing of the Yang-Mills and BF gauge invariance. UV finiteness to all orders of perturbation theory is proved in a gauge of the Landau type. (orig.)

  16. Superspace gauge fixing of topological Yang-Mills theories

    International Nuclear Information System (INIS)

    Constantinidis, Clisthenis P.; Piguet, Olivier; Spalenza, Wesley

    2004-01-01

    We revisit the construction of topological Yang-Mills theories of the Witten type with arbitrary space-time dimension and number of ''shift supersymmetry'' generators, using a superspace formalism. The super-BF structure of these theories is exploited in order to determine their actions uniquely, up to the ambiguities due to the fixing of the Yang-Mills and BF gauge invariance. UV finiteness to all orders of perturbation theory is proved in a gauge of the Landau type. (orig.)

  17. Exceptional confinement in G(2) gauge theory

    International Nuclear Information System (INIS)

    Holland, K.; Minkowski, P.; Pepe, M.; Wiese, U.-J.

    2003-01-01

    We study theories with the exceptional gauge group G(2). The 14 adjoint 'gluons' of a G(2) gauge theory transform as {3}, {3-bar} and {8} under the subgroup SU(3), and hence have the color quantum numbers of ordinary quarks, anti-quarks and gluons in QCD. Since G(2) has a trivial center, a 'quark' in the {7} representation of G(2) can be screened by 'gluons'. As a result, in G(2) Yang-Mills theory the string between a pair of static 'quarks' can break. In G(2) QCD there is a hybrid consisting of one 'quark' and three 'gluons'. In supersymmetric G(2) Yang-Mills theory with a {14} Majorana 'gluino' the chiral symmetry is Z(4) χ . Chiral symmetry breaking gives rise to distinct confined phases separated by confined-confined domain walls. A scalar Higgs field in the {7} representation breaks G(2) to SU(3) and allows us to interpolate between theories with exceptional and ordinary confinement. We also present strong coupling lattice calculations that reveal basic features of G(2) confinement. Just as in QCD, where dynamical quarks break the Z(3) symmetry explicitly, G(2) gauge theories confine even without a center. However, there is not necessarily a deconfinement phase transition at finite temperature

  18. Lattice chiral gauge theories with finely-grained fermions

    International Nuclear Information System (INIS)

    Hernandez, P.; Sundrum, R.

    1996-01-01

    The importance of lattice gauge field interpolation for our recent non-perturbative formulation of chiral gauge theory is emphasized. We illustrate how the requisite properties are satisfied by our recent four-dimensional non-abelian interpolation scheme, by going through the simpler case of U(1) gauge fields in two dimensions. (orig.)

  19. Construction of U-gauge Green's functions of gauge theories with spontaneous symmetry breaking and Slavnov identities

    International Nuclear Information System (INIS)

    Flume, R.

    1978-01-01

    The unitary (U) gauge Green's functions of the U(1) and SU(2) Higgs-Kibble models are constructed applying a renormalized point transformation and a non-local gauge changing transformation to a manifestly renormalizable (R gauge) version of the respective theory. It is shown that the cancellation mechanism known as 'tree graph unitarity' rendering in tree graph approximation a smooth high energy behaviour of the U gauge Green's functions on mass shell can in a natural way be extended to all orders of perturbation theory. The conditions imposed by this 'generalized tree graph unitarity' on the renormalization programme are shown to be equivalent with the requirement of renormalized Slavnov identities for the R gauge Green's functions

  20. Causal hydrodynamics of gauge theory plasmas from AdS/CFT duality

    International Nuclear Information System (INIS)

    Natsuume, Makoto; Okamura, Takashi

    2008-01-01

    We study causal hydrodynamics (Israel-Stewart theory) of gauge theory plasmas from the AdS/CFT duality. Causal hydrodynamics requires new transport coefficients (relaxation times) and we compute them for a number of supersymmetric gauge theories including the N=4 super Yang-Mills theory. However, the relaxation times obtained from the 'shear mode' do not agree with the ones from the 'sound mode', which implies that the Israel-Stewart theory is not a sufficient framework to describe the gauge theory plasmas.

  1. Weak interactions and gauge theories

    International Nuclear Information System (INIS)

    Gaillard, M.K.

    1979-12-01

    The status of the electroweak gauge theory, also known as quantum asthenodynamics (QAD), is examined. The major result is that the standard WS-GIM model describes the data well, although one should still look for signs of further complexity and better tests of its gauge theory aspect. A second important result is that the measured values of the three basic coupling constants of present-energy physics, g/sub s/, g, and √(5/3)g' of SU(3)/sub c/ x SU(2) 2 x U(1), are compatible with the idea that these interactions are unified at high energies. Much of the paper deals with open questions, and it takes up the following topics: the status of QAD, the scalar meson spectrum, the fermion spectrum, CP violation, and decay dynamics. 118 references, 20 figures

  2. A non-perturbative study of massive gauge theories

    DEFF Research Database (Denmark)

    Della Morte, Michele; Hernandez, Pilar

    2013-01-01

    and the lightest degrees of freedom are spin one vector particles with the same quantum numbers as the conserved current, we argue that the most general effective theory describing their low-energy dynamics must be a massive gauge theory. We present results of a exploratory numerical simulation of the model......We consider a non-perturbative formulation of an SU(2) massive gauge theory on a space-time lattice, which is also a discretised gauged non-linear chiral model. The lattice model is shown to have an exactly conserved global SU(2) symmetry. If a scaling region for the lattice model exists...... and find indications for the presence of a scaling region where both a triplet vector and a scalar remain light....

  3. Phase diagrams of exceptional and supersymmetric lattice gauge theories

    Energy Technology Data Exchange (ETDEWEB)

    Wellegehausen, Bjoern-Hendrik

    2012-07-10

    In this work different strongly-coupled gauge theories with and without fundamental matter have been studied on the lattice with an emphasis on the confinement problem and the QCD phase diagram at nonvanishing net baryon density as well as on possible supersymmetric extensions of the standard model of particle physics. In gauge theories with a non-trivial centre symmetry, as for instance SU(3)-Yang-Mills theory, confinement is intimately related to the centre of the gauge group, and the Polyakov loop serves as an order parameter for confinement. In QCD, this centre symmetry is explicitly broken by quarks in the fundamental representation of the gauge group. But still quarks and gluons are confined in mesons, baryons and glueballs at low temperatures and small densities, suggesting that centre symmetry is not responsible for the phenomenon of confinement. Therefore it is interesting to study pure gauge theories without centre symmetry. In this work this has been done by replacing the gauge group SU(3) of the strong interaction with the exceptional Lie group G{sub 2}, that has a trivial centre. To investigate G{sub 2} gauge theory on the lattice, a new and highly efficient update algorithm has been developed, based on a local HMC algorithm. Employing this algorithm, the proposed and already investigated first order phase transition from a confined to a deconfined phase has been confirmed, showing that indeed a first order phase transition without symmetry breaking or an order parameter is possible. In this context, also the deconfinement phase transition of the exceptional Lie groups F4 and E6 in three spacetime dimensions has been studied. It has been shown that both theories also possess a first order phase transition.

  4. Phase diagrams of exceptional and supersymmetric lattice gauge theories

    International Nuclear Information System (INIS)

    Wellegehausen, Bjoern-Hendrik

    2012-01-01

    In this work different strongly-coupled gauge theories with and without fundamental matter have been studied on the lattice with an emphasis on the confinement problem and the QCD phase diagram at nonvanishing net baryon density as well as on possible supersymmetric extensions of the standard model of particle physics. In gauge theories with a non-trivial centre symmetry, as for instance SU(3)-Yang-Mills theory, confinement is intimately related to the centre of the gauge group, and the Polyakov loop serves as an order parameter for confinement. In QCD, this centre symmetry is explicitly broken by quarks in the fundamental representation of the gauge group. But still quarks and gluons are confined in mesons, baryons and glueballs at low temperatures and small densities, suggesting that centre symmetry is not responsible for the phenomenon of confinement. Therefore it is interesting to study pure gauge theories without centre symmetry. In this work this has been done by replacing the gauge group SU(3) of the strong interaction with the exceptional Lie group G 2 , that has a trivial centre. To investigate G 2 gauge theory on the lattice, a new and highly efficient update algorithm has been developed, based on a local HMC algorithm. Employing this algorithm, the proposed and already investigated first order phase transition from a confined to a deconfined phase has been confirmed, showing that indeed a first order phase transition without symmetry breaking or an order parameter is possible. In this context, also the deconfinement phase transition of the exceptional Lie groups F4 and E6 in three spacetime dimensions has been studied. It has been shown that both theories also possess a first order phase transition.

  5. Lattice gauge theories

    International Nuclear Information System (INIS)

    Hasenfratz, A.; Hasenfratz, P.

    1985-01-01

    This paper deals almost exclusively with applications in QCD. Presumably QCD will remain in the center of lattice calculations in the near future. The existing techniques and the available computer resources should be able to produce trustworthy results in pure SU(3) gauge theory and in quenched hadron spectroscopy. Going beyond the quenched approximation might require some technical breakthrough or exceptional computer resources, or both. Computational physics has entered high-energy physics. From this point of view, lattice QCD is only one (although the most important, at present) of the research fields. Increasing attention is devoted to the study of other QFTs. It is certain that the investigation of nonasymptotically free theories, the Higgs phenomenon, or field theories that are not perturbatively renormalizable will be important research areas in the future

  6. On the WDVV equations in five-dimensional gauge theories

    NARCIS (Netherlands)

    Hoevenaars, L.K.; Martini, Ruud

    2003-01-01

    It is well known that the perturbative prepotentials of four-dimensional N = 2 supersymmetric Yang–Mills theories satisfy the generalized WDVV equations, regardless of the gauge group. In this Letter we study perturbative prepotentials of the five-dimensional theories for some classical gauge groups

  7. The cross-over points in lattice gauge theories with continuous gauge groups

    International Nuclear Information System (INIS)

    Cvitanovic, P.; Greensite, J.; Lautrup, B.

    1981-01-01

    We obtain a closed expression for the weak-to-strong coupling cross-over point in all Wilson type lattice gauge theories with continuous gauge groups. We use a weak-coupling expansion of the mean-field self-consistency equation. In all cases where our results can be compared with Monte Carlo calculations the agreement is excellent. (orig.)

  8. S-duality in N = 4 supersymmetric gauge theories with arbitrary gauge group

    International Nuclear Information System (INIS)

    Dorey, Nicholas; Fraser, Christophe; Hollowood, Timothy J.; Kneipp, Marco A.C.

    1996-12-01

    The Goddard, Nuyts and Olive conjecture for electric-magnetic duality in the Yang-Mills theory with an arbitrary gauge group G is extended by including a non-vanishing vacuum angle θ. This extended S-duality conjecture includes the case when the unbroken gauge group in non-Abelian and a definite prediction for the spectrum of dyons results. (author)

  9. Thermalization and confinement in strongly coupled gauge theories

    Directory of Open Access Journals (Sweden)

    Ishii Takaaki

    2016-01-01

    Full Text Available Quantum field theories of strongly interacting matter sometimes have a useful holographic description in terms of the variables of a gravitational theory in higher dimensions. This duality maps time dependent physics in the gauge theory to time dependent solutions of the Einstein equations in the gravity theory. In order to better understand the process by which “real world” theories such as QCD behave out of thermodynamic equilibrium, we study time dependent perturbations to states in a model of a confining, strongly coupled gauge theory via holography. Operationally, this involves solving a set of non-linear Einstein equations supplemented with specific time dependent boundary conditions. The resulting solutions allow one to comment on the timescale by which the perturbed states thermalize, as well as to quantify the properties of the final state as a function of the perturbation parameters. We comment on the influence of the dual gauge theory’s confinement scale on these results, as well as the appearance of a previously anticipated universal scaling regime in the “abrupt quench” limit.

  10. Gauge theories on a small lattice

    International Nuclear Information System (INIS)

    Robson, D.; Webber, D.M.

    1980-01-01

    We present exact solutions to U(1), SU(2), and SU(3) lattice gauge theories on a Kogut-Susskind lattice consisting of a single plaquette. We demonstrate precise equivalence between the U(1) theory and the harmonic oscillator on an infinite one-dimensional lattice, and between the SU(N) theory and an N-fermion Schroedinger equation. (orig.)

  11. Noncommutative gauge theory and symmetry breaking in matrix models

    International Nuclear Information System (INIS)

    Grosse, Harald; Steinacker, Harold; Lizzi, Fedele

    2010-01-01

    We show how the fields and particles of the standard model can be naturally realized in noncommutative gauge theory. Starting with a Yang-Mills matrix model in more than four dimensions, an SU(n) gauge theory on a Moyal-Weyl space arises with all matter and fields in the adjoint of the gauge group. We show how this gauge symmetry can be broken spontaneously down to SU(3) c xSU(2) L xU(1) Q [resp. SU(3) c xU(1) Q ], which couples appropriately to all fields in the standard model. An additional U(1) B gauge group arises which is anomalous at low energies, while the trace-U(1) sector is understood in terms of emergent gravity. A number of additional fields arise, which we assume to be massive, in a pattern that is reminiscent of supersymmetry. The symmetry breaking might arise via spontaneously generated fuzzy spheres, in which case the mechanism is similar to brane constructions in string theory.

  12. Wigner's little group as a gauge generator in linearized gravity theories

    International Nuclear Information System (INIS)

    Scaria, Tomy; Chakraborty, Biswajit

    2002-01-01

    We show that the translational subgroup of Wigner's little group for massless particles in 3 + 1 dimensions generates gauge transformation in linearized Einstein gravity. Similarly, a suitable representation of the one-dimensional translational group T(1) is shown to generate gauge transformation in the linearized Einstein-Chern-Simons theory in 2 + 1 dimensions. These representations are derived systematically from appropriate representations of translational groups which generate gauge transformations in gauge theories living in spacetime of one higher dimension by the technique of dimensional descent. The unified picture thus obtained is compared with a similar picture available for vector gauge theories in 3 + 1 and 2 + 1 dimensions. Finally, the polarization tensor of the Einstein-Pauli-Fierz theory in 2 + 1 dimensions is shown to split into the polarization tensors of a pair of Einstein-Chern-Simons theories with opposite helicities suggesting a doublet structure for the Einstein-Pauli-Fierz theory

  13. Superspace gauge fixing of topological Yang-Mills theories

    International Nuclear Information System (INIS)

    Constantinidis, Clisthenis P.; Piguet, Olivier; Spalenza, Wesley

    2003-10-01

    We revisit the construction of topological Yang-Mills theories of the Witten type with arbitrary space-time dimension and number of 'shift supersymmetry' generators, using a superspace formalism. The super-B F structure of these theories is exploited in order to determine their actions uniquely, up to the ambiguities due to the fixing of the Yang-Mills and B F gauge invariance. UV finiteness to all orders of perturbation theory is proved in a gauge of the Landau type. (author)

  14. Superspace gauge fixing of topological Yang-Mills theories

    Energy Technology Data Exchange (ETDEWEB)

    Constantinidis, Clisthenis P; Piguet, Olivier [Espirito Santo Univ. (UFES), Vitoria, ES (Brazil); Spalenza, Wesley

    2003-10-15

    We revisit the construction of topological Yang-Mills theories of the Witten type with arbitrary space-time dimension and number of 'shift supersymmetry' generators, using a superspace formalism. The super-B F structure of these theories is exploited in order to determine their actions uniquely, up to the ambiguities due to the fixing of the Yang-Mills and B F gauge invariance. UV finiteness to all orders of perturbation theory is proved in a gauge of the Landau type. (author)

  15. Non(anti)commutative gauge theories in harmonic superspace

    International Nuclear Information System (INIS)

    Quevedo Z., L.E.

    2006-01-01

    In this work we study the properties of non-singlet Q-deformed N=2 supersymmetric gauge theories, from a field-theoretical point of view. Starting from the supersymmetry breaking pattern induced by a general deformation matrix, we embark on the construction of the non-singlet deformed gauge transformation laws for all vector multiplet fields and their corresponding minimal Seiberg-Witten map. Several deformes super-Yang-Mills actions in components corresponding to different choices of the non-singlet deformation tensor are built. For a particular decomposition ansats of such tensor, we obtain exact actions describing the bosonic sector of the deformed N=(1,0) and the full action for enhances N=(1,1/2) residual supersymmetry. A tuned supersymmetry breaking of this enhanced action down to the N=(1,0) case is found by weakly restoring some discarded degrees of freedom of the deformation. Finally we find the associated residual supersymmetry transformations for the cases studied. The first part of this work, gives an overview of noncommutativity in quantum field theory and of harmonic superspace as needed to define noncommutative generalizations of extended gauge field theories. A study of general properties of non(anti)commutative structures in N=2 euclidean superspace and the (super)symmetry breaking pattern induced by Q-deformations follows. in addition, singlet-deformed super-Yang-Mills is given as an example. The second part deals with non-singlet Q-deformations of gauge theories. We introduce a decomposition ansatz for the deformation matrix, allowing an exact study of the deformed gauge transformations, and develop a general algorithm to solve the harmonic equations associated to this decomposition. A close expression for the gauge transformations of component fields is derived, along with the corresponding minimal Seiberg-Witten map to an equivalent commutative gauge theory. Finally we build deformed super-Yang-Mills actions and their corresponding

  16. Lattices gauge theories in terms of knots

    International Nuclear Information System (INIS)

    Vecernyes, P.

    1989-01-01

    Cluster expansion is developed in lattice gauge theories with finite gauge groups in d≥3 dimensions where the clusters are connected (d - 2)-dimensional surfaces which can branch along (d - 3)-cells. The interaction between them has a knot theoretical interpretation. It can be many body linking or knotting self-interaction. For small enough gauge coupling g the authors prove analyticity of the correlation functions in the variable exp(-1/g 2

  17. Ultraviolet stability of three-dimensional lattice pure gauge field theories

    International Nuclear Information System (INIS)

    Balaban, T.

    1985-01-01

    We prove the ultraviolet stability for three-dimensional lattice gauge field theories. We consider only the Wilson lattice approximation for pure Yang-Mills field theories. The proof is based on results of the previous papers on renormalization group method for lattice gauge theories. (orig.)

  18. Phase structure and critical properties of an abelian gauge theory

    Energy Technology Data Exchange (ETDEWEB)

    Mo, Sjur

    2001-12-01

    The main new results are presented in the form of three papers at the end of this thesis. The main topic is Monte-Carlo studies of the phase structure and critical properties of the phenomenological Ginzburg-Landau model, i.e. an abelian gauge theory. However, the first paper is totally different and deals with microscopic theory for lattice-fermions in a magnetic field. Paper I is about ''Fermion-pairing on a square lattice in extreme magnetic fields''. We consider the Cooper-problem on a two-dimensional, square lattice with a uniform, perpendicular magnetic field. Only rational flux fractions are considered. An extended (real-space) Hubbard model including nearest and next nearest neighbor interactions is transformed to ''k-space'', or more precisely, to the space of eigenfunctions of Harper's equation, which constitute basis functions of the magnetic translation group for the lattice. A BCS-like truncation of the interaction term is performed. Expanding the interactions in the basis functions of the irreducible representations of the point group C{sub 4{nu}} of the square lattice simplify calculations. The numerical results indicate enhanced binding compared to zero magnetic field, and thus re-entrant superconducting pairing at extreme magnetic fields, well beyond the point where the usual semi-classical treatment of the magnetic field breaks down. Paper II is about the ''Hausdorff dimension of critical fluctuations in abelian gauge theories''. Here we analyze the geometric properties of the line-like critical fluctuations (vortex loops) in the Ginzburg-Landau model in zero magnetic background field. By using a dual description, we obtain scaling relations between exponents of geometric arid thermodynamic nature. In particular we connect the anomalous scaling dimension {eta} of the dual matter field to the Hausdorff or fractal dimension D{sub H} of the critical fluctuations, in the original model

  19. Dilation operator in gauge theories

    International Nuclear Information System (INIS)

    Galayda, J.

    1984-01-01

    The electromagnetic field is expanded in a series of O(4) eigenstates of total spin, and quantized by specifying commutators on surfaces of constant x/sub μ/x/sup μ/ = R 2 in four-dimensional Euclidean space. It is demonstrated that, under an arbitrary gauge transformation, some of the O(4) eigenstates are invariant; these gauge-invariant states are labeled by SU(2)xSU(2) total (orbital plus internal) spin quantum numbers (A,B) and with Anot =B. Only these gauge-invariant states are nontrivial in the absence of sources, and are quantized. The leading-twist quantum states of the dilation field theory contain the minimum number of these dilation photons. The remaining spin degrees of freedom of the electromagnetic field are most simply written as a function of the form partial/sub μ/phi(x)+x/sub μ/psi(x)/R 2 . phi(x) is obviously devoid of physics while psi(x) is a classical field propagating between radial projections of two electric currents x/sub μ/ J/sup μ/(x) and y/sub μ/ J/sup μ/(y) only if x/sub μ/ x/sup μ/ = y/sub μ/ y/sup μ/. The quantization procedure described herein may be applied to non-Abelian theories. The procedure does not lead to a gauge-invariant decomposition of a non-Abelian field, but the identification of leading-twist quantum states is preserved in the zero-coupling limit

  20. Gauge transformations in relativistic two-particle constraint theory

    International Nuclear Information System (INIS)

    Jallouli, H.; Sazdjian, H.

    1996-01-01

    The forms of the local potentials in linear covariant gauges are investigated and relationships are found between them. The gauge transformation properties of the Green's function and of the Bethe-Salpeter wave function are reviewed. The infinitesimal gauge transformation laws of the constraint theory wave functions and potentials are determined. The case of the local approximation of potentials is considered. The general properties of the gauge transformations in the local approximation are studied. (K.A.)

  1. Maxwell-Chern-Simons theory in covariant and Coulomb gauges

    International Nuclear Information System (INIS)

    Haller, K.; Lim-Lombridas, E.

    1996-01-01

    We quantize quantum electrodynamics in 2 + 1 dimensions coupled to a Chern-Simons (CS) term and a charged spinor field, in covariant gauges and in the Coulomb gauge. The resulting Maxwell-Chern-Simons (MCS) theory describes charged fermions interacting with each other and with topologically massive propagating photons. We impose Gauss's law and the gauge conditions and investigate their effect on the dynamics and on the statistics of n-particle states. We construct charged spinor states that obey Gauss's law and the gauge conditions and transform the theory to representations in which these states constitute a Fock space. We demonstrate that, in these representations, the nonlocal interactions between charges and between charges and transverse currents-along with the interactions between currents and massive propagating photons-are identical in the different gauges we analyze in this and in earlier work. We construct the generators of the Poincare group, show that they implement the Poincare algebra, and explicitly demonstrate the effect of rotations and Lorentz boosts on the particle states. We show that the imposition of Gauss's law does not produce any open-quotes exoticclose quotes fractional statistics. In the case of the covariant gauges, this demonstration makes use of unitary transformations that provide charged particles with the gauge fields required by Gauss's law, but that leave the anticommutator algebra of the spinor fields untransformed. In the Coulomb gauge, we show that the anticommutators of the spinor fields apply to the Dirac-Bergmann constraint surfaces, on which Gauss's law and the gauge conditions obtain. We examine MCS theory in the large CS coupling constant limit, and compare that limiting form with CS theory, in which the Maxwell kinetic energy term is not included in the Larangian. 34 refs

  2. Holomorphic D7-branes and flavored N=1 gauge theories

    International Nuclear Information System (INIS)

    Ouyang, Peter

    2004-01-01

    We consider D7-branes in the gauge theory/string theory correspondence, using a probe approximation. The D7-branes have four directions embedded holomorphically in a non-compact Calabi-Yau 3-fold (which for specificity we take to be the conifold) and their remaining four directions are parallel to a stack of D3-branes transverse to the Calabi-Yau space. The dual gauge theory, which has N=1 supersymmetry, contains quarks which transform in the fundamental representation of the gauge group, and we identify the interactions of these quarks in terms of a superpotential. By activating three-form fluxes in the gravity background, we obtain a dual gauge theory with a cascade of Seiberg dualities. We find a supersymmetric supergravity solution for the leading backreaction effects of the D7-branes, valid for large radius. The cascading theory with flavors exhibits the interesting phenomenon that the rate of the cascade slows and can stop as the theory flows to the infrared

  3. Recursive relations for a quiver gauge theory

    International Nuclear Information System (INIS)

    Park, Jaemo; Sim, Woojoo

    2006-01-01

    We study the recursive relations for a quiver gauge theory with the gauge group SU(N 1 ) x SU(N 2 ) with bifundamental fermions transforming as (N 1 , N-bar 2 ). We work out the recursive relation for the amplitudes involving a pair of quark and antiquark and gluons of each gauge group. We realize directly in the recursive relations the invariance under the order preserving permutations of the gluons of the first and the second gauge group. We check the proposed relations for MHV, 6-point and 7-point amplitudes and find the agreements with the known results and the known relations with the single gauge group amplitudes. The proposed recursive relation is much more efficient in calculating the amplitudes than using the known relations with the amplitudes of the single gauge group

  4. Geometric measure theory

    CERN Document Server

    Waerden, B

    1996-01-01

    From the reviews: "... Federer's timely and beautiful book indeed fills the need for a comprehensive treatise on geometric measure theory, and his detailed exposition leads from the foundations of the theory to the most recent discoveries. ... The author writes with a distinctive style which is both natural and powerfully economical in treating a complicated subject. This book is a major treatise in mathematics and is essential in the working library of the modern analyst." Bulletin of the London Mathematical Society.

  5. Multi-leg one-loop gravity amplitudes from gauge theory

    International Nuclear Information System (INIS)

    Bern, Z.; Dixon, L.; Perelstein, M.; Rozowsky, J.S.

    1999-01-01

    By exploiting relations between gravity and gauge theories, we present two infinite sequences of one-loop n-graviton scattering amplitudes: the 'maximally helicity-violating' amplitudes in N = 8 supergravity, and the 'all-plus' helicity amplitudes in gravity with any minimally coupled massless matter content. The all-plus amplitudes correspond to self-dual field configurations and vanish in supersymmetric theories. We make use of the tree-level Kawai-Lewellen-Tye (KLT) relations between open and closed string theory amplitudes, which in the low-energy limit imply relations between gravity and gauge theory tree amplitudes. For n ≤ 6, we determine the all-plus amplitudes explicitly from their unitarity cuts. The KLT relations, applied to the cuts, allow us to extend to gravity a previously found 'dimension-shifting' relation between (the cuts of) the all-plus amplitudes in gauge theory and the maximally helicity-violating amplitudes in N = 4 super-Yang-Mills theory. The gravitational version of the relation lets us determine the n ≤ 6N = 8 supergravity amplitudes from the all-plus gravity amplitudes. We infer the two series of amplitudes for all n from their soft and collinear properties, which can also be derived from gauge theory using the KLT relations

  6. General quadratic gauge theory: constraint structure, symmetries and physical functions

    Energy Technology Data Exchange (ETDEWEB)

    Gitman, D M [Institute of Physics, University of Sao Paulo (Brazil); Tyutin, I V [Lebedev Physics Institute, Moscow (Russian Federation)

    2005-06-17

    How can we relate the constraint structure and constraint dynamics of the general gauge theory in the Hamiltonian formulation to specific features of the theory in the Lagrangian formulation, especially relate the constraint structure to the gauge transformation structure of the Lagrangian action? How can we construct the general expression for the gauge charge if the constraint structure in the Hamiltonian formulation is known? Whether we can identify the physical functions defined as commuting with first-class constraints in the Hamiltonian formulation and the physical functions defined as gauge invariant functions in the Lagrangian formulation? The aim of the present paper is to consider the general quadratic gauge theory and to answer the above questions for such a theory in terms of strict assertions. To fulfil such a programme, we demonstrate the existence of the so-called superspecial phase-space variables in terms of which the quadratic Hamiltonian action takes a simple canonical form. On the basis of such a representation, we analyse a functional arbitrariness in the solutions of the equations of motion of the quadratic gauge theory and derive the general structure of symmetries by analysing a symmetry equation. We then use these results to identify the two definitions of physical functions and thus prove the Dirac conjecture.

  7. Perturbative Quantum Gravity and its Relation to Gauge Theory

    Directory of Open Access Journals (Sweden)

    Bern Zvi

    2002-01-01

    Full Text Available In this review we describe a non-trivial relationship between perturbative gauge theory and gravity scattering amplitudes. At the semi-classical or tree-level, the scattering amplitudes of gravity theories in flat space can be expressed as a sum of products of well defined pieces of gauge theory amplitudes. These relationships were first discovered by Kawai, Lewellen, and Tye in the context of string theory, but hold more generally. In particular, they hold for standard Einstein gravity. A method based on $D$-dimensional unitarity can then be used to systematically construct all quantum loop corrections order-by-order in perturbation theory using as input thegravity tree amplitudes expressed in terms of gauge theory ones. More generally, the unitarity method provides a means for perturbatively quantizing massless gravity theories without the usual formal apparatus associated with the quantization of constrained systems. As one application, this method was used to demonstrate that maximally supersymmetric gravity is less divergent in the ultraviolet than previously thought.

  8. Gauge theories of gravitation a reader with commentaries

    CERN Document Server

    Blagojevic, Milutin

    2013-01-01

    In the last five decades, the gauge approach to gravity has represented a research area of increasing importance for our understanding of the physics of fundamental interactions. A full clarification of the gauge dynamics of gravity is expected to be the last missing link to the hidden structure of a consistent unification of all the fundamental interactions, based on the gauge principle. The aim of the present reprint volume, with commentaries by Milutin Blagojevi & 263; and Friedrich W Hehl, is to introduce graduate and advanced undergraduate students of theoretical or mathematical physics, or any other interested researcher, to the field of classical gauge theories of gravity. This is not just an ordinary reprint volume; it is a guide to the literature on gauge theories of gravity. The reader is encouraged first to study the introductory commentaries and to become familiar with the basic content of the reprints and related ideas, then he/she can choose to read a specific reprint or reprints, and after ...

  9. Nilpotent symmetries and Curci-Ferrari-type restrictions in 2D non-Abelian gauge theory: Superfield approach

    Science.gov (United States)

    Srinivas, N.; Malik, R. P.

    2017-11-01

    We derive the off-shell nilpotent symmetries of the two (1 + 1)-dimensional (2D) non-Abelian 1-form gauge theory by using the theoretical techniques of the geometrical superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism. For this purpose, we exploit the augmented version of superfield approach (AVSA) and derive theoretically useful nilpotent (anti-)BRST, (anti-)co-BRST symmetries and Curci-Ferrari (CF)-type restrictions for the self-interacting 2D non-Abelian 1-form gauge theory (where there is no interaction with matter fields). The derivation of the (anti-)co-BRST symmetries and all possible CF-type restrictions are completely novel results within the framework of AVSA to BRST formalism where the ordinary 2D non-Abelian theory is generalized onto an appropriately chosen (2, 2)-dimensional supermanifold. The latter is parametrized by the superspace coordinates ZM = (xμ,𝜃,𝜃¯) where xμ (with μ = 0, 1) are the bosonic coordinates and a pair of Grassmannian variables (𝜃,𝜃¯) obey the relationships: 𝜃2 = 𝜃¯2 = 0, 𝜃𝜃¯ + 𝜃¯𝜃 = 0. The topological nature of our 2D theory allows the existence of a tower of CF-type restrictions.

  10. Canonical Yang-Mills field theory with invariant gauge-families

    International Nuclear Information System (INIS)

    Yokoyama, Kan-ichi

    1978-01-01

    A canonical Yang-Mills field theory with indefinite metric is presented on the basis of a covariant gauge formalism for quantum electrodynamics. As the first step of the formulation, a many-gauge-field problem, in which many massless Abelian-gauge fields coexist, is treated from a new standpoint. It is shown that only a single pair of a gaugeon field and its associated one can govern the gauge structure of the whole system. The result obtained is further extended to cases of non-Abelian gauge theories. Gauge parameters for respective components of the Yang-Mills fields are introduced as a group vector. There exists a q-number local gauge transformation which connects relevant fields belonging to the same invariant gauge family with one another in a manifestly covariant way. In canonical quantization, the Faddeev-Popov ghosts are introduced in order to guarantee the existence of a desirable physical subspace with positive semi-definite metric. As to treatment of the Faddeev-Popov ghosts, Kugo and Ojima's approach is adopted. Three supplementary conditions which are consistent with one another constrain the physical subspace. (author)

  11. Three-Dimensional Gauge Theories and ADE Monopoles

    OpenAIRE

    Tong, David

    1998-01-01

    We study three-dimensional N=4 gauge theories with product gauge groups constructed from ADE Dynkin diagrams. One-loop corrections to the metric on the Coulomb branch are shown to coincide with the metric on the moduli space of well-seperated ADE monopoles. We propose that this correspondence is exact.

  12. On the character of scale symmetry breaking in gauge theories

    International Nuclear Information System (INIS)

    Gusijnin, V.P.; Kushnir, V.A.; Miransky, V.A.

    1988-01-01

    The problem of scale symmetry breaking in gauge theories is discussed. It is shown that the phenomenon of spontaneous breaking of scale symmetry in gauge theories is incompatible with the PCAAC dynamics. 12 refs

  13. Geometric low-energy effective action in a doubled spacetime

    Science.gov (United States)

    Ma, Chen-Te; Pezzella, Franco

    2018-05-01

    The ten-dimensional supergravity theory is a geometric low-energy effective theory and the equations of motion for its fields can be obtained from string theory by computing β functions. With d compact dimensions, an O (d , d ; Z) geometric structure can be added to it giving the supergravity theory with T-duality manifest. In this paper, this is constructed through the use of a suitable star product whose role is the one to implement the weak constraint on the fields and the gauge parameters in order to have a closed gauge symmetry algebra. The consistency of the action here proposed is based on the orthogonality of the momenta associated with fields in their triple star products in the cubic terms defined for d ≥ 1. This orthogonality holds also for an arbitrary number of star products of fields for d = 1. Finally, we extend our analysis to the double sigma model, non-commutative geometry and open string theory.

  14. Free Abelian 2-form gauge theory: BRST approach

    International Nuclear Information System (INIS)

    Malik, R.P.

    2008-01-01

    We discuss various symmetry properties of the Lagrangian density of a four- (3+1)-dimensional (4D) free Abelian 2-form gauge theory within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism. The present free Abelian gauge theory is endowed with a Curci-Ferrari type condition, which happens to be a key signature of the 4D non-Abelian 1-form gauge theory. In fact, it is due to the above condition that the nilpotent BRST and anti-BRST symmetries of our present theory are found to be absolutely anticommuting in nature. For the present 2-form theory, we discuss the BRST, anti-BRST, ghost and discrete symmetry properties of the Lagrangian densities and derive the corresponding conserved charges. The algebraic structure, obeyed by the above conserved charges, is deduced and the constraint analysis is performed with the help of physicality criteria, where the conserved and nilpotent (anti-)BRST charges play completely independent roles. These physicality conditions lead to the derivation of the above Curci-Ferrari type restriction, within the framework of the BRST formalism, from the constraint analysis. (orig.)

  15. Monopoles and confinement in lattice gauge theory

    International Nuclear Information System (INIS)

    Singh, V.

    1992-01-01

    The mechanism by which quarks, believed to be the fundamental constituents of matter, are prevented from existing in the free state is fundamental problems in physics. One of the most viable candidates for a hypothesis of confinement is the dual superconductor mechanism that likens quark confinement to the Meissner effect in superconductors. The peculiarities of quark interactions make a numerical approach to the subject a necessity, and therefore, much of the work in this area has been done through the methods of lattice gauge theory, with the simplicities afforded by putting spacetime on a four-dimensional grid. Over the years a large amount of indirect evidence has accumulated that the dual superconductor hypothesis does indeed lead to quark confinement but unambiguous evidence has eluded research efforts until recently. This work presents the first direct proof of a Meissner-like effect that leads to confinement, using the numerical techniques of lattice gauge theory. It is shown that for a U(1) lattice gauge theory, that serves as a toy model of the real world of quarks, a dual London relation and an electric fluxoid qauntization condition is satisfied, allowing the author to conclude that the vacuum in this case acts like an extreme type-II superconductor, and that quarks are confined. The author also shows that SU(2) lattice gauge theory, which is qualitatively different and another step closer to reality, shows a Meissner-like effect. In contrast to the U(1) case, the author's results are found consistent with a dual version of the Ginsburg-Landau theory of superconductor on the borderline between type-I and type-II. This approach paves the wave for a study of the more complicated theory, quantum chromodynamics, that is believed to describe quarks

  16. Gauging the twisted Poincare symmetry as a noncommutative theory of gravitation

    International Nuclear Information System (INIS)

    Chaichian, M.; Tureanu, A.; Oksanen, M.; Zet, G.

    2009-01-01

    Einstein's theory of general relativity was formulated as a gauge theory of Lorentz symmetry by Utiyama in 1956, while the Einstein-Cartan gravitational theory was formulated by Kibble in 1961 as the gauge theory of Poincare transformations. In this framework, we propose a formulation of the gravitational theory on canonical noncommutative space-time by covariantly gauging the twisted Poincare symmetry, in order to fulfil the requirement of covariance under the general coordinate transformations, an essential ingredient of the theory of general relativity. It appears that the twisted Poincare symmetry cannot be gauged by generalizing the Abelian twist to a covariant non-Abelian twist, nor by introducing a more general covariant twist element. The advantages of such a formulation as well as the related problems are discussed and possible ways out are outlined.

  17. Understanding geometric algebra for electromagnetic theory

    CERN Document Server

    Arthur, John W

    2011-01-01

    "This book aims to disseminate geometric algebra as a straightforward mathematical tool set for working with and understanding classical electromagnetic theory. It's target readership is anyone who has some knowledge of electromagnetic theory, predominantly ordinary scientists and engineers who use it in the course of their work, or postgraduate students and senior undergraduates who are seeking to broaden their knowledge and increase their understanding of the subject. It is assumed that the reader is not a mathematical specialist and is neither familiar with geometric algebra or its application to electromagnetic theory. The modern approach, geometric algebra, is the mathematical tool set we should all have started out with and once the reader has a grasp of the subject, he or she cannot fail to realize that traditional vector analysis is really awkward and even misleading by comparison"--Provided by publisher.

  18. Chirality conservation in the lattice gauge theory

    International Nuclear Information System (INIS)

    Peskin, M.E.

    1978-01-01

    The derivation of conservation laws corresponding to chiral invariance in quantum field theories of interacting quarks and gluons are studied. In particular there is interest in observing how these conservation laws are constrained by the requirement that the field theory be locally gauge invariant. To examine this question, a manifestly gauge-invariant definition of local operators in a quantum field theory is introduced, a definition which relies in an essential way on the use of the formulation of gauge fields on a lattice due to Wilson and Polyakov to regulate ultraviolet divergences. The conceptual basis of the formalism is set out and applied to a long-standing puzzle in the phenomenology of quark-gluon theories: the fact that elementary particle interactions reflect the conservation of isospin-carrying chiral currents but not of the isospin-singlet chiral current. It is well known that the equation for the isospin-singlet current contains an extra term, the operator F/sub mu neu/F/sup mu neu/, not present in the other chirality conservation laws; however, this term conventionally has the form of a total divergence and so still allows the definition of a conserved chiral current. It is found that, when the effects of maintaining gauge invariance are properly taken into account, the structure of this operator is altered by renormalization effects, so that it provides an explicit breaking of the unwanted chiral invariance. The relation between this argument, based on renormaliztion, is traced to a set of more heuristic arguments based on gauge field topology given by 't Hooft; it is shown that the discussion provides a validation, through short-distance analysis, of the picture 'Hooft has proposed. The formal derivation of conservation laws for chiral currents are set out in detail

  19. Toward a gauge field theory of gravity.

    Science.gov (United States)

    Yilmaz, H.

    Joint use of two differential identities (Bianchi and Freud) permits a gauge field theory of gravity in which the gravitational energy is localizable. The theory is compatible with quantum mechanics and is experimentally viable.

  20. An elementary introduction to the Gauge theory approach to gravity. 23

    International Nuclear Information System (INIS)

    Mukunda, N.

    1989-01-01

    Can all the forces be unified by a gauge group? Can we get a clue by studying gravity itself which is also a gauge theory by gauging the Poincare group?. The main problems have been in the understanding of the role of invariants of the Lie algebra of the group if one has general covariance. One is led to theories more general than general relativity in that, in addition to curvature, one also has torsion. These and other aspects of gravitation as a gauge theory are treated. (author). 11 refs.; 1 fig

  1. Origin of gauge invariance in string theory

    Science.gov (United States)

    Horowitz, G. T.; Strominger, A.

    1986-01-01

    A first quantization of the space-time embedding Chi exp mu and the world-sheet metric rho of the open bosonic string. The world-sheet metric rho decouples from S-matrix elements in 26 dimensions. This formulation of the theory naturally includes 26-dimensional gauge transformations. The gauge invariance of S-matrix elements is a direct consequence of the decoupling of rho. Second quantization leads to a string field Phi(Chi exp mu, rho) with a gauge-covariant equation of motion.

  2. New gauge symmetries in Witten's Ramond string field theory

    International Nuclear Information System (INIS)

    Kugo, Taichiro; Terao, Haruhiko

    1988-01-01

    Witten's Raymond string field theory is observed to possess new gauge symmetries, which guarantee the consistency and the equivalence of Witten's theory to the other formulation based on the constrained string field. The projection operator into the gauge-invariant sector is explicitly constructed using an operator similar to the picture changing operator. (orig.)

  3. Space-Time Diffeomorphisms in Noncommutative Gauge Theories

    Directory of Open Access Journals (Sweden)

    L. Román Juarez

    2008-07-01

    Full Text Available In previous work [Rosenbaum M. et al., J. Phys. A: Math. Theor. 40 (2007, 10367–10382] we have shown how for canonical parametrized field theories, where space-time is placed on the same footing as the other fields in the theory, the representation of space-time diffeomorphisms provides a very convenient scheme for analyzing the induced twisted deformation of these diffeomorphisms, as a result of the space-time noncommutativity. However, for gauge field theories (and of course also for canonical geometrodynamics where the Poisson brackets of the constraints explicitely depend on the embedding variables, this Poisson algebra cannot be connected directly with a representation of the complete Lie algebra of space-time diffeomorphisms, because not all the field variables turn out to have a dynamical character [Isham C.J., Kuchar K.V., Ann. Physics 164 (1985, 288–315, 316–333]. Nonetheless, such an homomorphic mapping can be recuperated by first modifying the original action and then adding additional constraints in the formalism in order to retrieve the original theory, as shown by Kuchar and Stone for the case of the parametrized Maxwell field in [Kuchar K.V., Stone S.L., Classical Quantum Gravity 4 (1987, 319–328]. Making use of a combination of all of these ideas, we are therefore able to apply our canonical reparametrization approach in order to derive the deformed Lie algebra of the noncommutative space-time diffeomorphisms as well as to consider how gauge transformations act on the twisted algebras of gauge and particle fields. Thus, hopefully, adding clarification on some outstanding issues in the literature concerning the symmetries for gauge theories in noncommutative space-times.

  4. Quantum field theory III. Gauge theory. A bridge between mathematicians and physicists

    International Nuclear Information System (INIS)

    Zeidler, Eberhard

    2011-01-01

    In this third volume of his modern introduction to quantum field theory, Eberhard Zeidler examines the mathematical and physical aspects of gauge theory as a principle tool for describing the four fundamental forces which act in the universe: gravitative, electromagnetic, weak interaction and strong interaction. Volume III concentrates on the classical aspects of gauge theory, describing the four fundamental forces by the curvature of appropriate fiber bundles. This must be supplemented by the crucial, but elusive quantization procedure. The book is arranged in four sections, devoted to realizing the universal principle force equals curvature: Part I: The Euclidean Manifold as a Paradigm Part II: Ariadne's Thread in Gauge Theory Part III: Einstein's Theory of Special Relativity Part IV: Ariadne's Thread in Cohomology For students of mathematics the book is designed to demonstrate that detailed knowledge of the physical background helps to reveal interesting interrelationships among diverse mathematical topics. Physics students will be exposed to a fairly advanced mathematics, beyond the level covered in the typical physics curriculum. Quantum Field Theory builds a bridge between mathematicians and physicists, based on challenging questions about the fundamental forces in the universe (macrocosmos), and in the world of elementary particles (microcosmos). (orig.)

  5. Gauge and integrable theories in loop spaces

    International Nuclear Information System (INIS)

    Ferreira, L.A.; Luchini, G.

    2012-01-01

    We propose an integral formulation of the equations of motion of a large class of field theories which leads in a quite natural and direct way to the construction of conservation laws. The approach is based on generalized non-abelian Stokes theorems for p-form connections, and its appropriate mathematical language is that of loop spaces. The equations of motion are written as the equality of a hyper-volume ordered integral to a hyper-surface ordered integral on the border of that hyper-volume. The approach applies to integrable field theories in (1+1) dimensions, Chern-Simons theories in (2+1) dimensions, and non-abelian gauge theories in (2+1) and (3+1) dimensions. The results presented in this paper are relevant for the understanding of global properties of those theories. As a special byproduct we solve a long standing problem in (3+1)-dimensional Yang-Mills theory, namely the construction of conserved charges, valid for any solution, which are invariant under arbitrary gauge transformations.

  6. Conformal gauge-Yukawa theories away from four dimensions

    Energy Technology Data Exchange (ETDEWEB)

    Codello, Alessandro; Langæble, Kasper [CP-Origins, University of Southern Denmark,Campusvej 55, Odense, DK-5230 (Denmark); Litim, Daniel F. [Department of Physics and Astronomy, University of Sussex,Brighton, BN1 9QH (United Kingdom); Sannino, Francesco [CP-Origins, University of Southern Denmark,Campusvej 55, Odense, DK-5230 (Denmark); Danish Institute for Advanced Study, Danish IAS, University of Southern Denmark,Campusvej 55, Odense, DK-5230 (Denmark)

    2016-07-22

    We present the phase diagram and associated fixed points for a wide class of Gauge-Yukawa theories in d=4+ϵ dimensions. The theories we investigate involve non-abelian gauge fields, fermions and scalars in the Veneziano-Witten limit. The analysis is performed in steps, we start with QCD{sub d} and then we add Yukawa interactions and scalars which we study at next-to- and next-to-next-to-leading order. Interacting infrared fixed points naturally emerge in dimensions lower than four while ultraviolet ones appear above four. We also analyse the stability of the scalar potential for the discovered fixed points. We argue for a very rich phase diagram in three dimensions while in dimensions higher than four certain Gauge-Yukawa theories are ultraviolet complete because of the emergence of an asymptotically safe fixed point.

  7. Mathematical and physical aspects of gauge theories

    International Nuclear Information System (INIS)

    Chatelet, G.; Paris-13 Univ., 93 - Saint-Denis

    1981-01-01

    We present here a survey of gauge theories, trying to relate the main mathematical and physical concepts. Part I is devoted to exhibiting parallel transport and connection as the adequate concepts for the constitution of the parametrized internal space of a particle. A covariant derivative provides the differential calculus, which is needed when one leaves the point-like description in microphysics. Part II deals with the so-called pure gauge theory and sketches the construction of the self-dual solutions of Yang-Mills equations. We briefly explain Guersey's method to get SU 2 self-dual potentials as quarternionic analytic maps from S 4 (first quarternionic projective space) into HPsub(n) (n-dimensional quarternionic projective space). Part III is devoted to the Goldstone's theorem and Higgs' mechanism used to provide a mass to gauge mesons. We describe a Salam-Weinberg model to illustrate these techniques. Part IV deals with the perturbative aspect. The Faddeev-Popov method, formerly conceived as a technique to get correct Feynmann rules, actually leads to a systematic study of the affine space of connections factored out by gauge transformations. (orig.)

  8. Deep inelastic scattering in an asymptotically free gauge theory

    International Nuclear Information System (INIS)

    Fujiwara, Tsutomu

    1977-01-01

    This paper reviews the success of the asymptotically free gauge theory which describes the deep inelastic lepton-hadron scattering. The asymptotically free gauge theory was discussed as well as the reason why the parton has the nature like free particles by the aid of the field theory. The asymptotically free gauge theory (AFGT) gives the prediction that the Bjorken scaling gives rise to logarithmic violation. The theory was applied to the exchange processes of single photon and two photons. First, this paper describes the approaches to the Bjorken scaling. The approaches are the discussion of the scaling law dependent on the model and the discussion of the scaling law independent of the model. The field theoretical treatment in described. This is called the method of the renormalization group introduced by Wilson. The asymptotically free gauge theory was formed on the basis of the Callan-Symanzik equation (CSE) and of the Weinberg's power counting theorem. The exact Bjorken scaling does not hold in the quantum field theory, at least there must be logarithmic violation. The pattern of the scaling violation cannot be clarified by the present data. Discussions concerning two gamma process are presented. The measurement of the photon-photon scattering process will give the judgement whether the prediction of the AFGT is correct or not. (Kato, T.)

  9. Scattering amplitudes in gauge theories

    CERN Document Server

    Henn, Johannes M

    2014-01-01

    At the fundamental level, the interactions of elementary particles are described by quantum gauge field theory. The quantitative implications of these interactions are captured by scattering amplitudes, traditionally computed using Feynman diagrams. In the past decade tremendous progress has been made in our understanding of and computational abilities with regard to scattering amplitudes in gauge theories, going beyond the traditional textbook approach. These advances build upon on-shell methods that focus on the analytic structure of the amplitudes, as well as on their recently discovered hidden symmetries. In fact, when expressed in suitable variables the amplitudes are much simpler than anticipated and hidden patterns emerge.   These modern methods are of increasing importance in phenomenological applications arising from the need for high-precision predictions for the experiments carried out at the Large Hadron Collider, as well as in foundational mathematical physics studies on the S-matrix in quantum ...

  10. N = 8 superconformal gauge theories and M2 branes

    International Nuclear Information System (INIS)

    Benvenuti, Sergio; Rodriguez-Gomez, Diego; Verlinde, Herman; Tonni, Erik

    2009-01-01

    Based on recent developments, in this letter we find 2+1 dimensional gauge theories with scale invariance and N = 8 supersymmetry. The gauge theories are defined by a Lagrangian and are based on an infinite set of 3-algebras, constructed as an extension of ordinary Lie algebras. Recent no-go theorems on the existence of 3-algebras are circumvented by relaxing the assumption that the invariant metric is positive definite. The gauge group is non compact, and its maximally compact subgroup can be chosen to be any ordinary Lie group, under which the matter fields are adjoints or singlets. Interestingly, the theories are parity invariant and do not admit any tunable coupling constant.

  11. From the geometric quantization to conformal field theory

    International Nuclear Information System (INIS)

    Alekseev, A.; Shatashvili, S.

    1990-01-01

    Investigation of 2d conformal field theory in terms of geometric quantization is given. We quantize the so-called model space of the compact Lie group, Virasoro group and Kac-Moody group. In particular, we give a geometrical interpretation of the Virasoro discrete series and explain that this type of geometric quantization reproduces the chiral part of CFT (minimal models, 2d-gravity, WZNW theory). In the appendix we discuss the relation between classical (constant) r-matrices and this geometrical approach. (orig.)

  12. Pure Gauge theory in crystal lattice and Coulomb gases

    International Nuclear Information System (INIS)

    Marchetti, D.H.U.

    1985-01-01

    A method for the construction of classical gases, starting from a pure gauge theory, is described. The method is applied to the U(1) gauge theory in two spatial dimensions. For this model it's seen the vaccua appearing as a consequence of the quantization ambiguity. The connection between the vaccua and the confinement is discussed. (Author) [pt

  13. Functional determinants in gauge theory and string theory

    International Nuclear Information System (INIS)

    Della Pietra, V.J.

    1988-01-01

    Determinants arise whenever Gaussian functional integrals are evaluated. As a result, they are pervasive in physics. In this thesis the author studied, in a mathematically precise fashion, some questions concerning functional determinants in Quantum Field Theory and String Theory. The emphasis is on deriving explicit general identities which can be applied to physical problems. In Chapters 1-3, he studies determinants of families of Weyl operators on compact manifolds. The motivation for this work comes from Chiral Gauge Theory. In a theory containing chiral Fermions coupled to Bosons y, a partial integration in the functional integral over the Fermi fields yields terms involving determinants of Weyl operators ∂y. In Chapter 4 he turns his attention to a problem in String Theory. In the Polyakov formulation of string perturbation theory, the partition function and scattering amplitudes are calculated as sums of contributions from different world sheet topologies. The contribution from surfaces of a particular topology is given by a functional integral, which, after gauge-fixing, can be expressed as an integral of a certain measure over an appropriate moduli space. For an arbitrary finite group acting on a compact manifold, he defines an analytic torsion for the invariant subcomplex of the de Rham complex, generalizing the definition given by Ray and Singer in the absence of a group action. Motivated by the work of Quillen, he uses this torsion to define a natural norm on the determinant line of the invariant cohomology

  14. Renormalization of gauge theories in the background-field approach arXiv

    CERN Document Server

    Barvinsky, Andrei O.; Herrero-Valea, Mario; Sibiryakov, Sergey M.; Steinwachs, Christian F.

    Using the background-field method we demonstrate the Becchi-Rouet-Stora-Tyutin (BRST) structure of counterterms in a broad class of gauge theories. Put simply, we show that gauge invariance is preserved by renormalization in local gauge field theories whenever they admit a sensible background-field formulation and anomaly-free path integral measure. This class encompasses Yang-Mills theories (with possibly Abelian subgroups) and relativistic gravity, including both renormalizable and non-renormalizable (effective) theories. Our results also hold for non-relativistic models such as Yang-Mills theories with anisotropic scaling or Horava gravity. They strengthen and generalize the existing results in the literature concerning the renormalization of gauge systems. Locality of the BRST construction is emphasized throughout the derivation. We illustrate our general approach with several explicit examples.

  15. Gauge field theories. 3. enl. ed.

    International Nuclear Information System (INIS)

    Frampton, Paul H.

    2008-01-01

    Gauge theories provide a unified framework to describe three of the four universal forces known so far: the quantum field theories of electromagnetism, the weak force and the strong force. They are an essential part of the so-called standard model of particles and matter. The first edition of this work was quickly adopted by universities and other institutions of higher learning around the world. Completely updated, this third edition continues to be an ideal reference on the subject. In total, more than a quarter of the content has been changed or added. The tried-and-tested logical structuring of the material on gauge invariance, quantization, and renormalization has been retained, while the chapters on electroweak interactions and model building have been revised. Completely new is the chapter on conformality. As in the past, Frampton emphasizes formalism rather than experiments and provides sufficient detail for readers wishing to do their own calculations or pursue theoretical physics research: - gauge invariance, - quantization, - renormalization, - electroweak forces, - renormalization group, - quantum chromodynamics, - model building, - conformality. (orig.)

  16. Development of unified gauge theories: retrospect

    International Nuclear Information System (INIS)

    Lee, B.W.

    1977-01-01

    The construction and development of unified gauge theory of weak, electromagnetic, and strong interactions is reviewed. The Weinberg and Lee contributions to this study are mainly considered as personal recollections

  17. Differential renormalization of gauge theories

    International Nuclear Information System (INIS)

    Aguila, F. del; Perez-Victoria, M.

    1998-01-01

    The scope of constrained differential renormalization is to provide renormalized expressions for Feynman graphs, preserving at the same time the Ward identities of the theory. It has been shown recently that this can be done consistently at least to one loop for Abelian and non-Abelian gauge theories. We briefly review these results, evaluate as an example the gluon self energy in both coordinate and momentum space, and comment on anomalies. (author)

  18. New relations for gauge-theory amplitudes

    International Nuclear Information System (INIS)

    Bern, Z.; Carrasco, J. J. M.; Johansson, H.

    2008-01-01

    We present an identity satisfied by the kinematic factors of diagrams describing the tree amplitudes of massless gauge theories. This identity is a kinematic analog of the Jacobi identity for color factors. Using this we find new relations between color-ordered partial amplitudes. We discuss applications to multiloop calculations via the unitarity method. In particular, we illustrate the relations between different contributions to a two-loop four-point QCD amplitude. We also use this identity to reorganize gravity tree amplitudes diagram by diagram, offering new insight into the structure of the Kawai-Lewellen-Tye (KLT) relations between gauge and gravity tree amplitudes. This insight leads to similar but novel relations. We expect this to be helpful in higher-loop studies of the ultraviolet properties of gravity theories.

  19. Lattice gauge theories, confinement, strings and all that

    International Nuclear Information System (INIS)

    Muenster, G.

    1980-11-01

    In this talk I would like to give an overview over some developments in lattice gauge theory, which might be of some interest for experimental physicists. In particular, I shall try to convince you that lattice gauge theory is not only a play-ground for theorists, but is able to produce numerical results for some non-perturbative quantities. And, of course, I would like to tell you about some work, which has been done here in Hamburg. (orig.)

  20. IR fixed points in SU(3 gauge theories

    Directory of Open Access Journals (Sweden)

    K.-I. Ishikawa

    2015-09-01

    Full Text Available We propose a novel RG method to specify the location of the IR fixed point in lattice gauge theories and apply it to the SU(3 gauge theories with Nf fundamental fermions. It is based on the scaling behavior of the propagator through the RG analysis with a finite IR cutoff, which we cannot remove in the conformal field theories in sharp contrast to the confining theories. The method also enables us to estimate the anomalous mass dimension in the continuum limit at the IR fixed point. We perform the program for Nf=16,12,8 and Nf=7 and indeed identify the location of the IR fixed points in all cases.

  1. Dynamics of SU(N) supersymmetric gauge theory

    Energy Technology Data Exchange (ETDEWEB)

    Douglas, M R [Rutgers - the State Univ., Piscataway, NJ (United States). Dept. of Physics and Astronomy; Shenker, S H [Rutgers - the State Univ., Piscataway, NJ (United States). Dept. of Physics and Astronomy

    1995-08-07

    We study the physics of the Seiberg-Witten and Argyres-Faraggi-Klemm-Lerche-Theisen-Yankielowicz solutions of D=4, N=2 and N=1 SU(N) supersymmetric gauge theory. The N=1 theory is confining and its effective Lagrangian is a spontaneously broken U(1){sup N-1} abelian gauge theory. We identify some features of its physics which see this internal structure, including a spectrum of different string tensions. We discuss the limit N{yields}{infinity}, identify a scaling regime in which instanton and monopole effects survive, and give exact results for the crossover from weak to strong coupling along a scaling trajectory. We find a large hierarchy of mass scales in the scaling regime, including very light W bosons, and the absence of weak coupling. The light W`s leave a novel imprint on the effective dual magnetic theory. The effective Lagrangian appears to be inadequate to understand the conventional large N limit of the confining N=1 theory. (orig.).

  2. Non-perturbative Green functions in quantum gauge theories

    International Nuclear Information System (INIS)

    Shabanov, S.V.

    1991-01-01

    Non-perturbative Green functions for gauge invariant variables are considered. The Green functions are found to be modified as compared with the usual ones in a definite gauge because of a physical configuration space (PCS) reduction. In the Yang-Mills theory with fermions this phenomenon follows from the Singer theorem about the absence of a global gauge condition for the fields tensing to zero at spatial infinity. 20 refs

  3. Studies on representation of the Lorentz group and gauge theory

    International Nuclear Information System (INIS)

    Hanitriarivo, R.

    2002-01-01

    This work is focused on studies about the representation of the Lorentz group and gauge theory. The mathematical tools required for the different studies are presented, as well as for the representation of the Lorentz group and for the gauge theory. Representation of the Lorentz group gives the possible types of fields and wave functions that describe particles: fermions are described by spinors and bosons are described by scalar or vector. Each of these entities (spinors, scalars, vectors) are characterized by their behavior under the action of Lorentz transformations.Gauge theory is used to describe the interactions between particles. [fr

  4. Geometric control theory and sub-Riemannian geometry

    CERN Document Server

    Boscain, Ugo; Gauthier, Jean-Paul; Sarychev, Andrey; Sigalotti, Mario

    2014-01-01

    This volume presents recent advances in the interaction between Geometric Control Theory and sub-Riemannian geometry. On the one hand, Geometric Control Theory used the differential geometric and Lie algebraic language for studying controllability, motion planning, stabilizability and optimality for control systems. The geometric approach turned out to be fruitful in applications to robotics, vision modeling, mathematical physics etc. On the other hand, Riemannian geometry and its generalizations, such as  sub-Riemannian, Finslerian  geometry etc., have been actively adopting methods developed in the scope of geometric control. Application of these methods  has led to important results regarding geometry of sub-Riemannian spaces, regularity of sub-Riemannian distances, properties of the group  of diffeomorphisms of sub-Riemannian manifolds, local geometry and equivalence of distributions and sub-Riemannian structures, regularity of the Hausdorff volume.

  5. Gauge structure of neutral-vector field theory. [Massive vector fields, massless limits

    Energy Technology Data Exchange (ETDEWEB)

    Kubo, R; Yokoyama, [Hiroshima univ., Takehara (Japan). Research Inst. for Theoretical Physics

    1975-03-01

    General aspects of gauge structure of neutral-vector field theory are investigated from an extended standpoint, where massive vector fields are treated in a form corresponding to the electromagnetic fields in a general gauge formalism reported previously. All results obtained are shown to have unique massless limits. It is shown that a generalized q-number gauge transformation for fields makes the theory invariant in cooperation with a simultaneous transformation for relevant gauge parameters. A method of differentiation with respect to a gauge variable is found to clarify some essential features of the gauge structure. Two possible types of gauge structure also emerge correspondingly to the massless case. A neutral-vector field theory proposed in a preceding paper is included in the present framework as the most preferable case.

  6. Gauge theories of the weak interactions

    International Nuclear Information System (INIS)

    Quinn, H.

    1978-01-01

    Lectures are given on the Weinberg--Salam or Weinberg--Salam--Glashow--Iliopoulos--Maiani gauge theory. The way it is put together and some possible variations in the literature are discussed. 53 references

  7. Linear bosonic and fermionic quantum gauge theories on curved spacetimes

    International Nuclear Information System (INIS)

    Hack, Thomas-Paul; Schenkel, Alexander

    2012-05-01

    We develop a general setting for the quantization of linear bosonic and fermionic field theories subject to local gauge invariance and show how standard examples such as linearized Yang-Mills theory and linearized general relativity fit into this framework. Our construction always leads to a well-defined and gauge-invariant quantum field algebra, the centre and representations of this algebra, however, have to be analysed on a case-by-case basis. We discuss an example of a fermionic gauge field theory where the necessary conditions for the existence of Hilbert space representations are not met on any spacetime. On the other hand, we prove that these conditions are met for the Rarita-Schwinger gauge field in linearized pure N=1 supergravity on certain spacetimes, including asymptotically flat spacetimes and classes of spacetimes with compact Cauchy surfaces. We also present an explicit example of a supergravity background on which the Rarita-Schwinger gauge field can not be consistently quantized.

  8. Linear bosonic and fermionic quantum gauge theories on curved spacetimes

    Energy Technology Data Exchange (ETDEWEB)

    Hack, Thomas-Paul [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Schenkel, Alexander [Bergische Univ., Wuppertal (Germany). Fachgruppe Physik

    2012-05-15

    We develop a general setting for the quantization of linear bosonic and fermionic field theories subject to local gauge invariance and show how standard examples such as linearized Yang-Mills theory and linearized general relativity fit into this framework. Our construction always leads to a well-defined and gauge-invariant quantum field algebra, the centre and representations of this algebra, however, have to be analysed on a case-by-case basis. We discuss an example of a fermionic gauge field theory where the necessary conditions for the existence of Hilbert space representations are not met on any spacetime. On the other hand, we prove that these conditions are met for the Rarita-Schwinger gauge field in linearized pure N=1 supergravity on certain spacetimes, including asymptotically flat spacetimes and classes of spacetimes with compact Cauchy surfaces. We also present an explicit example of a supergravity background on which the Rarita-Schwinger gauge field can not be consistently quantized.

  9. Classical field theory. On electrodynamics, non-Abelian gauge theories and gravitation. 2. ed.

    Energy Technology Data Exchange (ETDEWEB)

    Scheck, Florian

    2018-04-01

    Scheck's successful textbook presents a comprehensive treatment, ideally suited for a one-semester course. The textbook describes Maxwell's equations first in their integral, directly testable form, then moves on to their local formulation. The first two chapters cover all essential properties of Maxwell's equations, including their symmetries and their covariance in a modern notation. Chapter 3 is devoted to Maxwell's theory as a classical field theory and to solutions of the wave equation. Chapter 4 deals with important applications of Maxwell's theory. It includes topical subjects such as metamaterials with negative refraction index and solutions of Helmholtz' equation in paraxial approximation relevant for the description of laser beams. Chapter 5 describes non-Abelian gauge theories from a classical, geometric point of view, in analogy to Maxwell's theory as a prototype, and culminates in an application to the U(2) theory relevant for electroweak interactions. The last chapter 6 gives a concise summary of semi-Riemannian geometry as the framework for the classical field theory of gravitation. The chapter concludes with a discussion of the Schwarzschild solution of Einstein's equations and the classical tests of general relativity. The new concept of this edition presents the content divided into two tracks: the fast track for master's students, providing the essentials, and the intensive track for all wanting to get in depth knowledge of the field. Cleary labeled material and sections guide students through the preferred level of treatment. Numerous problems and worked examples will provide successful access to Classical Field Theory.

  10. A gauge field theory of fermionic continuous-spin particles

    Energy Technology Data Exchange (ETDEWEB)

    Bekaert, X., E-mail: xavier.bekaert@lmpt.univ-tours.fr [Laboratoire de Mathématiques et Physique Théorique, Unité Mixte de Recherche 7350 du CNRS, Fédération de Recherche 2964 Denis Poisson, Université François Rabelais, Parc de Grandmont, 37200 Tours (France); B.W. Lee Center for Fields, Gravity and Strings, Institute for Basic Science, Daejeon (Korea, Republic of); Najafizadeh, M., E-mail: mnajafizadeh@gmail.com [Laboratoire de Mathématiques et Physique Théorique, Unité Mixte de Recherche 7350 du CNRS, Fédération de Recherche 2964 Denis Poisson, Université François Rabelais, Parc de Grandmont, 37200 Tours (France); Department of Physics, Faculty of Sciences, University of Kurdistan, 66177-15177 Sanandaj (Iran, Islamic Republic of); Setare, M.R., E-mail: rezakord@ipm.ir [Department of Physics, Faculty of Sciences, University of Kurdistan, 66177-15177 Sanandaj (Iran, Islamic Republic of)

    2016-09-10

    In this letter, we suggest a local covariant action for a gauge field theory of fermionic Continuous-Spin Particles (CSPs). The action is invariant under gauge transformations without any constraint on both the gauge field and the gauge transformation parameter. The Fang–Fronsdal equations for a tower of massless fields with all half-integer spins arise as a particular limit of the equation of motion of fermionic CSPs.

  11. A gauge field theory of fermionic continuous-spin particles

    International Nuclear Information System (INIS)

    Bekaert, X.; Najafizadeh, M.; Setare, M.R.

    2016-01-01

    In this letter, we suggest a local covariant action for a gauge field theory of fermionic Continuous-Spin Particles (CSPs). The action is invariant under gauge transformations without any constraint on both the gauge field and the gauge transformation parameter. The Fang–Fronsdal equations for a tower of massless fields with all half-integer spins arise as a particular limit of the equation of motion of fermionic CSPs.

  12. Quantum field theory III. Gauge theory. A bridge between mathematicians and physicists

    Energy Technology Data Exchange (ETDEWEB)

    Zeidler, Eberhard [Max Planck Institute for Mathematics in the Sciences, Leipzig (Germany)

    2011-07-01

    In this third volume of his modern introduction to quantum field theory, Eberhard Zeidler examines the mathematical and physical aspects of gauge theory as a principle tool for describing the four fundamental forces which act in the universe: gravitative, electromagnetic, weak interaction and strong interaction. Volume III concentrates on the classical aspects of gauge theory, describing the four fundamental forces by the curvature of appropriate fiber bundles. This must be supplemented by the crucial, but elusive quantization procedure. The book is arranged in four sections, devoted to realizing the universal principle force equals curvature: Part I: The Euclidean Manifold as a Paradigm Part II: Ariadne's Thread in Gauge Theory Part III: Einstein's Theory of Special Relativity Part IV: Ariadne's Thread in Cohomology For students of mathematics the book is designed to demonstrate that detailed knowledge of the physical background helps to reveal interesting interrelationships among diverse mathematical topics. Physics students will be exposed to a fairly advanced mathematics, beyond the level covered in the typical physics curriculum. Quantum Field Theory builds a bridge between mathematicians and physicists, based on challenging questions about the fundamental forces in the universe (macrocosmos), and in the world of elementary particles (microcosmos). (orig.)

  13. Differential renormalization of gauge theories

    Energy Technology Data Exchange (ETDEWEB)

    Aguila, F. del; Perez-Victoria, M. [Dept. de Fisica Teorica y del Cosmos, Universidad de Granada, Granada (Spain)

    1998-10-01

    The scope of constrained differential renormalization is to provide renormalized expressions for Feynman graphs, preserving at the same time the Ward identities of the theory. It has been shown recently that this can be done consistently at least to one loop for Abelian and non-Abelian gauge theories. We briefly review these results, evaluate as an example the gluon self energy in both coordinate and momentum space, and comment on anomalies. (author) 9 refs, 1 fig., 1 tab

  14. Five-dimensional Lattice Gauge Theory as Multi-Layer World

    OpenAIRE

    Murata, Michika; So, Hiroto

    2003-01-01

    A five-dimensional lattice space can be decomposed into a number of four-dimens ional lattices called as layers. The five-dimensional gauge theory on the lattice can be interpreted as four-dimensional gauge theories on the multi-layer with interactions between neighboring layers. In the theory, there exist two independent coupling constants; $\\beta_4$ controls the dynamics inside a layer and $\\beta_5$ does the strength of the inter-layer interaction.We propose the new possibility to realize t...

  15. Phenomenology of muon number violation in spontaneously broken gauge theories

    International Nuclear Information System (INIS)

    Shanker, O.U.

    1980-01-01

    The phenomenology of muon number violation in gauge theories of weak and electromagnetic interactions is studied. In the first chapter a brief introduction to the concept of muon number and to spontaneously broken gauge theories is given. A review of the phenomenology and experimental situation regarding different muon number violating processes is made in the second chapter. A detailed phenomenological study of the μe conversion process μ - + (A,Z) → e - + (A,Z) is given in the third chapter. In the fourth chapter some specific gauge theories incorporating spontaneously broken horizontal gauge symmetries between different fermion generations are discussed with special reference to muon number violation in the theories. The μe conversion process seems to be a good process to search for muon number violation if it occurs. The K/sub L/-K/sub S/ mass difference is likely to constrain muon number violating rates to lie far below present experimental limits unless strangeness changing neutral currents changing strangeness by two units are suppressed

  16. Scattering amplitudes in gauge theories

    Energy Technology Data Exchange (ETDEWEB)

    Henn, Johannes M. [Institute for Advanced Study, Princeton, NJ (United States). School of Natural Sciences; Plefka, Jan C. [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik

    2014-03-01

    First monographical text on this fundamental topic. Course-tested, pedagogical and self-contained exposition. Includes exercises and solutions. At the fundamental level, the interactions of elementary particles are described by quantum gauge field theory. The quantitative implications of these interactions are captured by scattering amplitudes, traditionally computed using Feynman diagrams. In the past decade tremendous progress has been made in our understanding of and computational abilities with regard to scattering amplitudes in gauge theories, going beyond the traditional textbook approach. These advances build upon on-shell methods that focus on the analytic structure of the amplitudes, as well as on their recently discovered hidden symmetries. In fact, when expressed in suitable variables the amplitudes are much simpler than anticipated and hidden patterns emerge. These modern methods are of increasing importance in phenomenological applications arising from the need for high-precision predictions for the experiments carried out at the Large Hadron Collider, as well as in foundational mathematical physics studies on the S-matrix in quantum field theory. Bridging the gap between introductory courses on quantum field theory and state-of-the-art research, these concise yet self-contained and course-tested lecture notes are well-suited for a one-semester graduate level course or as a self-study guide for anyone interested in fundamental aspects of quantum field theory and its applications. The numerous exercises and solutions included will help readers to embrace and apply the material presented in the main text.

  17. Scattering amplitudes in gauge theories

    International Nuclear Information System (INIS)

    Henn, Johannes M.; Plefka, Jan C.

    2014-01-01

    First monographical text on this fundamental topic. Course-tested, pedagogical and self-contained exposition. Includes exercises and solutions. At the fundamental level, the interactions of elementary particles are described by quantum gauge field theory. The quantitative implications of these interactions are captured by scattering amplitudes, traditionally computed using Feynman diagrams. In the past decade tremendous progress has been made in our understanding of and computational abilities with regard to scattering amplitudes in gauge theories, going beyond the traditional textbook approach. These advances build upon on-shell methods that focus on the analytic structure of the amplitudes, as well as on their recently discovered hidden symmetries. In fact, when expressed in suitable variables the amplitudes are much simpler than anticipated and hidden patterns emerge. These modern methods are of increasing importance in phenomenological applications arising from the need for high-precision predictions for the experiments carried out at the Large Hadron Collider, as well as in foundational mathematical physics studies on the S-matrix in quantum field theory. Bridging the gap between introductory courses on quantum field theory and state-of-the-art research, these concise yet self-contained and course-tested lecture notes are well-suited for a one-semester graduate level course or as a self-study guide for anyone interested in fundamental aspects of quantum field theory and its applications. The numerous exercises and solutions included will help readers to embrace and apply the material presented in the main text.

  18. Geometric (Berry) phases in neutron molecular spectroscopy

    International Nuclear Information System (INIS)

    Lovesey, S.W.

    1992-02-01

    A theory of neutron scattering by nuclei in a molecule, accompanied by an electronic transition, is formulated with attention to gauge potentials and geometric phases in the Born-Oppenheimer scheme. Non-degenerate and nearly degenerate electronic levels are considered. For nearly degenerate levels it is shown that, the cross-section is free of the singular structure which characterizes the corresponding gauge potential for the phase, and much larger than for well separated electronic states. (author)

  19. An Ar threesome: Matrix models, 2d conformal field theories, and 4dN=2 gauge theories

    International Nuclear Information System (INIS)

    Schiappa, Ricardo; Wyllard, Niclas

    2010-01-01

    We explore the connections between three classes of theories: A r quiver matrix models, d=2 conformal A r Toda field theories, and d=4N=2 supersymmetric conformal A r quiver gauge theories. In particular, we analyze the quiver matrix models recently introduced by Dijkgraaf and Vafa (unpublished) and make detailed comparisons with the corresponding quantities in the Toda field theories and the N=2 quiver gauge theories. We also make a speculative proposal for how the matrix models should be modified in order for them to reproduce the instanton partition functions in quiver gauge theories in five dimensions.

  20. Introduction to dualities in gauge theories

    Energy Technology Data Exchange (ETDEWEB)

    Kneipp, Marco A.C. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)]. E-mail: kneipp@cbpf.br

    2000-12-01

    These notes present a pedagogical introduction to magnetic monopoles, supersymmetry and dualities in gauge theories. They are based on lectures given at the X Jorge Andre Swieca Summer School on Particles and Fields. (author)

  1. A study of the path-integral quantization of Abelian gauge theories when no explicit gauge-fixing term is included in the bilinear part of the gauge-field action

    International Nuclear Information System (INIS)

    Phillips, S.

    1985-01-01

    The mathematical problem of inverting the operator Δ x μν ≡ g μν g αβ δ x α δ x β -δ x μ δ x ν , as it arises in the path-integral quantization of an Abelian gauge theory, such as quantum electrodynamics, when no gauge-fixing Lagrangian field density is included, is studied in this article. Making use of the fact that the Schwinger source functions, which are introduced for the purpose of generating Green's functions, are free of divergence, a result that follows from the conversion of the exponentiated action into a Gaussian form, the apparently noninvertible partial differential equation, Δ x μν L ν (x) J μ (x), can, by the addition and subsequent subtraction of terms containing the divergence of the source function, be cast into a form that does possess a Green's function solution. The gauge-field propagator is the same as that obtained by the conventional technique, which involves gauge fixing when the gauge parameter, α, is set equal to one. Such an analysis suggests also that, provided the effect of fictitious particles that propagate only in closed loops are included for the study of Green's functions in non-Abelian gauge theories in Landau-type gauges, then, in quantizing either Abelian gauge theories or non-Abelian gauge theories in this generic kind of gauge, it is not necessary to add an explicit gauge-fixing term to the bilinear part of the gauge-field action

  2. Dual potentials in non-Abelian gauge theories

    International Nuclear Information System (INIS)

    Caticha, A.

    1988-01-01

    Motivated by the possibility that confinement and superconductivity are similar phenomena, dual potentials are introduced into Yang-Mills theory in two different ways. Both are extensions of Zwanziger's two-potential formalism for Abelian charges and monopoles to the non-Abelian case. In the first approach the dual potentials carry a color index and there is a rather simple, although nonlocal, dual-variable formulation. In the second approach dual variables are introduced into the so-called Abelian projection of the SU(2) Yang-Mills theory. An interesting feature is that the quartic contact interactions are absent and there is a special gauge choice for which the theory takes on a ''purely electromagnetic'' form. More important, however, is the appearance of an additional Abelian magnetic gauge symmetry the dynamical breaking of which may be associated with confinement

  3. Kohn-Luttinger effect in gauge theories

    International Nuclear Information System (INIS)

    Schaefer, T.

    2006-01-01

    Kohn and Luttinger showed that a many body system of fermions interacting via short range forces becomes superfluid even if the interaction is repulsive in all partial waves. In gauge theories such as QCD the interaction between fermions is long range and the assumptions of Kohn and Luttinger are not satisfied. We show that in a U(1) gauge theory the Kohn-Luttinger phenomenon does not take place. In QCD attractive channels always exist, but there are cases in which the primary pairing channel leaves some fermions ungapped. As an example we consider the unpaired fermion in the 2SC phase of QCD with two flavors. We show that it acquires a very small gap via a mechanism analogous to the Kohn-Luttinger effect. The gap is too small to be phenomenologically relevant

  4. A map between corner and link operators in lattice gauge theories

    International Nuclear Information System (INIS)

    Bars, I.

    1979-01-01

    A completely local gauge-invariant lattice gauge theory is formulated in terms of a new set of variables introduced earlier in the continuum. This theory uses local 'corner' variables defined on lattice sites only, as opposed to the conventional 'link' variables. It is shown via a map that the formulation gives identical results to the usual lattice gauge theory. The properties of the quantum commutators in the continuum limit is also discussed and contrasted for the two lattice approaches. In terms of the corner operators the quantized lattice theory is seen to be closely related to continuum QCD. (Auth.)

  5. On the stochastic quantization of gauge theories

    Energy Technology Data Exchange (ETDEWEB)

    Jona-Lasinio, G.; Parrinello, C.

    1988-11-03

    The non-gradient stochastic quantization scheme for gauge theories proposed by Zwanziger is analyzed in the semiclassical limit. Using ideas from the theory of small random perturbations of dynamical systems we derive a lower bound for the equilibrium distribution in a neighbourhood of a stable critical point of the drift. In this approach the calculation of the equilibrium distribution is reduced to the problem of finding a minimum for the large fluctuation functional associated to the Langevin equation. Our estimate follows from a simple upper bound for this minimum; in addition to the Yang-Mills action a gauge-fixing term which tends to suppress Gribov copies appears.

  6. Towards a theory of geometric graphs

    CERN Document Server

    Pach, Janos

    2004-01-01

    The early development of graph theory was heavily motivated and influenced by topological and geometric themes, such as the Konigsberg Bridge Problem, Euler's Polyhedral Formula, or Kuratowski's characterization of planar graphs. In 1936, when Denes Konig published his classical Theory of Finite and Infinite Graphs, the first book ever written on the subject, he stressed this connection by adding the subtitle Combinatorial Topology of Systems of Segments. He wanted to emphasize that the subject of his investigations was very concrete: planar figures consisting of points connected by straight-line segments. However, in the second half of the twentieth century, graph theoretical research took an interesting turn. In the most popular and most rapidly growing areas (the theory of random graphs, Ramsey theory, extremal graph theory, algebraic graph theory, etc.), graphs were considered as abstract binary relations rather than geometric objects. Many of the powerful techniques developed in these fields have been su...

  7. Non-Abelian gauge theory of fields associated with dyons

    International Nuclear Information System (INIS)

    Rajput, B.S.; Kumar, S.R.

    1983-01-01

    A suitable Lorentz invariant non-Abelian gauge theory of the fields associated with dyons has been constructed to describe the dual dynamics between colour isocharges and topological charges. It has been shown that the generalized particle current is gauge covariant and not conserved in non-Abelian theory. It has also been shown that in this theory the unphysical string variables and unphysical charged fields are not needed and that any extra constraint to maintain the dual symmetry of field equation and Lagrangian is also not needed. (author)

  8. Vortex operators in gauge field theories

    International Nuclear Information System (INIS)

    Polchinski, J.

    1980-07-01

    Several related aspects of the 't Hooft vortex operator are studied. The current picture of the vacuum of quantum chromodynamics, the idea of dual field theories, and the idea of the vortex operator are reviewed first. The Abelian vortex operator written in terms of elementary fields and the calculation of its Green's functions are considered. A two-dimensional solvable model of a Dirac string is presented. The expression of the Green's functions more neatly in terms of Wu and Yang's geometrical idea of sections is addressed. The renormalization of the Green's functions of two kinds of Abelian looplike operators, the Wilson loop and the vortex operator, is studied; for both operators only an overall multiplicative renormalization is needed. In the case of the vortex this involves a surprising cancellation. Next, the dependence of the Green's functions of the Wilson and 't Hooft operators on the nature of the vacuum is discussed. The cluster properties of the Green's functions are emphasized. It is seen that the vortex operator in a massive Abelian theory always has surface-like clustering. The form of Green's functions in terms of Feynman graphs is the same in Higgs and symmetric phases; the difference appears in the sum over all tadpole trees. Finally, systems having fields in the fundamental representation are considered. When these fields enter only weakly into the dynamics, a vortex-like operator is anticipated. Any such operator can no longer be local looplike, but must have commutators at long range. A U(1) lattice gauge theory with two matter fields, one singly charged (fundamental) and one doubly charged (adjoint), is examined. When the fundamental field is weakly coupled, the expected phase transitions are found. When it is strongly coupled, the operator still appears to be a good order parameter, a discontinuous change in its behavior leads to a new phase transition. 18 figures

  9. Coarse-graining free theories with gauge symmetries: the linearized case

    International Nuclear Information System (INIS)

    Bahr, Benjamin; Dittrich, Bianca; He Song

    2011-01-01

    Discretizations of continuum theories often do not preserve the gauge symmetry content. This occurs in particular for diffeomorphism symmetry in general relativity, which leads to severe difficulties in both canonical and covariant quantization approaches. We discuss here the method of perfect actions, which attempts to restore gauge symmetries by mirroring exactly continuum physics on a lattice via a coarse graining process. Analytical results can only be obtained via a perturbative approach, for which we consider the first step, namely the coarse graining of the linearized theory. The linearized gauge symmetries are exact also in the discretized theory; hence, we develop a formalism to deal with gauge systems. Finally, we provide a discretization of linearized gravity as well as a coarse graining map and show that with this choice the three-dimensional (3D) linearized gravity action is invariant under coarse graining.

  10. Correspondence between quantum gauge theories without ghost fields and their covariantly quantized theories with ghost fields

    International Nuclear Information System (INIS)

    Cheng Hung; Tsai Ercheng

    1986-01-01

    We give a correspondence formula which equates transition amplitudes in a quantum gauge field theory without ghost fields to those in a quantum theory with the gauge fields covariantly quantized and coupled to ghost fields. (orig.)

  11. Perturbative quantum gravity as a double copy of gauge theory.

    Science.gov (United States)

    Bern, Zvi; Carrasco, John Joseph M; Johansson, Henrik

    2010-08-06

    In a previous paper we observed that (classical) tree-level gauge-theory amplitudes can be rearranged to display a duality between color and kinematics. Once this is imposed, gravity amplitudes are obtained using two copies of gauge-theory diagram numerators. Here we conjecture that this duality persists to all quantum loop orders and can thus be used to obtain multiloop gravity amplitudes easily from gauge-theory ones. As a nontrivial test, we show that the three-loop four-point amplitude of N=4 super-Yang-Mills theory can be arranged into a form satisfying the duality, and by taking double copies of the diagram numerators we obtain the corresponding amplitude of N=8 supergravity. We also remark on a nonsupersymmetric two-loop test based on pure Yang-Mills theory resulting in gravity coupled to an antisymmetric tensor and dilaton.

  12. Generalization of trinification to theories with 3N SU(3) gauge groups

    International Nuclear Information System (INIS)

    Carone, Christopher D.

    2005-01-01

    We consider a natural generalization of trinification to theories with 3N SU(3) gauge groups. These theories have a simple moose representation and a gauge boson spectrum that can be interpreted via the deconstruction of a 5D theory with unified symmetry broken on a boundary. Although the matter and Higgs sectors of the theory have no simple extra-dimensional analog, gauge unification retains features characteristic of the 5D theory. We determine possible assignments of the matter and Higgs fields to unified multiplets and present theories that are viable alternatives to minimal trinified GUTs

  13. Differential formalism aspects of the gauge classical theories

    International Nuclear Information System (INIS)

    Stedile, E.

    1982-01-01

    The classical aspects of the gauge theories are shown using differential geometry as fundamental tool. Somme comments are done about Maxwell Electro-dynamics, classical Yang-Mills and gravitation theories. (L.C.) [pt

  14. Non-Abelian duality in N = 4 supersymmetric gauge theories

    International Nuclear Information System (INIS)

    Dorey, Nicholas; Fraser, Christophe; Hollowood, Timithy J.; Kneipp, Marco A.C.

    1996-03-01

    A semi-classical check of the Goddard-Nuyts-Olive (GNO) generalized duality conjecture for gauge theories with adjoint Higgs fields is performed for the case where the unbroken gauge group is non-Abelian. The monopole solutions of the theory transform under the non-Abelian part of the unbroken global symmetry and the associated component of the moduli space is a Lie group coset space. The well-known problems in introducing collective coordinates for these degrees-of-freedom are solved by considering suitable multi monopole configurations in which the long-range non-Abelian fields cancel. In the context of an N = 4 supersymmetric gauge theory, the multiplicity of BPS saturated states is given by the number of ground-states of a supersymmetric quantum mechanics on the compact internal moduli space. The resulting degeneracy is expressed as the Euler character of the coset space. In all cases the number of states is consistent with the dimensions of the multiplets of the unbroken dual gauge group, and hence the results provide strong support for the GNO conjecture. (author). 39 refs

  15. Classical gauge theories on the coadjoint orbits of infinite dimensional groups

    International Nuclear Information System (INIS)

    Grabowski, M.P.; Virginia Polytechnic Inst. and State Univ., Blacksburg; Tze Chiahsiung

    1991-01-01

    We reformulate several classical gauge theories on the coadjoint orbits of the semidirect product of the gauge group and the Weyl group. The construction is given for the Yang-Mills theories in arbitrary spacetime dimension d, Chern-Simons topological theory (d=3) and higher dimensional topological models of Horowitz (d≥4). (orig.)

  16. Supersymmetric gauge theories, quantization of M{sub flat}, and conformal field theory

    Energy Technology Data Exchange (ETDEWEB)

    Teschner, J.; Vartanov, G.S.

    2013-02-15

    We propose a derivation of the correspondence between certain gauge theories with N=2 supersymmetry and conformal field theory discovered by Alday, Gaiotto and Tachikawa in the spirit of Seiberg-Witten theory. Based on certain results from the literature we argue that the quantum theory of the moduli spaces of flat SL(2,R)-connections represents a nonperturbative ''skeleton'' of the gauge theory, protected by supersymmetry. It follows that instanton partition functions can be characterized as solutions to a Riemann-Hilbert type problem. In order to solve it, we describe the quantization of the moduli spaces of flat connections explicitly in terms of two natural sets of Darboux coordinates. The kernel describing the relation between the two pictures represents the solution to the Riemann Hilbert problem, and is naturally identified with the Liouville conformal blocks.

  17. QCD gauge symmetries through Faddeev-Jackiw symplectic method

    International Nuclear Information System (INIS)

    Abreu, E.M.C.; Mendes, A.C.R.; Neves, C.; Oliveira, W.; Silva, R.C.N.

    2013-01-01

    Full text: The FJ method is an approach that is geometrically motivated. It is based on the symplectic structure of the phase space. The first-order characteristic allows to obtain the Hamiltonian equations of motion from a variational principle. Its geometric structure of the Hamiltonian phase-space will be carried out directly from the equations of motion via the inverse of the so-called symplectic two-form, if the inverse exists. Few years after its publication, the FJ formalism was extended and through the years it has been applied to different systems. Gauge invariance is one of the most well established concepts in theoretical physics and it is one of the main ingredients in Standard Model theory. However, we can ask if it could have an alternative origin connected to another theory or principle. With this motivation in mind we will show in this paper that gauge invariance could be considered an emergent concept having its origin in the algebraic formalism of a well known method that deals with constrained systems, namely, the Faddeev-Jackiw (FJ) technique. Of course the gauge invariance idea is older than FJ's, but the results obtained here will show that the connection between both will prove that SU(3) and SU(3) X SU(2) X U(1) gauge groups, which are fundamental to important theories like QCD and Standard Model, can be obtained through FJ formalism. (author)

  18. On the structure of generalized monopole solutions in gauge-theories

    International Nuclear Information System (INIS)

    Horvath, Z.; Palla, L.

    1976-01-01

    A method is presented for constructing generalized 't Hooft monopole solutions in a gauge theory with an arbitrary gauge group. Restrictions arising from the condition of finite energy are derived. The radial oscillation of the solution is discussed. Using this method all the SU(3) solutions known in the literature are reproduced. Finite energy monopoles possessing magnetic charge in the range g 0 0 0 are found in SU(N) gauge theories. Different charge quantization conditions are analyzed to understand the structure of the solutions. (Auth.)

  19. Towards a manifestly gauge invariant and universal calculus for Jang-Mills theory

    International Nuclear Information System (INIS)

    Arnone, S.; Gatti, A.; Morris, T.R.

    2002-01-01

    A manifestly gauge invariant exact renormalization group for pure SU (N) Jang-Mills theory is proposed, along with the necessary gauge invariant regularisation which implements the effective cutoff. The latter is naturally incorporated by embedding the theory into a spontaneously broken SU(N/N) super-gauge theory, which guarantees finiteness to all orders in perturbation theory. The effective action, from which one extracts the physics, can be computed whilst manifestly preserving gauge invariance at each and every step. As an example, we give an elegant computation of the one-loop SU(N) Jang-Mills beta function, for the first time at finite N without any gauge fixing or ghosts. It is also completely independent of the details put in by hand, e.g. the choice of covariantisation and the cutoff profile, and, therefore, guides us to a procedure for streamlined calculations (Authors)

  20. Renormalization of supersymmetric gauge theories on orbifolds: Brane gauge couplings and higher derivative operators

    International Nuclear Information System (INIS)

    Groot Nibbelink, Stefan; Hillenbach, Mark

    2005-01-01

    We consider supersymmetric gauge theories coupled to hypermultiplets on five- and six-dimensional orbifolds and determine the bulk and local fixed point renormalizations of the gauge couplings. We infer from a component analysis that the hypermultiplet does not induce renormalization of the brane gauge couplings on the five-dimensional orbifold S 1 /Z 2 . This is not due to supersymmetry, since the bosonic and fermionic contributions cancel separately. We extend this investigation to T 2 /Z N orbifolds using supergraph techniques in six dimensions. On general Z N orbifolds the gauge couplings do renormalize at the fixed points, except for the Z 2 fixed points of even ordered orbifolds. To cancel the bulk one-loop divergences a dimension six higher derivative operator is needed, in addition to the standard bulk gauge kinetic term.

  1. Gauged supersymmetries in Yang-Mills theory

    International Nuclear Information System (INIS)

    Tissier, Matthieu; Wschebor, Nicolas

    2009-01-01

    In this paper we show that Yang-Mills theory in the Curci-Ferrari-Delbourgo-Jarvis gauge admits some up to now unknown local linear Ward identities. These identities imply some nonrenormalization theorems with practical simplifications for perturbation theory. We show, in particular, that all renormalization factors can be extracted from two-point functions. The Ward identities are shown to be related to supergauge transformations in the superfield formalism for Yang-Mills theory. The case of nonzero Curci-Ferrari mass is also addressed.

  2. Unified Gauge Theories and Reduction of Couplings: from Finiteness to Fuzzy Extra Dimensions

    Directory of Open Access Journals (Sweden)

    George Zoupanos

    2008-02-01

    Full Text Available Finite Unified Theories (FUTs are N = 1 supersymmetric Grand Unified Theories, which can be made all-loop finite, both in the dimensionless (gauge and Yukawa couplings and dimensionful (soft supersymmetry breaking terms sectors. This remarkable property, based on the reduction of couplings at the quantum level, provides a drastic reduction in the number of free parameters, which in turn leads to an accurate prediction of the top quark mass in the dimensionless sector, and predictions for the Higgs boson mass and the supersymmetric spectrum in the dimensionful sector. Here we examine the predictions of two such FUTs. Next we consider gauge theories defined in higher dimensions, where the extra dimensions form a fuzzy space (a finite matrix manifold. We reinterpret these gauge theories as four-dimensional theories with Kaluza-Klein modes. We then perform a generalized à la Forgacs-Manton dimensional reduction. We emphasize some striking features emerging such as (i the appearance of non-Abelian gauge theories in four dimensions starting from an Abelian gauge theory in higher dimensions, (ii the fact that the spontaneous symmetry breaking of the theory takes place entirely in the extra dimensions and (iii the renormalizability of the theory both in higher as well as in four dimensions. Then reversing the above approach we present a renormalizable four dimensional SU(N gauge theory with a suitable multiplet of scalar fields, which via spontaneous symmetry breaking dynamically develops extra dimensions in the form of a fuzzy sphere SN2. We explicitly find the tower of massive Kaluza-Klein modes consistent with an interpretation as gauge theory on M4 × S2, the scalars being interpreted as gauge fields on S2. Depending on the parameters of the model the low-energy gauge group can be SU(n, or broken further to SU(n1 × SU(n2 × U(1. Therefore the second picture justifies the first one in a renormalizable framework but in addition has the potential to

  3. Extended BRST symmetries in the gauge field theory

    International Nuclear Information System (INIS)

    Babalean, Aurel; Constantinescu, Radu; Ionescu, Carmen

    2001-01-01

    The BRST procedure provides one of the most powerful methods for the quantum description of the gauge field theories. As already stated, the unphysical degrees of freedom that appear in this case can be easily canceled by the introduction of the ghost type variables. In the Hamiltonian formalism, the structure of the ghost that must be used mainly depends on two factors: - the type of the theory, that this the relations among the constraints of the theory; - the extension of the symmetry to be implemented. The paper presents the structure of the extended phase space suitable for the BRST canonical quantization of a 1- reducible gauge theory in the frame of a BRST symmetry of order three. The corresponding BRST charges and the extended Hamiltonian are also constructed. (authors)

  4. New Methods in Supersymmetric Theories and Emergent Gauge Symmetry

    CERN Multimedia

    CERN. Geneva

    2014-01-01

    It is remarkable that light or even massless spin 1 particles can be composite. Consequently, gauge invariance is not fundamental but emergent. This idea can be realized in detail in supersymmetric gauge theories. We will describe the recent development of non-perturbative methods that allow to test this idea. One finds that the emergence of gauge symmetry is linked to some results in contemporary mathematics. We speculate on the possible applications of the idea of emergent gauge symmetry to realistic models.

  5. Duffin-Kemmer formulation of spin one-half particle gauge theory

    International Nuclear Information System (INIS)

    Samiullah, M.; Mansour, H.M.M.

    1981-02-01

    We have gauge formulated the spin one-half particle equation in the Duffin-Kemmer formalism of Barut et al. The theory distinguishes between the left and the right chiral states and has a built in chirality. As an example the theory has been applied to the Weinberg Salam model reproducing all its essential features. In view of the built in chirality a lattice gauge version of such a theory is expected to be useful. (author)

  6. U(1) Wilson lattice gauge theories in digital quantum simulators

    Science.gov (United States)

    Muschik, Christine; Heyl, Markus; Martinez, Esteban; Monz, Thomas; Schindler, Philipp; Vogell, Berit; Dalmonte, Marcello; Hauke, Philipp; Blatt, Rainer; Zoller, Peter

    2017-10-01

    Lattice gauge theories describe fundamental phenomena in nature, but calculating their real-time dynamics on classical computers is notoriously difficult. In a recent publication (Martinez et al 2016 Nature 534 516), we proposed and experimentally demonstrated a digital quantum simulation of the paradigmatic Schwinger model, a U(1)-Wilson lattice gauge theory describing the interplay between fermionic matter and gauge bosons. Here, we provide a detailed theoretical analysis of the performance and the potential of this protocol. Our strategy is based on analytically integrating out the gauge bosons, which preserves exact gauge invariance but results in complicated long-range interactions between the matter fields. Trapped-ion platforms are naturally suited to implementing these interactions, allowing for an efficient quantum simulation of the model, with a number of gate operations that scales polynomially with system size. Employing numerical simulations, we illustrate that relevant phenomena can be observed in larger experimental systems, using as an example the production of particle-antiparticle pairs after a quantum quench. We investigate theoretically the robustness of the scheme towards generic error sources, and show that near-future experiments can reach regimes where finite-size effects are insignificant. We also discuss the challenges in quantum simulating the continuum limit of the theory. Using our scheme, fundamental phenomena of lattice gauge theories can be probed using a broad set of experimentally accessible observables, including the entanglement entropy and the vacuum persistence amplitude.

  7. Matrix models from localization of five-dimensional supersymmetric noncommutative U(1) gauge theory

    International Nuclear Information System (INIS)

    Lee, Bum-Hoon; Ro, Daeho; Yang, Hyun Seok

    2017-01-01

    We study localization of five-dimensional supersymmetric U(1) gauge theory on S 3 ×ℝ θ 2 where ℝ θ 2 is a noncommutative (NC) plane. The theory can be isomorphically mapped to three-dimensional supersymmetric U(N→∞) gauge theory on S 3 using the matrix representation on a separable Hilbert space on which NC fields linearly act. Therefore the NC space ℝ θ 2 allows for a flexible path to derive matrix models via localization from a higher-dimensional supersymmetric NC U(1) gauge theory. The result shows a rich duality between NC U(1) gauge theories and large N matrix models in various dimensions.

  8. Physical analysis of some features of the gauge theories with Higgs sectors

    International Nuclear Information System (INIS)

    Beshtoev, Kh.M.

    1995-01-01

    A physical analysis of some features of the gauge theories with Higgs sectors is made. It is shown that we should assume gauge transformations in the fermion and Higgs sectors to be different (i.e., to have different charges) in order to remove contradictions arising in gauge theories with Higgs sectors. Then, the Higgs mechanism can be interpreted as some mechanism of gauge field shielding. In such a mechanism fermions remain without masses. The conclusion is made that in the standard theory of the development of the Universe, monopoles cannot survive at low temperatures. 15 refs

  9. Solution of quantum integrable systems from quiver gauge theories

    Energy Technology Data Exchange (ETDEWEB)

    Dorey, Nick [Department of Applied Mathematics and Theoretical Physics, University of Cambridge,Cambridge (United Kingdom); Zhao, Peng [Simons Center for Geometry and Physics, Stony Brook University,Stony Brook (United States)

    2017-02-23

    We construct new integrable systems describing particles with internal spin from four-dimensional N = 2 quiver gauge theories. The models can be quantized and solved exactly using the quantum inverse scattering method and also using the Bethe/Gauge correspondence.

  10. Spontaneous symmetry breakdown in gauge theories

    International Nuclear Information System (INIS)

    Scadron, M.D.

    1982-01-01

    The dynamical theory of spontaneous breakdown correctly predicts the bound states and relates the order parameters of electron-photon superconductivity and quark-gluon chiral symmetry. A similar statement cannot be made for the standard electro-weak gauge symmetry. (author)

  11. Status of glueball mass calculations in lattice gauge theory

    International Nuclear Information System (INIS)

    Kronfeld, A.S.

    1989-11-01

    The status of glueball spectrum calculations in lattice gauge theory is briefly reviewed, with focus on the comparison between Monte Carlo simulations and small-volume analytical calculations in SU(3). The agreement gives confidence that the large-volume Monte Carlo results are accurate, at least in the context of the pure gauge theory. An overview of some of the technical questions, which is aimed at non-experts, serves as an introduction. 19 refs., 1 fig

  12. Gauge theory of the post-Galilean groups

    International Nuclear Information System (INIS)

    Dimakis, A.

    1985-01-01

    By means of an extension of the field of real numbers we construct post-Galilean groups, which in a sense lay between the Galilean group and the Lorentz group. By gauging these groups we obtain a frame theory of gravitation, which comprises Newton--Cartan theory, general relativity, and an infinite number of intermediate theories. This leads to a better understanding of how the structural differences of the two main theories of gravitation arise

  13. Masslessness of ghosts in equivariantly gauge-fixed Yang-Mills theories

    International Nuclear Information System (INIS)

    Golterman, Maarten; Zimmerman, Leah

    2005-01-01

    We show that the one-loop ghost self-energy in an equivariantly gauge-fixed Yang-Mills theory vanishes at zero momentum. A ghost mass is forbidden by equivariant BRST symmetry, and our calculation confirms this explicitly. The four-ghost self interaction which appears in the equivariantly gauge-fixed Yang-Mills theory is needed in order to obtain this result

  14. Monopole dynamics of yang-mills theory without gauge-fixing

    International Nuclear Information System (INIS)

    Jia Duojie; Li Xiguo

    2003-01-01

    A new off-shell decomposition of SU(2) gauge field without any gauge fixing is proposed. This decomposition yields, for an appropriate gauge-fixing, a Skyme-Faddeev-like Wilsonian action and confirms the presence of high-order derivatives of a color-unit-vector at the classical level. The 't Hooft's conjecture that 'monopole' dynamics of infrared Yang-Mills theory is projection independent is also independently demonstrated

  15. Gauge theories from toric geometry and brane tilings

    International Nuclear Information System (INIS)

    Franco, Sebastian; Hanany, Amihay; Martelli, Dario; Sparks, James; Vegh, David; Wecht, Brian

    2006-01-01

    We provide a general set of rules for extracting the data defining a quiver gauge theory from a given toric Calabi-Yau singularity. Our method combines information from the geometry and topology of Sasaki-Einstein manifolds, AdS/CFT, dimers, and brane tilings. We explain how the field content, quantum numbers, and superpotential of a superconformal gauge theory on D3-branes probing a toric Calabi-Yau singularity can be deduced. The infinite family of toric singularities with known horizon Sasaki-Einstein manifolds L a,b,c is used to illustrate these ideas. We construct the corresponding quiver gauge theories, which may be fully specified by giving a tiling of the plane by hexagons with certain gluing rules. As checks of this construction, we perform a-maximisation as well as Z-minimisation to compute the exact R-charges of an arbitrary such quiver. We also examine a number of examples in detail, including the infinite subfamily L a,b,a , whose smallest member is the Suspended Pinch Point

  16. Quantum communication, reference frames, and gauge theory

    International Nuclear Information System (INIS)

    Enk, S. J. van

    2006-01-01

    We consider quantum communication in the case that the communicating parties not only do not share a reference frame but use imperfect quantum communication channels, in that each channel applies some fixed but unknown unitary rotation to each qubit. We discuss similarities and differences between reference frames within that quantum communication model and gauge fields in gauge theory. We generalize the concept of refbits and analyze various quantum communication protocols within the communication model

  17. The application of *-products to noncommutative geometry and gauge theory

    International Nuclear Information System (INIS)

    Sykora, A.

    2004-06-01

    Due to the singularities arising in quantum field theory and the difficulties in quantizing gravity it is often believed that the description of spacetime by a smooth manifold should be given up at small length scales or high energies. In this work we will replace spacetime by noncommutative structures arising within the framework of deformation quantization. The ordinary product between functions will be replaced by a *-product, an associative product for the space of functions on a manifold. We develop a formalism to realize algebras defined by relations on function spaces. For this purpose we construct the Weyl-ordered *-product and present a method how to calculate *-products with the help of commuting vector fields. Concepts developed in noncommutative differential geometry will be applied to this type of algebras and we construct actions for noncommutative field theories. In the classical limit these noncommutative theories become field theories on manifolds with nonvanishing curvature. It becomes clear that the application of *-products is very fruitful to the solution of noncommutative problems. In the semiclassical limit every *-product is related to a Poisson structure, every derivation of the algebra to a vector field on the manifold. Since in this limit many problems are reduced to a couple of differential equations the *-product representation makes it possible to construct noncommutative spaces corresponding to interesting Riemannian manifolds. Derivations of *-products makes it further possible to extend noncommutative gauge theory in the Seiberg-Witten formalism with covariant derivatives. The resulting noncommutative gauge fields may be interpreted as one forms of a generalization of the exterior algebra of a manifold. For the Formality *-product we prove the existence of the abelian Seiberg-Witten map for derivations of these *-products. We calculate the enveloping algebra valued non abelian Seiberg-Witten map pertubatively up to second order for

  18. Interfaces in hot gauge theory

    CERN Document Server

    Bronoff, S.

    1996-01-01

    The string tension at low T and the free energy of domain walls at high T can be computed from one and the same observable. We show by explicit calculation that domain walls in hot Z(2) gauge theory have good thermodynamical behaviour. This is due to roughening of the wall, which expresses the restoration of translational symmetry.

  19. Perturbative Gravity and Gauge Theory Relations: A Review

    Directory of Open Access Journals (Sweden)

    Thomas Søndergaard

    2012-01-01

    Full Text Available This paper is dedicated to the amazing Kawai-Lewellen-Tye relations, connecting perturbative gravity and gauge theories at tree level. The main focus is on n-point derivations and general properties both from a string theory and pure field theory point of view. In particular, the field theory part is based on some very recent developments.

  20. Webs of domain walls in supersymmetric gauge theories

    International Nuclear Information System (INIS)

    Eto, Minoru; Isozumi, Youichi; Nitta, Muneto; Ohashi, Keisuke; Sakai, Norisuke

    2005-01-01

    Webs of domain walls are constructed as 1/4 Bogomol'nyi-Prasad-Sommerfield (BPS) states in d=4, N=2 supersymmetric U(N C ) gauge theories with N F hypermultiplets in the fundamental representation. Webs of walls can contain any numbers of external legs and loops like (p,q) string/5-brane webs. We find the moduli space M of a 1/4 BPS equation for wall webs to be the complex Grassmann manifold. When moduli spaces of 1/2 BPS states (parallel walls) and the vacua are removed from M, the noncompact moduli space of genuine 1/4 BPS wall webs is obtained. All the solutions are obtained explicitly and exactly in the strong gauge coupling limit. In the case of Abelian gauge theory, we work out the correspondence between configurations of wall web and the moduli space CP N F -1

  1. Algebraic computing program for studying the gauge theory

    International Nuclear Information System (INIS)

    Zet, G.

    2005-01-01

    An algebraic computing program running on Maple V platform is presented. The program is devoted to the study of the gauge theory with an internal Lie group as local symmetry. The physical quantities (gauge potentials, strength tensors, dual tensors etc.) are introduced either as equations in terms of previous defined quantities (tensors), or by manual entry of the component values. The components of the strength tensor and of its dual are obtained with respect to a given metric of the space-time used for describing the gauge theory. We choose a Minkowski space-time endowed with spherical symmetry and give some example of algebraic computing that are adequate for studying electroweak or gravitational interactions. The field equations are also obtained and their solutions are determined using the DEtools facilities of the Maple V computing program. (author)

  2. The a theorem for Gauge-Yukawa theories beyond Banks-Zaks

    DEFF Research Database (Denmark)

    Antipin, Oleg; Gillioz, Marc; Mølgaard, Esben

    2013-01-01

    We investigate the a theorem for nonsupersymmetric gauge-Yukawa theories beyond the leading order in perturbation theory. The exploration is first performed in a model-independent manner and then applied to a specific relevant example. Here, a rich fixed point structure appears including the pres......We investigate the a theorem for nonsupersymmetric gauge-Yukawa theories beyond the leading order in perturbation theory. The exploration is first performed in a model-independent manner and then applied to a specific relevant example. Here, a rich fixed point structure appears including...

  3. A direct derivation of polynomial invariants from perturbative Chern-Simons gauge theory

    International Nuclear Information System (INIS)

    Ochiai, Tomoshiro

    2003-01-01

    There have been several methods to show that the expectation values of Wilson loop operators in the SU(N) Chern-Simons gauge theory satisfy the HOMFLY skein relation. We shall give another method from the perturbative method of the SU(N) Chern-Simons gauge theory in the light-cone gauge, which is more direct than already known methods

  4. A note on gauge fixing in theories of extended objects

    International Nuclear Information System (INIS)

    Sezgin, E.

    1989-08-01

    We discuss the light-cone type gauges (old and new) and the associated residual symmetries in theories of extended objects. We also discuss certain covariant gauges and in particular a covariant gauge for membranes which admits the contact diffeomorphisms of the world-volume as a residual symmetry. (author). 12 refs

  5. Atomic Quantum Simulations of Abelian and non-Abelian Gauge Theories

    CERN Multimedia

    CERN. Geneva

    2014-01-01

    Using a Fermi-Bose mixture of ultra-cold atoms in an optical lattice, in a collaboration of atomic and particle physicists, we have constructed a quantum simulator for a U(1) gauge theory coupled to fermionic matter. The construction is based on quantum link models which realize continuous gauge symmetry with discrete quantum variables. At low energies, quantum link models with staggered fermions emerge from a Hubbard-type model which can be quantum simulated. This allows investigations of string breaking as well as the real-time evolution after a quench in gauge theories, which are inaccessible to classical simulation methods. Similarly, using ultracold alkaline-earth atoms in optical lattices, we have constructed a quantum simulator for U(N) and SU(N) lattice gauge theories with fermionic matter based on quantum link models. These systems share qualitative features with QCD, including chiral symmetry breaking and restoration at non-zero temperature or baryon density. Unlike classical simulations, a quantum ...

  6. Integrability in N=2 superconformal gauge theorie

    Energy Technology Data Exchange (ETDEWEB)

    Pomoni, Elli [Deutsches Elektronen-Synchrotron DESY, Hamburg (Germany). Theory Group; National Technical Univ. of Athens (Greece). Physics Div.

    2013-10-15

    Any N=2 superconformal gauge theory (including N=4 SYM) contains a set of local operators made only out of fields in the N=2 vector multiplet that is closed under renormalization to all loops, namely the SU(2,1 vertical stroke 2) sector. For planar N=4 SYM the spectrum of local operators can be obtained by mapping the problem to an integrable model (a spin chain in perturbation theory), in principle for any value of the coupling constant. We present a diagrammatic argument that for any planar N=2 superconformal gauge theory the SU(2,1 vertical stroke 2) Hamiltonian acting on infinite spin chains is identical to all loops to that of N=4 SYM, up to a redefinition of the coupling constant. Thus, this sector is integrable and anomalous dimensions can be, in principle, read off from the N=4 ones up to this redefinition.

  7. Integrability in N=2 superconformal gauge theories

    International Nuclear Information System (INIS)

    Pomoni, Elli; National Technical Univ. of Athens

    2013-10-01

    Any N=2 superconformal gauge theory (including N=4 SYM) contains a set of local operators made only out of fields in the N=2 vector multiplet that is closed under renormalization to all loops, namely the SU(2,1 vertical stroke 2) sector. For planar N=4 SYM the spectrum of local operators can be obtained by mapping the problem to an integrable model (a spin chain in perturbation theory), in principle for any value of the coupling constant. We present a diagrammatic argument that for any planar N=2 superconformal gauge theory the SU(2,1 vertical stroke 2) Hamiltonian acting on infinite spin chains is identical to all loops to that of N=4 SYM, up to a redefinition of the coupling constant. Thus, this sector is integrable and anomalous dimensions can be, in principle, read off from the N=4 ones up to this redefinition.

  8. G{sub 2}-structures and quantization of non-geometric M-theory backgrounds

    Energy Technology Data Exchange (ETDEWEB)

    Kupriyanov, Vladislav G. [Centro de Matemática, Computação e Cognição, Universidade de Federal do ABC,Santo André, SP (Brazil); Tomsk State University,Tomsk (Russian Federation); Szabo, Richard J. [Department of Mathematics, Heriot-Watt University,Colin Maclaurin Building, Riccarton, Edinburgh EH14 4AS (United Kingdom); Maxwell Institute for Mathematical Sciences,Edinburgh (United Kingdom); The Higgs Centre for Theoretical Physics,Edinburgh (United Kingdom)

    2017-02-20

    We describe the quantization of a four-dimensional locally non-geometric M-theory background dual to a twisted three-torus by deriving a phase space star product for deformation quantization of quasi-Poisson brackets related to the nonassociative algebra of octonions. The construction is based on a choice of G{sub 2}-structure which defines a nonassociative deformation of the addition law on the seven-dimensional vector space of Fourier momenta. We demonstrate explicitly that this star product reduces to that of the three-dimensional parabolic constant R-flux model in the contraction of M-theory to string theory, and use it to derive quantum phase space uncertainty relations as well as triproducts for the nonassociative geometry of the four-dimensional configuration space. By extending the G{sub 2}-structure to a Spin(7)-structure, we propose a 3-algebra structure on the full eight-dimensional M2-brane phase space which reduces to the quasi-Poisson algebra after imposing a particular gauge constraint, and whose deformation quantisation simultaneously encompasses both the phase space star products and the configuration space triproducts. We demonstrate how these structures naturally fit in with previous occurences of 3-algebras in M-theory.

  9. Extended monopoles in gauge field theories

    International Nuclear Information System (INIS)

    Horvath, Z.; Palla, L.

    1977-04-01

    The paper gives a review of the 't Hooft monopole and briefly discusses the general topological considerations connected with monopoles. A method is presented for constructing explicit monopole solutions in any gauge theory. Some stability questions and time-dependent problems are also considered

  10. Lattice gauge theory on the hypercube

    International Nuclear Information System (INIS)

    Apostolakis, J.; Baillie, C.; Ding, Hong-Qiang; Flower, J.

    1988-01-01

    Lattice gauge theory, an extremely computationally intensive problem, has been run successfully on hypercubes for a number of years. Herein we give a flavor of this work, discussing both the physics and the computing behind it. 19 refs., 5 figs., 27 tabs

  11. Bootstrapping non-commutative gauge theories from L∞ algebras

    Science.gov (United States)

    Blumenhagen, Ralph; Brunner, Ilka; Kupriyanov, Vladislav; Lüst, Dieter

    2018-05-01

    Non-commutative gauge theories with a non-constant NC-parameter are investigated. As a novel approach, we propose that such theories should admit an underlying L∞ algebra, that governs not only the action of the symmetries but also the dynamics of the theory. Our approach is well motivated from string theory. We recall that such field theories arise in the context of branes in WZW models and briefly comment on its appearance for integrable deformations of AdS5 sigma models. For the SU(2) WZW model, we show that the earlier proposed matrix valued gauge theory on the fuzzy 2-sphere can be bootstrapped via an L∞ algebra. We then apply this approach to the construction of non-commutative Chern-Simons and Yang-Mills theories on flat and curved backgrounds with non-constant NC-structure. More concretely, up to the second order, we demonstrate how derivative and curvature corrections to the equations of motion can be bootstrapped in an algebraic way from the L∞ algebra. The appearance of a non-trivial A∞ algebra is discussed, as well.

  12. Applications of Jarzynski's relation in lattice gauge theories

    DEFF Research Database (Denmark)

    Nada, Alessandro; Caselle, Michele; Costagliola, Gianluca

    2016-01-01

    Jarzynski's equality is a well-known result in statistical mechanics, relating free-energy differences between equilibrium ensembles with fluctuations in the work performed during non-equilibrium transformations from one ensemble to the other. In this work, an extension of this relation to lattice...... gauge theory will be presented, along with numerical results for the ℤ2 gauge model in three dimensions and for the equation of state in SU(2) Yang-Mills theory in four dimensions. Then, further applications will be discussed, in particular for the Schrödinger functional and for the study of QCD...

  13. Phases of renormalized lattice gauge theories with fermions

    International Nuclear Information System (INIS)

    Caracciolo, S.; Menotti, P.; and INFN Sezione di Pisa, Italy)

    1979-01-01

    Starting from the formulation of gauge theories on a lattice we derive renormalization group transformation of the Migdal-Kadanoff type in the presence of fermions. We consider the effect of the fermion vacuum polarization on the gauge Lagrangian but we neglect fermion mass renormalization. We work out the weak coupling and strong coupling expansion in the same framework. Asymptotic freedom is recovered for the non-Abelian case provided the number of fermion multiplets is lower than a critical number. Fixed points are determined both for the U (1) and SU (2) case. We determine the renormalized trajectories and the phases of the theory

  14. Algebraic isomorphism in two-dimensional anomalous gauge theories

    International Nuclear Information System (INIS)

    Carvalhaes, C.G.; Belvedere, L.V.; Filho, H.B.; Natividade, C.P.

    1997-01-01

    The operator solution of the anomalous chiral Schwinger model is discussed on the basis of the general principles of Wightman field theory. Some basic structural properties of the model are analyzed taking a careful control on the Hilbert space associated with the Wightman functions. The isomorphism between gauge noninvariant and gauge invariant descriptions of the anomalous theory is established in terms of the corresponding field algebras. We show that (i) the Θ-vacuum representation and (ii) the suggested equivalence of vector Schwinger model and chiral Schwinger model cannot be established in terms of the intrinsic field algebra. copyright 1997 Academic Press, Inc

  15. Noncritical String Liouville Theory and Geometric Bootstrap Hypothesis

    Science.gov (United States)

    Hadasz, Leszek; Jaskólski, Zbigniew

    The applications of the existing Liouville theories for the description of the longitudinal dynamics of noncritical Nambu-Goto string are analyzed. We show that the recently developed DOZZ solution to the Liouville theory leads to the cut singularities in tree string amplitudes. We propose a new version of the Polyakov geometric approach to Liouville theory and formulate its basic consistency condition — the geometric bootstrap equation. Also in this approach the tree amplitudes develop cut singularities.

  16. Self-consistent normal ordering of gauge field theories

    International Nuclear Information System (INIS)

    Ruehl, W.

    1987-01-01

    Mean-field theories with a real action of unconstrained fields can be self-consistently normal ordered. This leads to a considerable improvement over standard mean-field theory. This concept is applied to lattice gauge theories. First an appropriate real action mean-field theory is constructed. The equations determining the Gaussian kernel necessary for self-consistent normal ordering of this mean-field theory are derived. (author). 4 refs

  17. The potentials of the gauged N=8 supergravity theories

    International Nuclear Information System (INIS)

    Hull, C.M.

    1985-01-01

    The potentials of the SO(p,q) gaugings of N=8 supergravity are investigated for critical points. The SO(7,1) gauging has no G 2 -invariant critical points, the SO(6,2) theory has no SU(3) invariant critical points and the SO(5,3) gauging has only one SO(5)-invariant critical point, with positive cosmological constant, SO(5) x SO(3) symmetry and no supersymmetry. (orig.)

  18. Can EPR non-locality be geometrical?

    International Nuclear Information System (INIS)

    Ne'eman, Y.

    1995-01-01

    The presence in Quantum Mechanics of non-local correlations is one of the two fundamentally non-intuitive features of that theory. The non-local correlations themselves fall into two classes: EPR and Geometrical. The non-local characteristics of the geometrical type are well-understood and are not suspected of possibly generating acausal features, such as faster-than-light propagation of information. This has especially become true since the emergence of a geometrical treatment for the relevant gauge theories, i.e. Fiber Bundle geometry, in which the quantum non-localities are seen to correspond to pure homotopy considerations. This aspect is reviewed in section 2. Contrary-wise, from its very conception, the EPR situation was felt to be paradoxical. It has been suggested that the non-local features of EPR might also derive from geometrical considerations, like all other non-local characteristics of QM. In[7], one of the authors was able to point out several plausibility arguments for this thesis, emphasizing in particular similarities between the non-local correlations provided by any gauge field theory and those required by the preservation of the quantum numbers of the original EPR state-vector, throughout its spatially-extended mode. The derivation was, however, somewhat incomplete, especially because of the apparent difference between, on the one hand, the closed spatial loops arising in the analysis of the geometrical non-localities, from Aharonov-Bohm and Berry phases to magnetic monopoles and instantons, and on the other hand, in the EPR case, the open line drawn by the positions of the two moving decay products of the disintegrating particle. In what follows, the authors endeavor to remove this obstacle and show that as in all other QM non-localities, EPR is somehow related to closed loops, almost involving homotopy considerations. They develop this view in section 3

  19. Holographic description of large N gauge theory

    International Nuclear Information System (INIS)

    Lee, Sung-Sik

    2011-01-01

    Based on the earlier work [S.-S. Lee, Nucl. Rev. B 832 (2010) 567], we derive a holographic dual for the D-dimensional U(N) lattice gauge theory from a first principle construction. The resulting theory is a lattice field theory of closed loops, dubbed as lattice loop field theory which is defined on a (D+1)-dimensional space. The lattice loop field theory is well defined non-perturbatively, and it becomes weakly coupled and local in the large N limit with a large 't Hooft coupling.

  20. Cosmic string in compactified gauge theory

    International Nuclear Information System (INIS)

    Nakamura, A.; Hirenzaki, S.; Shiraishi, K.

    1989-08-01

    A solution of the vortex type is given in a six-dimensional SU(2)xU(1) pure gauge theory coupled to Einstein gravity in a compactified background geometry. We construct the solution of an effective Abelian-Higgs model in terms of dimensional reduction. The solution, however, has a peculiarity in its physically relevant quantity, a deficit angle, which is given as a function of the ratio of the gauge couplings of SU(2) and U(1). The size of the extra space (sphere) is shown to vary with the distance from the axis of the 'string'. (author)

  1. The energy–momentum tensor(s in classical gauge theories

    Directory of Open Access Journals (Sweden)

    Daniel N. Blaschke

    2016-11-01

    Full Text Available We give an introduction to, and review of, the energy–momentum tensors in classical gauge field theories in Minkowski space, and to some extent also in curved space–time. For the canonical energy–momentum tensor of non-Abelian gauge fields and of matter fields coupled to such fields, we present a new and simple improvement procedure based on gauge invariance for constructing a gauge invariant, symmetric energy–momentum tensor. The relationship with the Einstein–Hilbert tensor following from the coupling to a gravitational field is also discussed.

  2. Gauge field governing parallel transport along mixed states

    International Nuclear Information System (INIS)

    Uhlmann, A.

    1990-01-01

    At first a short account is given of some basic notations and results on parallel transport along mixed states. A new connection form (gauge field) is introduced to give a geometric meaning to the concept of parallelity in the theory of density operators. (Author) 11 refs

  3. Connection dynamics of a gauge theory of gravity coupled with matter

    International Nuclear Information System (INIS)

    Yang, Jian; Banerjee, Kinjal; Ma, Yongge

    2013-01-01

    We study the coupling of the gravitational action, which is a linear combination of the Hilbert–Palatini term and the quadratic torsion term, to the action of Dirac fermions. The system possesses local Poincare invariance and hence belongs to Poincare gauge theory (PGT) with matter. The complete Hamiltonian analysis of the theory is carried out without gauge fixing but under certain ansatz on the coupling parameters, which leads to a consistent connection dynamics with second-class constraints and torsion. After performing a partial gauge fixing, all second-class constraints can be solved, and a SU(2)-connection dynamical formalism of the theory can be obtained. Hence, the techniques of loop quantum gravity (LQG) can be employed to quantize this PGT with non-zero torsion. Moreover, the Barbero–Immirzi parameter in LQG acquires its physical meaning as the coupling parameter between the Hilbert–Palatini term and the quadratic torsion term in this gauge theory of gravity. (paper)

  4. In what sense the canonical perturbation theory is gauge-invariant

    International Nuclear Information System (INIS)

    Chen, C.Y.

    1992-07-01

    It is shown that the time-dependent canonical perturbation theory in classical mechanics has unsatisfactory features when dealing with electromagnetic perturbed fields (the perturbed vector potential A-tilde ≠ 0). As a numerical apparatus, the theory relates to gauge-dependent vectors larger than expected. As an analytic apparatus, the theory is involved in unphysical concepts and yields inherently non-gauge-invariant formalisms. By defining the root cause of the problem, an alternative approach is accordingly introduced. (author). 8 refs, 2 figs

  5. Vortex operators in gauge field theories

    International Nuclear Information System (INIS)

    Polchinski, J.G.

    1980-01-01

    We study several related aspects of the t Hooft vortex operator. The first chapter reviews the current picture of the vacuum of quantum chromodynamics, the idea of dual field theories, and the idea of the vortex operator. The second chapter deals with the Abelian vortex operator written in terms of elementary fields and with the calculation of its Green's functions. The Dirac veto problem appears in a new guise. We present a two dimensional solvable model of a Dirac string. This leads us to a new solution of the veto problem; we discuss its extension to four dimensions. We then show how the Green's functions can be expressed more neatly in terms of Wu and Yang's geometrical idea of sections. In the third chapter we discuss the dependence of the Green's functions of the Wilson and t Hooft operators on the nature of the vacuum. In the fourth chapter we consider systems which have fields in the fundamental representation, so that there are no vortex operators. When these fields enter only weakly into the dynamics, as is the case in QCD and in real superconductors, we would expect to be able to define a vortex-like operator. We show that any such operator can no longer be local looplike, but must have commutators at long range. We can still find an operator with useful properties, its cluster property, though more complicated than that of the usual vortex operator, still appears to distinguish Higgs, confining and perturbative phases. To test this, we consider a U(1) lattice gauge theory with two matter fields, one singly charged (fundamental) and one doubly charged (adjoint)

  6. An introduction to gauge theories

    International Nuclear Information System (INIS)

    Iliopoulos, J.

    1976-01-01

    These lecture notes present an introduction to gauge theories: the systematics of Yang-Mills theories, spontaneous symmetry breaking, and Higgs mechanism. The treatment is simple, stressing the general principles rather than detailed calculations. We present the Weinberg-Salam model as an example of a renormalizable theory of weak and electromagnetic interactions of leptons, and we show that the extension of these ideas into the hadronic world requires the introduction of charm and colour. Finally, we try to include strong interactions into the scheme, guided by the experimental results of deep-inelastic lepton-nucleon scattering. We derive and solve the Callan-Symanzik equation, and we introduce the concepts of asymptotic freedom and quark confinement. (Author)

  7. Renormalization of non-abelian gauge theories in curved space-time

    International Nuclear Information System (INIS)

    Freeman, M.D.

    1984-01-01

    We use indirect, renormalization group arguments to calculate the gravitational counterterms needed to renormalize an interacting non-abelian gauge theory in curved space-time. This method makes it straightforward to calculate terms in the trace anomaly which first appear at high order in the coupling constant, some of which would need a 4-loop calculation to find directly. The role of gauge invariance in the theory is considered, and we discuss briefly the effect of using coordinate-dependent gauge-fixing terms. We conclude by suggesting possible applications of this work to models of the very early universe

  8. The chiral bosonization in non-Abelian gauge theories

    International Nuclear Information System (INIS)

    Andrianov, A.A.; Novozhilov, Y.

    1985-01-01

    The chiral bosonization in non-Abelian gauge theories is described starting directly from the QCD functional. For a given mass scale Λ, the QCD may be equivalently represented by colour chiral fields, gauge fields and high energy fermions. The effective action for colour chiral fields may admit the existence of a colour Skyrmion-boson with the baryon number 2/3. (author)

  9. Unification and geometrization of physics in the cosmological context

    International Nuclear Information System (INIS)

    Heller, M.; Watykanskie Obserwatorium Astronomiczne, Vatican

    1991-01-01

    Einstein belived that a good physical theory should posses an ''inner perfection''. Trace the inner perfection of the present gauge theories by contemplating their geometric structures (in terms of fibre bundles). The search for the ultimate symmetry of the unification of physics unavoidably leads to the unification of physics and cosmology. 4 figs., 23 refs. (author)

  10. Energy and angular-momentum non-conservation in four-dimensional gauge theories

    International Nuclear Information System (INIS)

    Manohar, A.

    1985-01-01

    We study energy and angular-momentum non-conservation on four-dimensional chiral gauge theories using Landau levels. These effects are physical manifestations of the usual gauge anomaly, and enable us to understand in a semi-classical approximation why anomaly cancellation is required for a consistent field theory. (orig.)

  11. Composite gauge bosons of transmuted gauge symmetry

    International Nuclear Information System (INIS)

    Terazawa, Hidezumi.

    1987-10-01

    It is shown that effective gauge theories of composite gauge bosons describing the dynamics of composite quarks and leptons can be transmuted from the subcolor gauge theory describing that of subquarks due to the condensation of subquarks and that the equality of effective gauge coupling constants can result as in a grand unified gauge theory. (author)

  12. Cluster-enriched Yang-Baxter equation from SUSY gauge theories

    Science.gov (United States)

    Yamazaki, Masahito

    2018-04-01

    We propose a new generalization of the Yang-Baxter equation, where the R-matrix depends on cluster y-variables in addition to the spectral parameters. We point out that we can construct solutions to this new equation from the recently found correspondence between Yang-Baxter equations and supersymmetric gauge theories. The S^2 partition function of a certain 2d N=(2,2) quiver gauge theory gives an R-matrix, whereas its FI parameters can be identified with the cluster y-variables.

  13. Quantum effects from a purely geometrical relativity theory

    International Nuclear Information System (INIS)

    Ellis, Homer G

    2005-01-01

    A purely geometrical relativity theory results from a construction that produces from three-dimensional space a happy unification of Kaluza's five-dimensional theory and Weyl's conformal theory. The theory can provide geometrical explanations for the following observed phenomena, among others: (a) visibility lifetimes of elementary particles of lengths inversely proportional to their rest masses; (b) the equality of charge magnitude among all charged particles interacting at an event; (c) the propensity of electrons in atoms to be seen in discretely spaced orbits; and (d) 'quantum jumps' between those orbits. This suggests the possibility that the theory can provide a deterministic underpinning of quantum mechanics like that provided to thermodynamics by the molecular theory of gases

  14. On the equivalence of vacuum equations of gauge quadratic theory of gravity and general relativity theory

    International Nuclear Information System (INIS)

    Zhitnikov, V.V.; Ponomarev, V.N.

    1986-01-01

    An attempt is made to compare the solution of field equations, corresponding to quadratic equations for the fields (g μν , Γ μν α ) in gauge gravitation theory (GGT) with general relativity theory solutions. Without restrictions for a concrete type of metrics only solutions of equations, for which torsion turns to zero, are considered. Equivalence of vacuum equations of gauge quadratic theory of gravity and general relativity theory is proved using the Newman-Penrose formalism

  15. Gauge theories of infinite dimensional Hamiltonian superalgebras

    International Nuclear Information System (INIS)

    Sezgin, E.

    1989-05-01

    Symplectic diffeomorphisms of a class of supermanifolds and the associated infinite dimensional Hamiltonian superalgebras, H(2M,N) are discussed. Applications to strings, membranes and higher spin field theories are considered: The embedding of the Ramond superconformal algebra in H(2,1) is obtained. The Chern-Simons gauge theory of symplectic super-diffeomorphisms is constructed. (author). 29 refs

  16. Origin of Abelian gauge symmetries in heterotic/F-theory duality

    International Nuclear Information System (INIS)

    Cvetič, Mirjam; Grassi, Antonella; Klevers, Denis; Poretschkin, Maximilian; Song, Peng

    2016-01-01

    We study aspects of heterotic/F-theory duality for compactifications with Abelian gauge symmetries. We consider F-theory on general Calabi-Yau manifolds with a rank one Mordell-Weil group of rational sections. By rigorously performing the stable degeneration limit in a class of toric models, we derive both the Calabi-Yau geometry as well as the spectral cover describing the vector bundle in the heterotic dual theory. We carefully investigate the spectral cover employing the group law on the elliptic curve in the heterotic theory. We find in explicit examples that there are three different classes of heterotic duals that have U(1) factors in their low energy effective theories: split spectral covers describing bundles with S(U(m)×U(1)) structure group, spectral covers containing torsional sections that seem to give rise to bundles with SU(m)×ℤ_k structure group and bundles with purely non-Abelian structure groups having a centralizer in E_8 containing a U(1) factor. In the former two cases, it is required that the elliptic fibration on the heterotic side has a non-trivial Mordell-Weil group. While the number of geometrically massless U(1)’s is determined entirely by geometry on the F-theory side, on the heterotic side the correct number of U(1)’s is found by taking into account a Stückelberg mechanism in the lower-dimensional effective theory. In geometry, this corresponds to the condition that sections in the two half K3 surfaces that arise in the stable degeneration limit of F-theory can be glued together globally.

  17. CP and other gauge symmetries in string theory

    International Nuclear Information System (INIS)

    Dine, M.; Leigh, R.G.; MacIntire, D.A.

    1992-01-01

    We argue that CP is a gauge symmetry in string theory. As a consequence, CP cannot be explicitly broken either perturbatively or nonperturbatively; there can be no nonperturbative CP-violating parameters. String theory is thus an example of a theory where all θ angles arise due to spontaneous CP violation, and are in principle calculable

  18. Prospects for gauge theories

    International Nuclear Information System (INIS)

    Bailin, D.

    1980-01-01

    The author reviews the present status of the standard model of weak and electromagnetic interactions and of QCD and examines the likely avenues of future development. The most attractive possibility is that there is a ''grand unified theory'' (GUT) which describes all known interactions except gravity, and in which the only input energy scale is the Planck mass. The GUTs so far proposed share the deficiency that they offer no explanation of the (>=3) observed fermion generations. The author reviews the 'horizontal' symmetries invented to bring order to the fermion sector. Typically such theories have non-minimal Higgs content, so he reviews the processes whereby charged or neutral scalars may be found. The incorporation of supersymmetry into the gauge theory of strong, weak and electromagnetic interactions is another attractive prospect and he discusses briefly the attempts to do this and the likely experimental signatures of such a scheme. (Auth.)

  19. Theory of a gauge gravitational field at localization of the Einstein group

    International Nuclear Information System (INIS)

    Tunyak, V.N.

    1985-01-01

    Theory of a gauge gravitational field when localizing a group of movements of the Einstein homogeneous static Universe (the R x SO Einstein group (4)) has been formulated. Proceeding from tetrade components of the Einstein Universe the relation between the Riemann metrics and gauge fields of the Einstein group has been established. Metric coherence with torsion transforming to the Kristoffel coherence of the Einstein Universe has been found when switching out gauge fields. It is shown that within the limit of infinite radius of the Einstein Universe curvature the given Einstein-invariant gauge theory transforms to the tetrade gravitation theory with localized triade rotations. Exact solutions in the form of nonsingular cosmological models have been obtained

  20. Representations of l-p-i functionals in gauge field theories

    International Nuclear Information System (INIS)

    Bordag, M.; Kaschluhn, L.; Matveev, V.A.; Robaschik, D.

    1981-01-01

    A representation of the functions which solve by construction the Slavnov-Taylor identities and contain independent coefficient functions is given. These solutions show the different role of the gauge field which acts in some respect as an ordinary field. The Slavnov-Taylor identities are solved for axial gauge conditions in non-Abelian gauge field theory and in quantum electrodynamics