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...
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
Higher spin gauge theory on fuzzy \\boldsymbol {S^4_N}
Sperling, Marcus; Steinacker, Harold C.
2018-02-01
We examine in detail the higher spin fields which arise on the basic fuzzy sphere S^4N in the semi-classical limit. The space of functions can be identified with functions on classical S 4 taking values in a higher spin algebra associated to \
On Killing tensors and cubic vertices in higher-spin gauge theories
International Nuclear Information System (INIS)
Bekaert, X.; Boulanger, N.; Leclercq, S.; Cnockaert, S.
2006-01-01
The problem of determining all consistent non-Abelian local interactions is reviewed in flat space-time. The antifield-BRST formulation of the free theory is an efficient tool to address this problem. Firstly, it allows to compute all on-shell local Killing tensor fields, which are important because of their deep relationship with higher-spin algebras. Secondly, under the sole assumptions of locality and Poincare invariance, all non-trivial consistent deformations of a sum of spin-three quadratic actions deforming the Abelian gauge algebra were determined. They are compared with lower-spin cases. (Abstract Copyright [2006], Wiley Periodicals, Inc.)
Systematics of higher-spin gauge fields
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de Wit, B.; Freedman, D.Z.
1980-01-01
Free-field theories for symmetric tensor and tensor-spinor gauge fields have recently been obtained which describe massless particles of arbitrary integer or half-integer spin. An independent discussion of these field theories is given here, based on a hierarchy of generalized Christoffel symbols with simple gauge transformation properties. The necessity of certain constraints on gauge fields and parameters is easily seen. Wave equations and Lagrangians are expressed in terms of the Christoffel symbols, and the independent modes of the system are counted in covariant gauges. Minimal-coupling inconsistency and a combined system of higher-spin boson gauge fields interacting with relativistic particles is discussed
On the uniqueness of minimal coupling in higher-spin gauge theory
International Nuclear Information System (INIS)
Boulanger, Nicolas; Sundell, Per; Leclercq, Serge
2008-01-01
We address the uniqueness of the minimal couplings between higher-spin fields and gravity. These couplings are cubic vertices built from gauge non-invariant connections that induce non-abelian deformations of the gauge algebra. We show that Fradkin-Vasiliev's cubic 2-s-s vertex, which contains up to 2s-2 derivatives dressed by a cosmological constant Λ, has a limit where: (i) Λ → 0; (ii) the spin-2 Weyl tensor scales non-uniformly with s; and (iii) all lower-derivative couplings are scaled away. For s = 3 the limit yields the unique non-abelian spin 2-3-3 vertex found recently by two of the authors, thereby proving the uniqueness of the corresponding FV vertex. We extend the analysis to s = 4 and a class of spin 1-s-s vertices. The non-universality of the flat limit high-lightens not only the problematic aspects of higher-spin interactions with Λ = 0 but also the strongly coupled nature of the derivative expansion of the fully nonlinear higher-spin field equations with Λ≠0, wherein the standard minimal couplings mediated via the Lorentz connection are subleading at energy scales (|Λ|) 1/2 || E || M p . Finally, combining our results with those obtained by Metsaev, we give the complete list of all the manifestly covariant cubic couplings of the form 1-s-s and 2-s-s , in Minkowski background.
Invariant functionals in higher-spin theory
Directory of Open Access Journals (Sweden)
M.A. Vasiliev
2017-03-01
Full Text Available A new construction for gauge invariant functionals in the nonlinear higher-spin theory is proposed. Being supported by differential forms closed by virtue of the higher-spin equations, invariant functionals are associated with central elements of the higher-spin algebra. In the on-shell AdS4 higher-spin theory we identify a four-form conjectured to represent the generating functional for 3d boundary correlators and a two-form argued to support charges for black hole solutions. Two actions for 3d boundary conformal higher-spin theory are associated with the two parity-invariant higher-spin models in AdS4. The peculiarity of the spinorial formulation of the on-shell AdS3 higher-spin theory, where the invariant functional is supported by a two-form, is conjectured to be related to the holomorphic factorization at the boundary. The nonlinear part of the star-product function F⁎(B(x in the higher-spin equations is argued to lead to divergencies in the boundary limit representing singularities at coinciding boundary space–time points of the factors of B(x, which can be regularized by the point splitting. An interpretation of the RG flow in terms of proposed construction is briefly discussed.
String fields, higher spins and number theory
Polyakov, Dimitri
2018-01-01
The book aims to analyze and explore deep and profound relations between string field theory, higher spin gauge theories and holography the disciplines that have been on the cutting edge of theoretical high energy physics and other fields. These intriguing relations and connections involve some profound ideas in number theory, which appear to be part of a unifying language to describe these connections.
Holography and higher-spin theories
International Nuclear Information System (INIS)
Petkou, T.
2005-01-01
I review recent work on the holographic relation between higher-spin theories in Anti-de Sitter spaces and conformal field theories. I present the main results of studies concerning the higher-spin holographic dual of the three-dimensional O(N) vector model. I discuss the special role played by certain double-trace deformations in Conformal Field Theories that have higher-spin holographic duals. Moreover, I show that duality transformations in a U(1) gauge theory on AdS 4 induce boundary double-trace deformations and argue that a similar effect takes place in the holography of linearized higher-spin theories on AdS 4 . (Abstract Copyright [2005], Wiley Periodicals, Inc.)
Charges in nonlinear higher-spin theory
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Didenko, V.E. [I.E. Tamm Department of Theoretical Physics, Lebedev Physical Institute,Leninsky prospect 53, 119991, Moscow (Russian Federation); Misuna, N.G. [I.E. Tamm Department of Theoretical Physics, Lebedev Physical Institute,Leninsky prospect 53, 119991, Moscow (Russian Federation); Moscow Institute of Physics and Technology,Institutsky lane 9, 141700, Dolgoprudny, Moscow region (Russian Federation); Vasiliev, M.A. [I.E. Tamm Department of Theoretical Physics, Lebedev Physical Institute,Leninsky prospect 53, 119991, Moscow (Russian Federation)
2017-03-30
Nonlinear higher-spin equations in four dimensions admit a closed two-form that defines a gauge-invariant global charge as an integral over a two-dimensional cycle. In this paper we argue that this charge gives rise to partitions depending on various lower- and higher-spin chemical potentials identified with modules of topological fields in the theory. The vacuum contribution to the partition is calculated to the first nontrivial order for a solution to higher-spin equations that generalizes AdS{sub 4} Kerr black hole of General Relativity. The resulting partition is non-zero being in parametric agreement with the ADM-like behavior of a rotating source. The linear response of chemical potentials to the partition function is also extracted. The explicit unfolded form of 4d GR black holes is given. An explicit formula relating asymptotic higher-spin charges expressed in terms of the generalized higher-spin Weyl tensor with those expressed in terms of Fronsdal fields is obtained.
Charges in nonlinear higher-spin theory
International Nuclear Information System (INIS)
Didenko, V.E.; Misuna, N.G.; Vasiliev, M.A.
2017-01-01
Nonlinear higher-spin equations in four dimensions admit a closed two-form that defines a gauge-invariant global charge as an integral over a two-dimensional cycle. In this paper we argue that this charge gives rise to partitions depending on various lower- and higher-spin chemical potentials identified with modules of topological fields in the theory. The vacuum contribution to the partition is calculated to the first nontrivial order for a solution to higher-spin equations that generalizes AdS 4 Kerr black hole of General Relativity. The resulting partition is non-zero being in parametric agreement with the ADM-like behavior of a rotating source. The linear response of chemical potentials to the partition function is also extracted. The explicit unfolded form of 4d GR black holes is given. An explicit formula relating asymptotic higher-spin charges expressed in terms of the generalized higher-spin Weyl tensor with those expressed in terms of Fronsdal fields is obtained.
Partially massless higher-spin theory
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Brust, Christopher [Perimeter Institute for Theoretical Physics,31 Caroline St. N, Waterloo, Ontario N2L 2Y5 (Canada); Hinterbichler, Kurt [CERCA, Department of Physics, Case Western Reserve University,10900 Euclid Ave, Cleveland, OH 44106 (United States)
2017-02-16
We study a generalization of the D-dimensional Vasiliev theory to include a tower of partially massless fields. This theory is obtained by replacing the usual higher-spin algebra of Killing tensors on (A)dS with a generalization that includes “third-order” Killing tensors. Gauging this algebra with the Vasiliev formalism leads to a fully non-linear theory which is expected to be UV complete, includes gravity, and can live on dS as well as AdS. The linearized spectrum includes three massive particles and an infinite tower of partially massless particles, in addition to the usual spectrum of particles present in the Vasiliev theory, in agreement with predictions from a putative dual CFT with the same symmetry algebra. We compute the masses of the particles which are not fixed by the massless or partially massless gauge symmetry, finding precise agreement with the CFT predictions. This involves computing several dozen of the lowest-lying terms in the expansion of the trilinear form of the enlarged higher-spin algebra. We also discuss nuances in the theory that occur in specific dimensions; in particular, the theory dramatically truncates in bulk dimensions D=3,5 and has non-diagonalizable mixings which occur in D=4,7.
Partially massless higher-spin theory
International Nuclear Information System (INIS)
Brust, Christopher; Hinterbichler, Kurt
2017-01-01
We study a generalization of the D-dimensional Vasiliev theory to include a tower of partially massless fields. This theory is obtained by replacing the usual higher-spin algebra of Killing tensors on (A)dS with a generalization that includes “third-order” Killing tensors. Gauging this algebra with the Vasiliev formalism leads to a fully non-linear theory which is expected to be UV complete, includes gravity, and can live on dS as well as AdS. The linearized spectrum includes three massive particles and an infinite tower of partially massless particles, in addition to the usual spectrum of particles present in the Vasiliev theory, in agreement with predictions from a putative dual CFT with the same symmetry algebra. We compute the masses of the particles which are not fixed by the massless or partially massless gauge symmetry, finding precise agreement with the CFT predictions. This involves computing several dozen of the lowest-lying terms in the expansion of the trilinear form of the enlarged higher-spin algebra. We also discuss nuances in the theory that occur in specific dimensions; in particular, the theory dramatically truncates in bulk dimensions D=3,5 and has non-diagonalizable mixings which occur in D=4,7.
Star-product functions in higher-spin theory and locality
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Vasiliev, M.A. [I.E. Tamm Department of Theoretical Physics, Lebedev Physical Institute,Leninsky prospect 53, 119991, Moscow (Russian Federation)
2015-06-04
Properties of the functional classes of star-product elements associated with higher-spin gauge fields and gauge parameters are elaborated. Cohomological interpretation of the nonlinear higher-spin equations is given. An algebra ℋ, where solutions of the nonlinear higher-spin equations are valued, is found. A conjecture on the classes of star-product functions underlying (non)local maps and gauge transformations in the nonlinear higher-spin theory is proposed.
Spinning particle approach to higher spin field theory
International Nuclear Information System (INIS)
Corradini, Olindo
2011-01-01
We shortly review on the connection between higher-spin gauge field theories and supersymmetric spinning particle models. In such approach the higher spin equations of motion are linked to the first-class constraint algebra associated with the quantization of particle models. Here we consider a class of spinning particle models characterized by local O(N)-extended supersymmetry since these models are known to provide an alternative approach to the geometric formulation of higher spin field theory. We describe the canonical quantization of the models in curved target space and discuss the obstructions that appear in presence of an arbitrarily curved background. We then point out the special role that conformally flat spaces appear to have in such models and present a derivation of the higher-spin curvatures for maximally symmetric spaces.
Higher-spin-matter gauge interactions in 2+1 dimensions
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Vasiliev, M.A.
1997-01-01
We discuss general properties of higher-spin gauge theories paying particular attention to specificities of higher-spin gauge interactions of massive matter fields in 2+1 dimensional space-time. The main conclusions are that the parameter of mass M appears as a module characterizing an appropriate vacuum solution of the full non-linear model and that M affects a structure of a global vacuum higher-spin symmetry which leaves invariant the chosen vacuum solution. Special attention is paid to local Lorentz symmetry as a guiding principle which fixes a form of non-linear higher-spin equations formulated as some zero-curvature conditions supplemented with non-linear constraints. (orig.)
Perturbative analysis in higher-spin theories
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Didenko, V.E. [I.E. Tamm Department of Theoretical Physics, Lebedev Physical Institute,Leninsky prospect 53, 119991, Moscow (Russian Federation); Misuna, N.G. [Moscow Institute of Physics and Technology,Institutsky lane 9, 141700, Dolgoprudny, Moscow region (Russian Federation); Vasiliev, M.A. [I.E. Tamm Department of Theoretical Physics, Lebedev Physical Institute,Leninsky prospect 53, 119991, Moscow (Russian Federation)
2016-07-28
A new scheme of the perturbative analysis of the nonlinear HS equations is developed giving directly the final result for the successive application of the homotopy integrations which appear in the standard approach. It drastically simplifies the analysis and results from the application of the standard spectral sequence approach to the higher-spin covariant derivatives, allowing us in particular to reduce multiple homotopy integrals resulting from the successive application of the homotopy trick to a single integral. Efficiency of the proposed method is illustrated by various examples. In particular, it is shown how the Central on-shell theorem of the free theory immediately results from the nonlinear HS field equations with no intermediate computations.
Topics in field theory-higher spins, CFT, and gravity
International Nuclear Information System (INIS)
Yang, Z.
1990-01-01
Several topics in field theory are investigated. (1) Massive higher spin actions are obtained as gauge theories from the dimensional reduction of the corresponding massless ones. (2) The author considers a model of spin4 and spin2 interaction through the Bel-Robinson tensor of spin2 field, which in conserved at free level. The coupling is inconsistent, yet there are indications that adding still higher spin couplings would be a promising direction to achieve consistency. (3) Energy and Stability of Einstein-Gauss-Bonnet models of gravity are studied. It is shown that flat space is stable while AdS is not. (4) Gauged Wess-Zumino-Witten models are studied in detail. The equivalence to GKO construction of conformal field theory is considered. BRST quantization of the models is given. (5) Nonrenormalizability of quantum gravity is, in the binomial first order metric formulation, traced to a mismatch between the symmetries of its quadratic and cubic term. (6) The possibility that the gravitational model defined in D = 3 by an action which is the sum of Einstein and Chern-Simons terms is a viable quantum theory is investigated. It is shown that it is compatible with power-counting renormalizability. Gauge invariant regularizations, however, have not been found to exist. Detailed BRS analysis shows that there are possible anomalies
Irreversibility and higher-spin conformal field theory
Anselmi, Damiano
2000-08-01
I discuss the properties of the central charges c and a for higher-derivative and higher-spin theories (spin 2 included). Ordinary gravity does not admit a straightforward identification of c and a in the trace anomaly, because it is not conformal. On the other hand, higher-derivative theories can be conformal, but have negative c and a. A third possibility is to consider higher-spin conformal field theories. They are not unitary, but have a variety of interesting properties. Bosonic conformal tensors have a positive-definite action, equal to the square of a field strength, and a higher-derivative gauge invariance. There exists a conserved spin-2 current (not the canonical stress tensor) defining positive central charges c and a. I calculate the values of c and a and study the operator-product structure. Higher-spin conformal spinors have no gauge invariance, admit a standard definition of c and a and can be coupled to Abelian and non-Abelian gauge fields in a renormalizable way. At the quantum level, they contribute to the one-loop beta function with the same sign as ordinary matter, admit a conformal window and non-trivial interacting fixed points. There are composite operators of high spin and low dimension, which violate the Ferrara-Gatto-Grillo theorem. Finally, other theories, such as conformal antisymmetric tensors, exhibit more severe internal problems. This research is motivated by the idea that fundamental quantum field theories should be renormalization-group (RG) interpolations between ultraviolet and infrared conformal fixed points, and quantum irreversibility should be a general principle of nature.
On the gauge symmetries of Maxwell-like higher-spin Lagrangians
International Nuclear Information System (INIS)
Francia, Dario; Lyakhovich, Simon L.; Sharapov, Alexey A.
2014-01-01
In their simplest form, metric-like Lagrangians for higher-spin massless fields are usually assumed to display constrained gauge symmetries, unless auxiliary fields are introduced or locality is foregone. Specifically, in its standard incarnation, gauge invariance of Maxwell-like Lagrangians relies on parameters with vanishing divergence. We find an alternative form of the corresponding local symmetry involving unconstrained gauge parameters of mixed-symmetry type, described by rectangular two-row Young diagrams and entering high-derivative gauge transformations. The resulting gauge algebra appears to be reducible and we display the full pattern of gauge-for-gauge parameters, testing its correctness via the corresponding counting of degrees of freedom. The algebraic techniques applied in this work also allow us to elucidate some general properties of linear gauge systems. In particular, we establish the general fact that any linear local field theory always admits unconstrained, local, and finitely reducible parametrization of the gauge symmetry. Incidentally, this shows that massless higher spins admit a local unconstrained formulation with no need for auxiliary fields
Irreversibility and higher-spin conformal field theory
Anselmi, D
2000-01-01
I discuss the idea that quantum irreversibility is a general principle of nature and a related "conformal hypothesis", stating that all fundamental quantum field theories should be renormalization-group (RG) interpolations between ultraviolet and infrared conformal fixed points. In particular, the Newton constant should be viewed as a low-energy effect of the RG scale. This approach leads naturally to consider higher-spin conformal field theories, which are here classified, as candidate high-energy theories. Bosonic conformal tensors have a positive-definite action, equal to the square of a field strength, and a higher-derivative gauge invariance. The central charges c and a are well defined and positive. I calculate their values and study the operator-product structure. Fermionic theories have no gauge invariance and can be coupled to Abelian and non-Abelian gauge fields in a renormalizable way. At the quantum level, they contribute to the one-loop beta function with the same sign as ordinary matter, admit a...
Light-front higher-spin theories in flat space
Ponomarev, Dmitry; Skvortsov, Evgeny
2017-03-01
We revisit the problem of interactions of higher-spin fields in flat space. We argue that all no-go theorems can be avoided by the light-cone approach, which results in more interaction vertices as compared to the usual covariant approaches. It is stressed that there exist two-derivative gravitational couplings of higher-spin fields. We show that some reincarnation of the equivalence principle still holds for higher-spin fields—the strength of gravitational interaction does not depend on spin. Moreover, it follows from the results by Metsaev that there exists a complete chiral higher-spin theory in four dimensions. We give a simple derivation of this theory and show that the four-point scattering amplitude vanishes. Also, we reconstruct the quartic vertex of the scalar field in the unitary higher-spin theory, which turns out to be perturbatively local.
Light-front higher-spin theories in flat space
International Nuclear Information System (INIS)
Ponomarev, Dmitry; Skvortsov, Evgeny
2017-01-01
We revisit the problem of interactions of higher-spin fields in flat space. We argue that all no-go theorems can be avoided by the light-cone approach, which results in more interaction vertices as compared to the usual covariant approaches. It is stressed that there exist two-derivative gravitational couplings of higher-spin fields. We show that some reincarnation of the equivalence principle still holds for higher-spin fields—the strength of gravitational interaction does not depend on spin. Moreover, it follows from the results by Metsaev that there exists a complete chiral higher-spin theory in four dimensions. We give a simple derivation of this theory and show that the four-point scattering amplitude vanishes. Also, we reconstruct the quartic vertex of the scalar field in the unitary higher-spin theory, which turns out to be perturbatively local. (paper)
Unitarity in three-dimensional flat space higher spin theories
International Nuclear Information System (INIS)
Grumiller, D.; Riegler, M.; Rosseel, J.
2014-01-01
We investigate generic flat-space higher spin theories in three dimensions and find a no-go result, given certain assumptions that we spell out. Namely, it is only possible to have at most two out of the following three properties: unitarity, flat space, non-trivial higher spin states. Interestingly, unitarity provides an (algebra-dependent) upper bound on the central charge, like c=42 for the Galilean W_4"("2"−"1"−"1") algebra. We extend this no-go result to rule out unitary “multi-graviton” theories in flat space. We also provide an example circumventing the no-go result: Vasiliev-type flat space higher spin theory based on hs(1) can be unitary and simultaneously allow for non-trivial higher-spin states in the dual field theory.
Higher-Spin Triplet Fields and String Theory
Directory of Open Access Journals (Sweden)
D. Sorokin
2010-01-01
Full Text Available We review basic properties of reducible higher-spin multiplets, called triplets, and demonstrate how they naturally appear as part of the spectrum of String Field Theory in the tensionless limit. We show how in the frame-like formulation the triplet fields are endowed with the geometrical meaning of being components of higher-spin vielbeins and connections and present actions describing their free dynamics.
Conformal higher spin theory and twistor space actions
Hähnel, Philipp; McLoughlin, Tristan
2017-12-01
We consider the twistor description of conformal higher spin theories and give twistor space actions for the self-dual sector of theories with spin greater than two that produce the correct flat space-time spectrum. We identify a ghost-free subsector, analogous to the embedding of Einstein gravity with cosmological constant in Weyl gravity, which generates the unique spin-s three-point anti-MHV amplitude consistent with Poincaré invariance and helicity constraints. By including interactions between the infinite tower of higher-spin fields we give a geometric interpretation to the twistor equations of motion as the integrability condition for a holomorphic structure on an infinite jet bundle. Finally, we conjecture anti-self-dual interaction terms which give an implicit definition of a twistor action for the full conformal higher spin theory.
Gauge invariant Lagrangian formulation of massive higher spin fields in (A)dS3 space
International Nuclear Information System (INIS)
Buchbinder, I.L.; Snegirev, T.V.; Zinoviev, Yu.M.
2012-01-01
We develop the frame-like formulation of massive bosonic higher spin fields in the case of three-dimensional (A)dS space with the arbitrary cosmological constant. The formulation is based on gauge invariant description by involving the Stueckelberg auxiliary fields. The explicit form of the Lagrangians and the gauge transformation laws are found. The theory can be written in terms of gauge invariant objects similar to the massless theories, thus allowing us to hope to use the same methods for investigation of interactions. In the massive spin 3 field example we are able to rewrite the Lagrangian using the new the so-called separated variables, so that the study of Lagrangian formulation reduces to finding the Lagrangian containing only half of the fields. The same construction takes places for arbitrary integer spin field as well. Further working in terms of separated variables, we build Lagrangian for arbitrary integer spin and write it in terms of gauge invariant objects. Also, we demonstrate how to restore the full set of variables, thus receiving Lagrangian for the massive fields of arbitrary spin in the terms of initial fields.
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.)
Cubic interaction in extended theories of massless higher-spin fields
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Fradkin, E S; Vasiliev, M A
1987-08-17
A cubic interaction of all massless higher-spin fields with s greater than or equal to 1 is constructed, based on the extended higher-spin superalgebras suggested previously by one of us (M.V.). This interaction incorporates gravitational and Yang-Mills interactions of massless higher-spin fields, which turn out to be consistent in the cubic order. An essential novel feature of the gravitational higher-spin interaction is its non-analyticity in the cosmological constant. An explicit form is found for deformed higher-spin gauge transformations leaving the action invariant.
Higher spin currents in the orthogonal coset theory
Energy Technology Data Exchange (ETDEWEB)
Ahn, Changhyun [Kyungpook National University, Department of Physics, Taegu (Korea, Republic of)
2017-06-15
In the coset model (D{sub N}{sup (1)} + D{sub N}{sup (1)}, D{sub N}{sup (1)}) at levels (k{sub 1}, k{sub 2}), the higher spin 4 current that contains the quartic WZW currents contracted with a completely symmetric SO(2N) invariant d tensor of rank 4 is obtained. The three-point functions with two scalars are obtained for any finite N and k{sub 2} with k{sub 1} = 1. They are determined also in the large N 't Hooft limit. When one of the levels is the dual Coxeter number of SO(2N), k{sub 1} = 2N - 2, the higher spin (7)/(2) current, which contains the septic adjoint fermions contracted with the above d tensor and the triple product of structure constants, is obtained from the operator product expansion (OPE) between the spin (3)/(2) current living in the N = 1 superconformal algebra and the above higher spin 4 current. The OPEs between the higher spin (7)/(2), 4 currents are described. For k{sub 1} = k{sub 2} = 2N - 2 where both levels are equal to the dual Coxeter number of SO(2N), the higher spin 3 current of U(1) charge (4)/(3), which contains the six products of spin (1)/(2) (two) adjoint fermions contracted with the product of the d tensor and two structure constants, is obtained. The corresponding N = 2 higher spin multiplet is determined by calculating the remaining higher spin (7)/(2), (7)/(2), 4 currents with the help of two spin (3)/(2) currents in the N = 2 superconformal algebra. The other N = 2 higher spin multiplet, whose U(1) charge is opposite to the one of the above N = 2 higher spin multiplet, is obtained. The OPE between these two N = 2 higher spin multiplets is also discussed. (orig.)
Algebraic construction of interacting higher spin field theories
International Nuclear Information System (INIS)
Fougere, F.
1991-10-01
We develop a general framework which we believe may provide some insights into the structure of interacting 'high spin' field theories. A finite or infinite set of classical spin fields is described by means of a field defined on an enlarged spacetime manifold. The free action and its gauge symmetries are gathered into a nilpotent differential operator on this manifold. In particular, the choice of Grassmann-valued extra coordinates leads to theories involving only a finite set of fields, the possible contents (spin multiplicities, degree of reducibility, etc.) of which are classified according to the representations of a unitary algebra. The interacting theory is characterized by a functional of the field on the enlarged manifold. We show that there is among these functionals a natural graded Lie algebra structure allowing one to rewrite the gauge invariance condition of the action in a concise form which is a nonlinear generalization of the nilpotency condition of the free theory. We obtain the general solution of this 'classical master equation' , which can be built recurrently starting form the cubic vertex, and we study its symmetries. Our formalism lends itself to a systematic introduction of additional conditions, such as locality, polynomiality, etc. We write down the general form of the solutions exhibiting a scale invariance. The case of a spin 1 field yields, as a unique solution, Yang-Mills theory. In view of quantization, we show that the solution of the classical master equation straightforwardly provides a solution of the (quantum) Batalin-Vilkoviski master equation. One may then obtain a gauge fixed action in the usual way
Equations of motion of higher-spin gauge fields as a free differential algebra
International Nuclear Information System (INIS)
Vasil'ev, M.A.
1988-01-01
It is shown that the introduction of auxiliary dynamical variables that generalize the gravitational Weyl tensor permits one to reduce the equations of motion of free massless fields of all spins in the anti-de Sitter O(3,2) space to a form characteristic of free differential algebras. The equations of motion of auxiliary gauge fields introduced previously are modified analogously. Arguments are presented to the effect that the equations of motion of interacting massless fields of all spins should be described in terms of a free differential algebra which is a deformation of a known free differential algebra generated by 1- and 0-forms in the adjoint representation of a nonabelian superalgebra of higher spins and auxiliary fields
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)
Notes on strings and higher spins
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Sagnotti, A
2013-01-01
This review is devoted to the intriguing and still largely unexplored links between string theory and higher spins, the types of excitations that lie behind their most cherished properties. A closer look at higher spin fields provides some further clues that string theory describes a broken phase of a higher spin gauge theory. Conversely, string amplitudes contain a wealth of information on higher spin interactions that can clarify long-standing issues related to their infrared behavior. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Higher spin theories and holography’. (review)
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)
Conformal higher-spin symmetries in twistor string theory
Directory of Open Access Journals (Sweden)
D.V. Uvarov
2014-12-01
Full Text Available It is shown that similarly to massless superparticle, classical global symmetry of the Berkovits twistor string action is infinite-dimensional. We identify its superalgebra, whose finite-dimensional subalgebra contains psl(4|4,R superalgebra. In quantum theory this infinite-dimensional symmetry breaks down to SL(4|4,R one.
Non-Abelian tensor gauge fields and higher-spin extension of standard model
International Nuclear Information System (INIS)
Savvidy, G.
2006-01-01
We suggest an extension of the gauge principle which includes non-Abelian tensor gauge fields. The invariant Lagrangian is quadratic in the field strength tensors and describes interaction of charged tensor gauge bosons of arbitrary large integer spin 1,2,l. Non-Abelian tensor gauge fields can be viewed as a unique gauge field with values in the infinite-dimensional current algebra associated with compact Lie group. The full Lagrangian exhibits also enhanced local gauge invariance with double number of gauge parameters which allows to eliminate all negative norm states of the nonsymmetric second-rank tensor gauge field, which describes therefore two polarizations of helicity-two massless charged tensor gauge boson and the helicity-zero ''axion'' The geometrical interpretation of the enhanced gauge symmetry with double number of gauge parameters is not yet known. (Abstract Copyright [2006], Wiley Periodicals, Inc.)
Exceptional F(4) higher-spin theory in AdS{sub 6} at one-loop and other tests of duality
Energy Technology Data Exchange (ETDEWEB)
Günaydin, Murat [Institute for Gravitation and the Cosmos Physics Department, Pennsylvania State University, University Park, PA 16802 (United States); Skvortsov, Evgeny [Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians University Munich, Theresienstr. 37, D-80333 Munich (Germany); Lebedev Institute of Physics, Leninsky ave. 53, 119991 Moscow (Russian Federation); Tran, Tung [Department of Physics, Brown University, Providence, Rhode Island 02912 (United States)
2016-11-28
We study the higher-spin gauge theory in six-dimensional anti-de Sitter space AdS{sub 6} that is based on the exceptional Lie superalgebra F(4). The relevant higher-spin algebra was constructed in http://arxiv.org/abs/1409.2185. We determine the spectrum of the theory and show that it contains the physical fields of the Romans F(4) gauged supergravity. The full spectrum consists of an infinite tower of unitary supermultiplets of F(4) which extend the Romans multiplet to higher spins plus a single short supermultiplet. Motivated by applications to this novel supersymmetric higher-spin theory as well as to other theories, we extend the known one-loop tests of AdS/CFT duality in various directions. The spectral zeta-function is derived for the most general case of fermionic and mixed-symmetry fields, which allows one to test the Type-A and B theories and supersymmetric extensions thereof in any dimension. We also study higher-spin doubletons and partially-massless fields. While most of the tests are successfully passed, the Type-B theory in all even dimensional anti-de Sitter spacetimes presents an interesting puzzle: the free energy as computed from the bulk is not equal to that of the free fermion on the CFT side, though there is some systematics to the discrepancy.
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
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)
Algebraic aspects of the higher-spin problem
Energy Technology Data Exchange (ETDEWEB)
Vasiliev, M A [European Organization for Nuclear Research, Geneva (Switzerland)
1991-03-21
A general algebraic construction is established, which underlies the previously proposed consistent equations of interacting gauge fields of all spins in 3+1 dimensions. This construction makes a verification of the consistency (gauge invariance) of the higher-spin equations trivial and indicates how these equations can be generalized to higher dimensions and/or conformal-type higher-spin theories. (orig.).
Massless representations and admissibility condition for higher spin superalgebras
Energy Technology Data Exchange (ETDEWEB)
Konstein, S E; Vasiliev, M A
1989-01-16
Massless particle representations of various infinite-dimensional higher spin superalgebras proposed previously are constructed. We analyse which of higher spin superalgebras obey the requirement (the admissibility condition) of possessing massless unitary representations with the same spectra of spins as predicted by the structure of gauge fields originating from these superalgebras. It is argued that those higher spin superalgebras, which obey the admissibility condition, can serve as rigid supersymmetries in nontrivial consistent gauge theories of massless fields of all spins.
Partially massless higher-spin theory II: one-loop effective actions
Energy Technology Data Exchange (ETDEWEB)
Brust, Christopher [Perimeter Institute for Theoretical Physics,31 Caroline St. N, Waterloo, Ontario, N2L 2Y5 (Canada); Hinterbichler, Kurt [CERCA, Department of Physics, Case Western Reserve University,10900 Euclid Ave, Cleveland, OH, 44106 (United States)
2017-01-30
We continue our study of a generalization of the D-dimensional linearized Vasiliev higher-spin equations to include a tower of partially massless (PM) fields. We compute one-loop effective actions by evaluating zeta functions for both the “minimal” and “non-minimal” parity-even versions of the theory. Specifically, we compute the log-divergent part of the effective action in odd-dimensional Euclidean AdS spaces for D=7 through 19 (dual to the a-type conformal anomaly of the dual boundary theory), and the finite part of the effective action in even-dimensional Euclidean AdS spaces for D=4 through 8 (dual to the free energy on a sphere of the dual boundary theory). We pay special attention to the case D=4, where module mixings occur in the dual field theory and subtlety arises in the one-loop computation. The results provide evidence that the theory is UV complete and one-loop exact, and we conjecture and provide evidence for a map between the inverse Newton’s constant of the partially massless higher-spin theory and the number of colors in the dual CFT.
Partially massless higher-spin theory II: one-loop effective actions
International Nuclear Information System (INIS)
Brust, Christopher; Hinterbichler, Kurt
2017-01-01
We continue our study of a generalization of the D-dimensional linearized Vasiliev higher-spin equations to include a tower of partially massless (PM) fields. We compute one-loop effective actions by evaluating zeta functions for both the “minimal” and “non-minimal” parity-even versions of the theory. Specifically, we compute the log-divergent part of the effective action in odd-dimensional Euclidean AdS spaces for D=7 through 19 (dual to the a-type conformal anomaly of the dual boundary theory), and the finite part of the effective action in even-dimensional Euclidean AdS spaces for D=4 through 8 (dual to the free energy on a sphere of the dual boundary theory). We pay special attention to the case D=4, where module mixings occur in the dual field theory and subtlety arises in the one-loop computation. The results provide evidence that the theory is UV complete and one-loop exact, and we conjecture and provide evidence for a map between the inverse Newton’s constant of the partially massless higher-spin theory and the number of colors in the dual CFT.
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)
CERN. Geneva
2014-01-01
The conjectured relation between higher spin theories on anti de-Sitter (AdS) spaces and weakly coupled conformal field theories is reviewed. I shall then outline the evidence in favour of a concrete duality of this kind, relating a specific higher spin theory on AdS3 to a family of 2d minimal model CFTs. Finally, I shall explain how this relation fits into the framework of the familiar stringy AdS/CFT correspondence.
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
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)
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
Topics in phase-shift analysis and higher spin field theory
International Nuclear Information System (INIS)
Reisen, J.C.J.M.
1983-01-01
The first part of this thesis considers several aspects of the existence of phase-shift ambiguities. The subject is introduced with a few remarks on scattering theory and previous work in this area is discussed. The mathematical restrictions of presenting such problems clearly are considered and the construction of different unitary amplitudes which correspond to the same differential cross section is described. So far, examples of phase-shift ambiguities have only been found for rather special cases but the author shows that these results can be considerably generalized for spinless elastic scattering, leading to properties of phase-shift ambiguities being revealed that were previously absent. These properties are discussed in detail. Phase-shift ambiguities for the spin-0-spin-1/2 elastic scattering are then considered and again generalized. The second part of this thesis is concerned with the investigation of a free field theory for both massive and massless particles with higher spin (1, 2 and 3). A root method has been used which is described and shown to lead to the free field equations and the subsidiary conditions. A field equation and Lagrangian are constructed for massive particles and the former is then used to derive a massless field equation and Lagrangian. The relation between massive and massless field equations is investigated in more detail and particularly the expressions for the amplitude describing exchange of a particle between two external sources are compared. (Auth./C.F.)
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
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....
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)
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.)
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
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
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
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.
Gauge theory and renormalization
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
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...
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
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
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
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
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.)
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)
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
Digital lattice gauge theories
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.
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.)
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)
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
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.)
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.)
Higher spin resolution of a toy big bang
Krishnan, Chethan; Roy, Shubho
2013-08-01
Diffeomorphisms preserve spacetime singularities, whereas higher spin symmetries need not. Since three-dimensional de Sitter space has quotients that have big-bang/big-crunch singularities and since dS3-gravity can be written as an SL(2,C) Chern-Simons theory, we investigate SL(3,C) Chern-Simons theory as a higher-spin context in which these singularities might get resolved. As in the case of higher spin black holes in AdS3, the solutions are invariantly characterized by their holonomies. We show that the dS3 quotient singularity can be desingularized by an SL(3,C) gauge transformation that preserves the holonomy: this is a higher spin resolution the cosmological singularity. Our work deals exclusively with the bulk theory, and is independent of the subtleties involved in defining a CFT2 dual to dS3 in the sense of dS/CFT.
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.
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.
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)
Higher-spin fields in braneworlds
Energy Technology Data Exchange (ETDEWEB)
Germani, Cristiano [DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom)]. E-mail: c.germani@damtp.cam.ac.uk; Kehagias, Alex [Physics Division, National Technical University of Athens, 15780 Zografou Campus, Athens (Greece)]. E-mail: kehagias@central.ntua.gr
2005-10-03
The dynamics of higher-spin fields in braneworlds is discussed. In particular, we study fermionic and bosonic higher-spin fields in AdS{sub 5} and their localization on branes. We find that four-dimensional zero modes exist only for spin-one fields, if there are no couplings to the boundaries. If boundary couplings are allowed, as in the case of the bulk graviton, all bosons acquire a zero mode irrespective of their spin. We show that there are boundary conditions for fermions, which generate chiral zero modes in the four-dimensional spectrum. We also propose a gauge invariant on-shell action with cubic interactions by adding non-minimal couplings, which depend on the Weyl tensor. In addition, consistent couplings between higher-spin fields and matter on the brane are presented. Finally, in the AdS/CFT correspondence, where bulk 5D theories on AdS are related to 4D CFTs, we explicitly discuss the holographic picture of higher-spin theories in AdS{sub 5} with and without boundaries.
Higher-spin currents in the Gross-Neveu model at 1/n"2
International Nuclear Information System (INIS)
Manashov, A.N.
2016-10-01
We calculate the anomalous dimensions of higher-spin currents, both singlet and non-singlet, in the Gross - Neveu model at the 1/n"2 order. It was conjectured that in the critical regime this model is dual to a higher-spin gauge theory on AdS_4. The AdS/CFT correspondence predicts that the masses of higher-spin fields correspond to the scaling dimensions of the singlet currents in the Gross - Neveu model.
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)
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
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.)
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
Higher-spin symmetry in one and two dimensions, (1)
International Nuclear Information System (INIS)
Fradkin, E.S.; Linetsky, V.Ya.
1989-09-01
Higher spin theories in one and two dimensions are considered. The analysis of the ghost sector is carried out and a possible analogy with the ghost sector of the superparticle and the Green-Schwarz superstring in the covariant gauge is discussed. (author)
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
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.)
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
International Nuclear Information System (INIS)
Kerner, R.
1983-01-01
The mathematical background for a graded extension of gauge theories is investigated. After discussing the general properties of graded Lie algebras and what may serve as a model for a graded Lie group, the graded fiber bundle is constructed. Its basis manifold is supposed to be the so-called superspace, i.e. the product of the Minkowskian space-time with the Grassmann algebra spanned by the anticommuting Lorentz spinors; the vertical subspaces tangent to the fibers are isomorphic with the graded extension of the SU(N) Lie algebra. The connection and curvature are defined then on this bundle; the two different gradings are either independent of each other, or may be unified in one common grading, which is equivalent to the choice of the spin-statistics dependence. The Yang-Mills lagrangian is investigated in the simplified case. The conformal symmetry breaking is discussed, as well as some other physical consequences of the model. (orig.)
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
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
Higher Spin Extension of Fefferman-Graham Construction
Directory of Open Access Journals (Sweden)
Xavier Bekaert
2018-01-01
Full Text Available Fefferman-Graham ambient construction can be formulated as sp ( 2 -algebra relations on three Hamiltonian constraint functions on ambient space. This formulation admits a simple extension that leads to higher-spin fields, both conformal gauge fields and usual massless fields on anti-de Sitter spacetime. For the bulk version of the system, we study its possible on-shell version which is formally consistent and reproduces conformal higher-spin fields on the boundary. Interpretation of the proposed on-shell version crucially depends on the choice of the functional class. Although the choice leading to fully interacting higher-spin theory in the bulk is not known, we demonstrate that the system has a vacuum solution describing general higher-spin flat backgrounds. Moreover, we propose a functional class such that the system describes propagation of higher-spin fields over any higher-spin flat background, reproducing all the structures that determine the known nonlinear higher-spin equations.
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.
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
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
Introduction to gauge theories
International Nuclear Information System (INIS)
Okun, L.B.
1984-01-01
These lecture notes contain the text of five lectures and a Supplement. The lectures were given at the JINR-CERN School of Physics, Tabor, Czechoslovakia, 5-18 June 1983. The subgect of the lecinvariancetures: gauge of electromagnetic and weak interactions, higgs and supersymmetric particles. The Supplement contains reprints (or excerpts) of some classical papers on gauge invariance by V. Fock, F. London, O. Klein and H. Weyl, in which the concept of gauge invariance was introduced and developed
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)
Hard amplitudes in gauge theories
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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
On higher-spin supertranslations and superrotations
Energy Technology Data Exchange (ETDEWEB)
Campoleoni, Andrea [Université Libre de Bruxelles and International Solvay Institutes,ULB-Campus Plaine CP231, B-1050 Brussels (Belgium); Francia, Dario; Heissenberg, Carlo [Scuola Normale Superiore and INFN,Piazza dei Cavalieri 7, I-56126 Pisa (Italy)
2017-05-22
We study the large gauge transformations of massless higher-spin fields in four-dimensional Minkowski space. Upon imposing suitable fall-off conditions, providing higher-spin counterparts of the Bondi gauge, we observe the existence of an infinite-dimensional asymptotic symmetry algebra. The corresponding Ward identities can be held responsible for Weinberg’s factorisation theorem for amplitudes involving soft particles of spin greater than two.
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
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)
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
Gauge Theories of Vector Particles
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.
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
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
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.)
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.)
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
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
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
Higher spins and matter interacting in dimension three
International Nuclear Information System (INIS)
Kessel, Pan; Gómez, Gustavo Lucena; Skvortsov, Evgeny; Taronna, Massimo
2015-01-01
The spectrum of Prokushkin-Vasiliev Theory is puzzling in light of the Gaberdiel-Gopakumar conjecture because it generically contains an additional sector besides higher-spin gauge and scalar fields. We find the unique truncation of the theory avoiding this problem to order 2 in perturbations around AdS_3. The second-order backreaction on the physical gauge sector induced by the scalars is computed explicitly. The cubic action for the physical fields is determined completely. The subtle issue of the allowed class of pseudo-local field redefinitions is discussed.
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
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
Higher-spin currents in the Gross-Neveu model at 1/n{sup 2}
Energy Technology Data Exchange (ETDEWEB)
Manashov, A.N. [Institut für Theoretische Physik, Universität Hamburg,Hamburg, D-22761 (Germany); Institut für Theoretische Physik, Universität Regensburg,Regensburg, D-93040 (Germany); Skvortsov, E.D. [Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians University Munich, Theresienstr. 37, Munich, D-80333 (Germany); Lebedev Institute of Physics,Leninsky ave. 53, Moscow, 119991 (Russian Federation)
2017-01-30
We calculate the anomalous dimensions of higher-spin currents, both singlet and non-singlet, in the Gross-Neveu model at the 1/n{sup 2} order. It was conjectured that in the critical regime this model is dual to a higher-spin gauge theory on AdS{sub 4}. The AdS/CFT correspondence predicts that the masses of higher-spin fields correspond to the scaling dimensions of the singlet currents in the Gross-Neveu model.
Interfaces in hot gauge theory
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.
Gauge symmetry breaking in gauge theories -- in search of clarification
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
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)
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
Gauge theory and variational principles
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
An introduction to gauge theories
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.
Interactions in higher-spin gravity: a holographic perspective
Sleight, Charlotte
2017-09-01
This review is an elaboration of recent results on the holographic re-construction of metric-like interactions in higher-spin gauge theories on anti-de Sitter space (AdS), employing their conjectured duality with free conformal field theories (CFTs). After reviewing the general approach and establishing the necessary intermediate results, we extract explicit expressions for the complete cubic action on AdSd+1 and the quartic self-interaction of the scalar on AdS4 for the type A minimal bosonic higher-spin theory from the three- and four- point correlation functions of single-trace operators in the free scalar O(N) vector model. For this purpose tools were developed to evaluate tree-level three-point Witten diagrams involving totally symmetric fields of arbitrary integer spin and mass, and the conformal partial wave expansions of their tree-level four-point Witten diagrams. We also discuss the implications of the holographic duality on the locality properties of interactions in higher-spin gauge theories.
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
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.)
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.)
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.
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
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
Scattering amplitudes in gauge theories
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 ...
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)
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
BROOKHAVEN: Lattice gauge theory symposium
Energy Technology Data Exchange (ETDEWEB)
Anon.
1986-12-15
Originally introduced by Kenneth Wilson in the early 70s, the lattice formulation of a quantum gauge theory became a hot topic of investigation after Mike Creutz, Laurence Jacobs and Claudio Rebbi demonstrated in 1979 the feasibility of meaningful computer simulations. The initial enthusiasm led gradually to a mature research effort, with continual attempts to improve upon previous results, to develop better computational techniques and to find new domains of application.
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).
Area-preserving diffeomorphisms and higher-spin algebras
Energy Technology Data Exchange (ETDEWEB)
Bergshoeff, E [European Organization for Nuclear Research, Geneva (Switzerland). Theory Div.; Blencowe, M P; Stelle, K S [Imperial Coll. of Science and Technology, London (UK). Blackett Lab.
1990-03-01
We show that there exists a one-parameter family of infinite-dimensional algebras that includes the bosonic d=3 Fradkin-Vasiliev higher-spin algebra and the non-Euclidean version of the algebra of area-preserving diffeomorphisms of the two-sphere S{sup 2} as two distinct members. The non-Euclidean version of the area preserving algebra corresponds to the algebra of area-preserving diffeomorphisms of the hyperbolic space S{sup 1,1}, and can be rewritten as lim{sub Nyieldsinfinity} su(N,N). As an application of our results, we formulate a new d=2+1 massless higher-spin field theory as the gauge theory of the area-preserving diffeomorphisms of S{sup 1,1}. (orig.).
On the conformal higher spin unfolded equation for a three-dimensional self-interacting scalar field
Energy Technology Data Exchange (ETDEWEB)
Nilsson, Bengt E.W. [Fundamental Physics, Chalmers University of Technology,SE-412 96 Göteborg (Sweden)
2016-08-24
We propose field equations for the conformal higher spin system in three dimensions coupled to a conformal scalar field with a sixth order potential. Both the higher spin equation and the unfolded equation for the scalar field have source terms and are based on a conformal higher spin algebra which we treat as an expansion in multi-commutators. Explicit expressions for the source terms are suggested and subjected to some simple tests. We also discuss a cascading relation between the Chern-Simons action for the higher spin gauge theory and an action containing a term for each spin that generalizes the spin 2 Chern-Simons action in terms of the spin connection expressed in terms of the frame field. This cascading property is demonstrated in the free theory for spin 3 but should work also in the complete higher spin theory.
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.)
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.
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.
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
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.)
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.)
Gauge theory of glass transition
International Nuclear Information System (INIS)
Vasin, Mikhail
2011-01-01
A new analytical approach for the description of the glass transition in a frustrated system is suggested. The theory is based on the non-equilibrium dynamics technique, and takes into account the interaction of the local order field with the massive gauge field, which describes frustration-induced plastic deformation. The glass transition is regarded as a phase transition interrupted because of the premature critical slowing-down of one of the degrees of freedom caused by the frustrations. It is shown that freezing of the system appears when the correlation length and relaxation time of the gauge field diverge. The Vogel–Fulcher–Tammann relation for the transition kinetics and the critical exponent for the nonlinear susceptibility, 2.5∼ t correlation function dependence on time, and explains the boson peak appearance on this curve. In addition, the function of the glass transition temperature value with cooling rate is derived; this dependence fully conforms with known experimental data
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.)
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
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)
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.)
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.)
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)
An introduction to gauge theories
International Nuclear Information System (INIS)
Iliopoulos, J.
1977-01-01
The CERN-JINR School of Physics is meant to give young experimental physicists an introduction to the theoretical aspects of recent advances in elementary particle physics. This paper presents 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. The author presents the Weinberg-Salam model as an example of a renormalizable theory of weak and electromagnetic interactions of leptons, and it is shown that the extension of these ideas into the hadronic world requires the introduction of charm and colour. Finally, an attempt is made to include strong interactions into the scheme, guided by the experimental results of deep-inelastic lepton-nucleon scattering. The Callan-Symanzik equation, and the concepts of asymptotic freedom and quark confinement are introduced. (Auth.)
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
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
International Nuclear Information System (INIS)
Jacob, Maurice
1976-01-01
The charm is a new elementary constituent introduced in the SU(4) framework to explain the properties of the psi particles; its introduction definites the essential properties of the four quarks, u, d, s, c in the SU(4) framework. The discovery of charmed particles (two mesons four quarks u,d,s,c in the SU(4) framework. The discovery of charmed particles (two mesons and one baryons) confirms a series of previsions that derive from the introduction of gauge theories: weak neutral currents, W meson, unification of weak interactions and electrodynamics. Beyonds charm the introduction of colored quarks and gluon exchanges gives to strong interactions the simplicity of electrodynamics [fr
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
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
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
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
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
Gauge Theories in the Twentieth Century
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
Particle physics and gauge theories
International Nuclear Information System (INIS)
Morel, A.
1985-01-01
These notes are intended to help readers not familiar with particle physics in entering the domain of gauge field theory applied to the so-called standard model of strong and electroweak interactions. The introduction is considerably enlarged in order to give non specialists a general overview of present days ''elementary'' particle physics. The Glashow-Salam-Weinberg model is then treated, with the details which its unquestioned successes deserve, most probably for a long time. Finally SU(5) is presented as a prototype of these developments of particle physics which aim at a unification of all forces. Although its intrinsic theoretical difficulties and the non-observation of a sizable proton decay rate do not qualify this model as a realistic one, it has many of the properties expected from a ''good'' unified theory. In particular, it allows one to study interesting connections between particle physics and cosmology. 35 refs.
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.
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
Marginal deformations of 3d supersymmetric U(N) model and broken higher spin symmetry
Energy Technology Data Exchange (ETDEWEB)
Hikida, Yasuaki [Center for Gravitational Physics, Yukawa Institute for Theoretical Physics, Kyoto University,Kyoto 606-8502 (Japan); Wada, Taiki [Department of Physical Sciences, College of Science and Engineering, Ritsumeikan University,Shiga 525-8577 (Japan)
2017-03-08
We examine the marginal deformations of double-trace type in 3d supersymmetric U(N) model with N complex free bosons and fermions. We compute the anomalous dimensions of higher spin currents to the 1/N order but to all orders in the deformation parameters by mainly applying the conformal perturbation theory. The 3d field theory is supposed to be dual to 4d supersymmetric Vasiliev theory, and the marginal deformations are argued to correspond to modifying boundary conditions for bulk scalars and fermions. Thus the modification should break higher spin gauge symmetry and generate the masses of higher spin fields. We provide supports for the dual interpretation by relating bulk computation in terms of Witten diagrams to boundary one in conformal perturbation theory.
Marginal deformations of 3d supersymmetric U(N) model and broken higher spin symmetry
International Nuclear Information System (INIS)
Hikida, Yasuaki; Wada, Taiki
2017-01-01
We examine the marginal deformations of double-trace type in 3d supersymmetric U(N) model with N complex free bosons and fermions. We compute the anomalous dimensions of higher spin currents to the 1/N order but to all orders in the deformation parameters by mainly applying the conformal perturbation theory. The 3d field theory is supposed to be dual to 4d supersymmetric Vasiliev theory, and the marginal deformations are argued to correspond to modifying boundary conditions for bulk scalars and fermions. Thus the modification should break higher spin gauge symmetry and generate the masses of higher spin fields. We provide supports for the dual interpretation by relating bulk computation in terms of Witten diagrams to boundary one in conformal perturbation theory.
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
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
Cosmology and unified gauge theory
Oraifeartaigh, L.
1981-09-01
Theoretical points in common between cosmology and unified gauge theory (UGT) are reviewed, with attention given to areas of one which have proven useful for the other. The underlying principles for both theoretical frameworks are described, noting the differences in scale, i.e., 10 to the 25th cm in cosmology and 10 to the -15th cm for UGT. Cosmology has produced bounds on the number of existing neutrino species, and also on the mass of neutrinos, two factors of interest in particle physics. Electrons, protons, and neutrinos, having been spawned from the same massive leptons, each composed of three quarks, have been predicted to be present in equal numbers in the Universe by UGT, in line with necessities of cosmology. The Grand UGT also suggests specific time scales for proton decay, thus accounting for the observed baryon assymmetry.
Observables and microscopic entropy of higher spin black holes
Compère, Geoffrey; Jottar, Juan I.; Song, Wei
2013-11-01
In the context of recently proposed holographic dualities between higher spin theories in AdS3 and (1 + 1)-dimensional CFTs with symmetry algebras, we revisit the definition of higher spin black hole thermodynamics and the dictionary between bulk fields and dual CFT operators. We build a canonical formalism based on three ingredients: a gauge-invariant definition of conserved charges and chemical potentials in the presence of higher spin black holes, a canonical definition of entropy in the bulk, and a bulk-to-boundary dictionary aligned with the asymptotic symmetry algebra. We show that our canonical formalism shares the same formal structure as the so-called holomorphic formalism, but differs in the definition of charges and chemical potentials and in the bulk-to-boundary dictionary. Most importantly, we show that it admits a consistent CFT interpretation. We discuss the spin-2 and spin-3 cases in detail and generalize our construction to theories based on the hs[ λ] algebra, and on the sl( N,[InlineMediaObject not available: see fulltext.]) algebra for any choice of sl(2 ,[InlineMediaObject not available: see fulltext.]) embedding.
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...
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
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
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
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
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.)
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
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.
Constant curvature algebras and higher spin action generating functions
International Nuclear Information System (INIS)
Hallowell, K.; Waldron, A.
2005-01-01
The algebra of differential geometry operations on symmetric tensors over constant curvature manifolds forms a novel deformation of the sl(2,R)-bar R 2 Lie algebra. We present a simple calculus for calculations in its universal enveloping algebra. As an application, we derive generating functions for the actions and gauge invariances of massive, partially massless and massless (for both Bose and Fermi statistics) higher spins on constant curvature backgrounds. These are formulated in terms of a minimal set of covariant, unconstrained, fields rather than towers of auxiliary fields. Partially massless gauge transformations are shown to arise as degeneracies of the flat, massless gauge transformation in one dimension higher. Moreover, our results and calculus offer a considerable simplification over existing techniques for handling higher spins. In particular, we show how theories of arbitrary spin in dimension d can be rewritten in terms of a single scalar field in dimension 2d where the d additional dimensions correspond to coordinate differentials. We also develop an analogous framework for spinor-tensor fields in terms of the corresponding superalgebra
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
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
Toward a gauge field theory of gravity.
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.
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
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
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)
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.
Monopole charges in unified gauge theories
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).
On induced action for conformal higher spins in curved background
Energy Technology Data Exchange (ETDEWEB)
Beccaria, Matteo, E-mail: matteo.beccaria@le.infn.it [Dipartimento di Matematica e Fisica Ennio De Giorgi, Università del Salento & INFN, Via Arnesano, 73100 Lecce (Italy); Tseytlin, Arkady A., E-mail: tseytlin@imperial.ac.uk [The Blackett Laboratory, Imperial College, London SW7 2AZ (United Kingdom)
2017-06-15
We continue the investigation of the structure of the action for a tower of conformal higher spin fields in non-trivial 4d background metric recently discussed in Grigoriev and Tseytlin (2016). The action is defined as an induced one from path integral of a conformal scalar field in curved background coupled to higher spin fields. We analyze in detail the dependence of the quadratic part of the induced action on the spin 1 and spin 3 fields, determining the presence of a curvature-dependent mixed spin 1–3 term. One consequence is that the pure spin 3 kinetic term cannot be gauge-invariant on its own beyond the leading term in small curvature expansion. We also compute the non-zero contribution of the 1–3 mixing term to the conformal anomaly c-coefficient. One is thus to determine all such mixing terms before addressing the question of possible vanishing of the total c-coefficient in the conformal higher spin theory.
On induced action for conformal higher spins in curved background
Directory of Open Access Journals (Sweden)
Matteo Beccaria
2017-06-01
Full Text Available We continue the investigation of the structure of the action for a tower of conformal higher spin fields in non-trivial 4d background metric recently discussed in Grigoriev and Tseytlin (2016 [15]. The action is defined as an induced one from path integral of a conformal scalar field in curved background coupled to higher spin fields. We analyze in detail the dependence of the quadratic part of the induced action on the spin 1 and spin 3 fields, determining the presence of a curvature-dependent mixed spin 1–3 term. One consequence is that the pure spin 3 kinetic term cannot be gauge-invariant on its own beyond the leading term in small curvature expansion. We also compute the non-zero contribution of the 1–3 mixing term to the conformal anomaly c-coefficient. One is thus to determine all such mixing terms before addressing the question of possible vanishing of the total c-coefficient in the conformal higher spin theory.
Theories of higher spin particles
International Nuclear Information System (INIS)
Akshay, Y.S.; Sudarshan, Ananth
2015-01-01
One of the aims of theoretical physics is to understand the fundamental constituents of Nature and the interactions between them. The Standard Model of particle physics is currently our best description of Nature. It has been phenomenally successful in describing physics upto energy scales of a few hundred GeV. The SM contains matter particles (fermions), force carriers or mediators and the Higgs (bosons). The fermionic particles that make up all the visible matter around us are the leptons (electron, muon, tau, their respective neutrinos) and quarks (up, down, top, bottom, charm and strange). The force carriers of the SM mediate three of the four fundamental forces in Nature. The photon (γ) mediates the electromagnetic force, the W+,W-,Z mediate the weak force and the gluons (g) mediate the strong force. The Higgs boson plays an important role in the generation of masses for various particles
Quantizing higher-spin gravity in free-field variables
Campoleoni, Andrea; Fredenhagen, Stefan; Raeymaekers, Joris
2018-02-01
We study the formulation of massless higher-spin gravity on AdS3 in a gauge in which the fundamental variables satisfy free field Poisson brackets. This gauge choice leaves a small portion of the gauge freedom unfixed, which should be further quotiented out. We show that doing so leads to a bulk version of the Coulomb gas formalism for W N CFT's: the generators of the residual gauge symmetries are the classical limits of screening charges, while the gauge-invariant observables are classical W N charges. Quantization in these variables can be carried out using standard techniques and makes manifest a remnant of the triality symmetry of W ∞[λ]. This symmetry can be used to argue that the theory should be supplemented with additional matter content which is precisely that of the Prokushkin-Vasiliev theory. As a further application, we use our formulation to quantize a class of conical surplus solutions and confirm the conjecture that these are dual to specific degenerate W N primaries, to all orders in the large central charge expansion.
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
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.)
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.)
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
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)
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, ...
Radiative processes in gauge theories
International Nuclear Information System (INIS)
Berends, F.A.; Kleiss, R.; Danckaert, D.; Causmaecker, P. De; Gastmans, R.; Troost, W.; Tai Tsun Wu
1982-01-01
It is shown how the introduction of explicit polarization vectors of the radiated gauge particles leads to great simplifications in the calculation of bremsstrahlung processes at high energies. (author)
Thermodynamics of higher spin black holes in AdS3
International Nuclear Information System (INIS)
Boer, Jan de; Jottar, Juan I.
2014-01-01
We discuss the thermodynamics of recently constructed three-dimensional higher spin black holes in SL(N,ℝ)×SL(N,ℝ) Chern-Simons theory with generalized asymptotically-anti-de Sitter boundary conditions. From a holographic perspective, these bulk theories are dual to two-dimensional CFTs with W N symmetry algebras, and the black hole solutions are dual to thermal states with higher spin chemical potentials and charges turned on. Because the notion of horizon area is not gauge-invariant in the higher spin theory, the traditional approaches to the computation of black hole entropy must be reconsidered. One possibility, explored in the recent literature, involves demanding the existence of a partition function in the CFT, and consistency with the first law of thermodynamics. This approach is not free from ambiguities, however, and in particular different definitions of energy result in different expressions for the entropy. In the present work we show that there are natural definitions of the thermodynamically conjugate variables that follow from careful examination of the variational principle, and moreover agree with those obtained via canonical methods. Building on this intuition, we derive general expressions for the higher spin black hole entropy and free energy which are written entirely in terms of the Chern-Simons connections, and are valid for both static and rotating solutions. We compare our results to other proposals in the literature, and provide a new and efficient way to determine the generalization of the Cardy formula to a situation with higher spin charges
Thermodynamics of higher spin black holes in AdS3
de Boer, Jan; Jottar, Juan I.
2014-01-01
We discuss the thermodynamics of recently constructed three-dimensional higher spin black holes in SL( N, ) × SL( N, ) Chern-Simons theory with generalized asymptotically-anti-de Sitter boundary conditions. From a holographic perspective, these bulk theories are dual to two-dimensional CFTs with WN symmetry algebras, and the black hole solutions are dual to thermal states with higher spin chemical potentials and charges turned on. Because the notion of horizon area is not gauge-invariant in the higher spin theory, the traditional approaches to the computation of black hole entropy must be reconsidered. One possibility, explored in the recent literature, involves demanding the existence of a partition function in the CFT, and consistency with the first law of thermodynamics. This approach is not free from ambiguities, however, and in particular different definitions of energy result in different expressions for the entropy. In the present work we show that there are natural definitions of the thermodynamically conjugate variables that follow from careful examination of the variational principle, and moreover agree with those obtained via canonical methods. Building on this intuition, we derive general expressions for the higher spin black hole entropy and free energy which are written entirely in terms of the Chern-Simons connections, and are valid for both static and rotating solutions. We compare our results to other proposals in the literature, and provide a new and efficient way to determine the generalization of the Cardy formula to a situation with higher spin charges.
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
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.
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.)
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.)
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)
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
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
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.)
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
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.
Weyl gravity as a gauge theory
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.
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.
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
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
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.)
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
Experimental tests of gauge theories
International Nuclear Information System (INIS)
Haidt, D.
1984-11-01
This series of five lectures is intended to provide the experimental basis to the theoretical courses on gauge symmetries delivered by C. Jarlskog and R. Petronzio. The framework is the standard model. The experimental material is taken mainly from lepton-hadron and e + e - -experiments. (orig./HSI)
Higher spins and matter interacting in dimension three
Czech Academy of Sciences Publication Activity Database
Kessel, P.; Lucena Gómez, Gustavo; Skvortsov, E.; Taronna, M.
2015-01-01
Roč. 2015, č. 11 (2015), s. 104 ISSN 1029-8479 R&D Projects: GA ČR(CZ) GA14-31689S Institutional support: RVO:68378271 Keywords : Higher Spin Gravity * Higher Spin Symmetry * AdS-CFT correspondence * Chern-Simons Theories Subject RIV: BD - Theory of Information Impact factor: 6.023, year: 2015
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.)
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.)
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.)
Cubic interactions of Maxwell-like higher spins
Energy Technology Data Exchange (ETDEWEB)
Francia, Dario [Scuola Normale Superiore and INFN,Piazza dei Cavalieri, 7 I-56126 Pisa (Italy); Monaco, Gabriele Lo [Dipartimento di Fisica, Università di Pisa,Piazza Fibonacci, 3, I-56126, Pisa (Italy); Dipartimento di Fisica, Università di Milano-Bicocca,Piazza della Scienza 3, I-20126 Milano (Italy); Mkrtchyan, Karapet [Max Planck Institut für Gravitationsphysik,Am Mühlenberg 1, Potsdam 14476 (Germany)
2017-04-12
We study the cubic vertices for Maxwell-like higher-spins in flat and (A)dS background spaces of any dimension. Reducibility of their free spectra implies that a single cubic vertex involving any three fields subsumes a number of couplings among different particles of various spins. The resulting vertices do not involve traces of the fields and in this sense are simpler than their Fronsdal counterparts. We propose an extension of both the free theory and of its cubic deformation to a more general class of partially reducible systems, that one can obtain from the original theory upon imposing trace constraints of various orders. The key to our results is a version of the Noether procedure allowing to systematically account for the deformations of the transversality conditions to be imposed on the gauge parameters at the free level.
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)
Topological resolution of gauge theory singularities
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.
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.
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)
Origin of gauge invariance in string theory
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.
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
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
Gauge field theories an introduction with applications
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
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
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
Entanglement entropy and higher spin holography in AdS{sub 3}
Energy Technology Data Exchange (ETDEWEB)
Boer, Jan de; Jottar, Juan I. [Institute for Theoretical Physics, University of Amsterdam,Science Park 904, Postbus 94485, 1090 GL Amsterdam (Netherlands)
2014-04-14
A holographic correspondence has been recently developed between higher spin theories in three-dimensional anti-de Sitter space (AdS{sub 3}) and two-dimensional Conformal Field Theories (CFTs) with extended symmetries. A class of such dualities involves SL(N,R)×SL(N,R) Chern-Simons gauge theories in the (2+1)-dimensional bulk spacetime, and CFTs with W{sub N} symmetry algebras on the (1+1)-dimensional boundary. The topological character of the bulk theory forces one to reconsider standard geometric notions such as black hole horizons and entropy, as well as the usual holographic dictionary. Motivated by this challenge, in this note we present a proposal to compute entanglement entropy in the W{sub N} CFTs via holographic methods. In particular, we introduce a functional constructed from Wilson lines in the bulk Chern-Simons theory that captures the entanglement entropy in the CFTs dual to standard AdS{sub 3} gravity, corresponding to SL(2,R)×SL(2,R) gauge group, and admits an immediate generalization to the higher spin case. We explicitly evaluate this functional for several known solutions of the bulk theory, including charged black holes dual to thermal CFT states carrying higher spin charge, and show that it reproduces expected features of entanglement entropy, study whether it obeys strong subadditivity, and moreover show that it reduces to the thermal entropy in the appropriate limit.
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
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.)
Perturbative Quantum Gravity from Gauge Theory
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.
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.)
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
Observables and Microcospic Entropy of Higher Spin Black Holes
Compère, G.; Jottar, J.I.; Song, W.
2013-01-01
In the context of recently proposed holographic dualities between higher spin theories in AdS3 and (1 + 1)-dimensional CFTs with W symmetry algebras, we revisit the definition of higher spin black hole thermodynamics and the dictionary between bulk fields and dual CFT operators. We build a canonical
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.
Topologically Massive Higher Spin Gravity
Bagchi, A.; Lal, S.; Saha, A.; Sahoo, B.
2011-01-01
We look at the generalisation of topologically massive gravity (TMG) to higher spins, specifically spin-3. We find a special "chiral" point for the spin-three, analogous to the spin-two example, which actually coincides with the usual spin-two chiral point. But in contrast to usual TMG, there is the
Dual symmetry in gauge theories
International Nuclear Information System (INIS)
Koshkarov, A.L.
1997-01-01
Continuous dual symmetry in electrodynamics, Yang-Mills theory and gravitation is investigated. Dual invariant which leads to badly nonlinear motion equations is chosen as a Lagrangian of the pure classical dual nonlinear electrodynamics. In a natural manner some dual angle which is determined by the electromagnetic strengths at the point of the time-space appears in the model. Motion equations may well be interpreted as the equations of the standard Maxwell theory with source. Alternative interpretation is the quasi-Maxwell linear theory with magnetic charge. Analogous approach is possible in the Yang-Mills theory. In this case the dual-invariant non-Abelian theory motion equations possess the same instanton solutions as the conventional Yang-Mills equations have. An Abelian two-parameter dual group is found to exist in gravitation. Irreducible representations have been obtained: the curvature tensor was expanded into the sum of twice anti-self-dual and self-dual parts. Gravitational instantons are defined as (real )solutions to the usual duality equations. Central symmetry solutions to these equations are obtained. The twice anti-self-dual part of the curvature tensor may be used for introduction of new gravitational equations generalizing Einstein''s equations. However, the theory obtained reduces to the conformal-flat Nordstroem theory
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
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.
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.
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
Phenomenology of unified gauge theories
International Nuclear Information System (INIS)
Ellis, J.
1983-01-01
Part I of these lectures treats the standard Glashow-Weinberg-Salam model of weak and electromagnetic interactions, discussing in turn its basic structure and weak neutral currents, charged currents, mixing angles and CP violation, and the phenomenology of weak vector and Higgs bosons. Part II of the lectures discusses the structure of theories of dynamical symmetry breaking such as technicolour, phenomenological consequences, frustrations and alternatives. The third part of these lectures offers the standard menu of grand unified theories (GUTs) of the strong, weak and electromagnetic interactions, including an hors d'oeuvre of constraints on the parameters of the standard model, a main course of baryon number violating processes, and desserts which violate lepton number and CP. The fourth and final part goes through different attempts to remedy the inadequacies of previous theories by invoking supersymmetry and reaching out towards gravitation. (orig./HSI)
Geometry of supersymmetric gauge theories
International Nuclear Information System (INIS)
Gieres, F.
1988-01-01
This monograph gives a detailed and pedagogical account of the geometry of rigid superspace and supersymmetric Yang-Mills theories. While the core of the text is concerned with the classical theory, the quantization and anomaly problem are briefly discussed following a comprehensive introduction to BRS differential algebras and their field theoretical applications. Among the treated topics are invariant forms and vector fields on superspace, the matrix-representation of the super-Poincare group, invariant connections on reductive homogeneous spaces and the supermetric approach. Various aspects of the subject are discussed for the first time in textbook and are consistently presented in a unified geometric formalism
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)
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
An effective theory of massive gauge bosons
International Nuclear Information System (INIS)
Doria, R.M.; Helayel Neto, J.A.
1986-01-01
The coupling of a group-valued massive scalar field to a gauge field through a symmetric rank-2 field strenght is studied. By considering energies very small compared with the mass of the scalar and invoking the decoupling theorem, one is left with a low-energy effective theory describing a dynamics of massive vector fields. (Author) [pt
Moving vortices in noncommutative gauge theory
International Nuclear Information System (INIS)
Horvathy, P.A.; Stichel, P.C.
2004-01-01
Exact time-dependent solutions of nonrelativistic noncommutative Chern-Simons gauge theory are presented in closed analytic form. They are different from (indeed orthogonal to) those discussed recently by Hadasz, Lindstroem, Rocek and von Unge. Unlike theirs, our solutions can move with an arbitrary constant velocity, and can be obtained from the previously known static solutions by the recently found 'exotic' boost symmetry
Pauli-Guersey symmetry in gauge theories
International Nuclear Information System (INIS)
Stern, J.
1983-05-01
Gauge theories with massless or massive fermions in a selfcontragredient representation exhibit global symmetries of Pauli-Guersey type. Some of them are broken spontaneously leading to a difermion Goldstone bosons. An example of a boson version of the Pauli-Guersey symmetry is provided by the Weinberg-Salam model in the limit THETAsub(w)→O
Witten index calculation in supersymmetric gauge theory
International Nuclear Information System (INIS)
Smilga, A.V.
1984-01-01
Direct calculation of the Witten index Isub(W) in the SU(2) SUSY Yang-Mills theiory is performed using the periodic boundary conditions. Our result is Isub(W)--1 which disagrees with the Witten's result: Isub(W)=N for the SU(N) gauge group. The principle physical conclusion of SUSY unbreaking in this theory remains intact
Exotic configurations for gauge theory strings
International Nuclear Information System (INIS)
Yajnik, U.A.
1987-01-01
This paper discusses a class of string configurations occuring in nonabelian gauge theories, which are such that a component of the charged scalar field responsible for the string has a nonvanishing expectation value in the core of the string. A systematic procedure is given for setting up the ansatz for such configurations. (orig.)
Gauge theories of the weak interactions
International Nuclear Information System (INIS)
Quinn, H.
1978-08-01
Two lectures are presented on the Weinberg--Salam--Glashow--Iliopoulos--Maiani gauge theory for weak interactions. An attempt is made to give some impressions of the generality of this model, how it was developed, variations found in the literature, and the status of the standard model. 21 references
Recent advances in lattice gauge theories
Indian Academy of Sciences (India)
Abstract. Recent progress in the ﬁeld of lattice gauge theories is brieﬂy reviewed for a nonspecialist audience. While the emphasis is on the latest and more deﬁnitive results that have emerged prior to this symposium, an effort has been made to provide them with minimal technicalities.
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
Quantum Critical Behaviour of Semisimple Gauge Theories
DEFF Research Database (Denmark)
Kamuk Esbensen, Jacob; Ryttov, Thomas A.; Sannino, Francesco
2016-01-01
(M)_R \\times U(1) $ of the theory. To avoid gauge anomalies we add lepton-like particles. At the two-loops level an intriguing phase diagram appears. We uncover phases in which one, two or three fixed points exist and discuss the associated flows of the coupling constants. We discover a phase featuring...
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.
Monte Carlo algorithms for lattice gauge theory
International Nuclear Information System (INIS)
Creutz, M.
1987-05-01
Various techniques are reviewed which have been used in numerical simulations of lattice gauge theories. After formulating the problem, the Metropolis et al. algorithm and some interesting variations are discussed. The numerous proposed schemes for including fermionic fields in the simulations are summarized. Langevin, microcanonical, and hybrid approaches to simulating field theories via differential evolution in a fictitious time coordinate are treated. Some speculations are made on new approaches to fermionic simulations
Coset space dimensional reduction of gauge theories
Energy Technology Data Exchange (ETDEWEB)
Kapetanakis, D. (Physik Dept., Technische Univ. Muenchen, Garching (Germany)); Zoupanos, G. (CERN, Geneva (Switzerland))
1992-10-01
We review the attempts to construct unified theories defined in higher dimensions which are dimensionally reduced over coset spaces. We employ the coset space dimensional reduction scheme, which permits the detailed study of the resulting four-dimensional gauge theories. In the context of this scheme we present the difficulties and the suggested ways out in the attempts to describe the observed interactions in a realistic way. (orig.).
Coset space dimensional reduction of gauge theories
International Nuclear Information System (INIS)
Kapetanakis, D.; Zoupanos, G.
1992-01-01
We review the attempts to construct unified theories defined in higher dimensions which are dimensionally reduced over coset spaces. We employ the coset space dimensional reduction scheme, which permits the detailed study of the resulting four-dimensional gauge theories. In the context of this scheme we present the difficulties and the suggested ways out in the attempts to describe the observed interactions in a realistic way. (orig.)
Large transverse momentum behavior of gauge theories
International Nuclear Information System (INIS)
Coquereaux, Robert; De Rafael, Eduardo.
1977-05-01
The large transverse momentum behavior of Compton scattering and Moeller scattering in Quantum Electrodynamics; and of elastic quark-quark scattering in Quantum Chromodynamics are examined in perturbation theory. The results strongly suggest that the large transverse momentum regime in gauge theories is governed by a differential equation of the Callan-Symanzik type with a suitable momentum dependent anomalous dimension term. An explicit solution for the quark-quark elastic scattering amplitude at large transverse momentum is given
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
Higher spin fields and the Gelfand-Dickey algebra
International Nuclear Information System (INIS)
Bakas, I.
1989-01-01
We show that in 2-dimensional field theory, higher spin algebras are contained in the algebra of formal pseudodifferential operators introduced by Gelfand and Dickey to describe integrable nonlinear differential equations in Lax form. The spin 2 and 3 algebras are discussed in detail and the generalization to all higher spins is outlined. This provides a conformal field theory approach to the representation theory of Gelfand-Dickey algebras. (orig.)
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
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
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.)
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.)
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)
Quiver gauge theories and integrable lattice models
International Nuclear Information System (INIS)
Yagi, Junya
2015-01-01
We discuss connections between certain classes of supersymmetric quiver gauge theories and integrable lattice models from the point of view of topological quantum field theories (TQFTs). The relevant classes include 4d N=1 theories known as brane box and brane tilling models, 3d N=2 and 2d N=(2,2) theories obtained from them by compactification, and 2d N=(0,2) theories closely related to these theories. We argue that their supersymmetric indices carry structures of TQFTs equipped with line operators, and as a consequence, are equal to the partition functions of lattice models. The integrability of these models follows from the existence of extra dimension in the TQFTs, which emerges after the theories are embedded in M-theory. The Yang-Baxter equation expresses the invariance of supersymmetric indices under Seiberg duality and its lower-dimensional analogs.
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
Extended higher-spin superalgebras and their massless representations
Energy Technology Data Exchange (ETDEWEB)
Konstein, S E; Vasiliev, M A [AN SSSR, Moscow (USSR). Fizicheskij Inst.
1990-02-12
Three two-parameter sequences of infinite-dimensional extended higher-spin superalgebras are constructed, which give rise to consistent equations of motion of interacting gauge fields of all spins in four dimensions. In the Yang-Mills sector of spin-1 gauge fields, these higher-spin superalgebras reduce to u(n) + u(m), o(n) + o(m) and usp(n) + usp(m) with arbitrary integer parameters n {ge} 0 and m {ge} 0 (n and m are assumed to be even for symplectic algebras). Massless unitary representations of the proposed higher-spin superalgebras are analyzed. It is shown that all these superalgebras obey the admissibility condition which requires them to possess massless unitary representations with just the same spectra of spins as follows from the structure of the related higher-spin gauge fields. We argue that the infinite-dimensional (super)algebras listed in this article classify all possible higher-spin rigid (super)symmetries in four dimensions. (orig.).
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
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.
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.
Higher-spin extended conformal algebras and W-gravities
International Nuclear Information System (INIS)
Hull, C.M.
1991-01-01
The construction of classical W 3 gravity is reviewed. It is suggested that the hidden symmetry for quantum W 3 gravity in the chiral gauge is not SL(3, R) but a group contraction of this, ISL(2, R). This is extended to W N gravity, and the case of W 4 gravity is presented in detail. The gauge transformations are realized on D free bosons, with the spin-n conserved current (2 ≤ n ≤ N) taking the form d sub(i i ...i n ) δ + Φ sup(i 1 ) δ + Φ sup(i n ) for some constant tensor d sub(i i ...i n ). The d-tensors must satisfy N-2 non-linear algebraic constraints and these constraints are shown to be satisfied if the d-tensors are taken to be the structure-tensors of an Nth degree Jordan algebra. The relation with Jordan algebras is used to give solutions of the d-tensor constraints for any value of D, N. The free-boson construction of the W N algebras is generalized to give a Sugaware-type construction of a large class of classical extended conformal algebras. The chiral gauging of any classical extended conformal algebra is shown to require only a linear Noether coupling to world-sheet gauge-fields, while gauging a non-chiral algebra in general leads to a non-polynomial action. A number of examples are examined, including W ∞ W-supergravity, Knizhnik-Berschadsky supergravity and 'W N/M ' algebras. Theories of higher-spin W-gravity of the type described are only possible in one and two space-time dimensions, and the one-dimensional cases is briefly discussed. The covariant formulation of W-gravity is briefly discussed and the relation between classical and quantum extended conformal algebras is analyzed. (orig.)
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
Strong dynamics and lattice gauge theory
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
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
Conformal bootstrap with slightly broken higher spin symmetry
Energy Technology Data Exchange (ETDEWEB)
Alday, Luis F. [Mathematical Institute, University of Oxford,Andrew Wiles Building, Radcliffe Observatory Quarter,Woodstock Road, Oxford, OX2 6GG (United Kingdom); Zhiboedov, Alexander [Center for the Fundamental Laws of Nature,Harvard University, Cambridge, MA 02138 (United States)
2016-06-16
We consider conformal field theories with slightly broken higher spin symmetry in arbitrary spacetime dimensions. We analyze the crossing equation in the double light-cone limit and solve for the anomalous dimensions of higher spin currents γ{sub s} with large spin s. The result depends on the symmetries and the spectrum of the unperturbed conformal field theory. We reproduce all known results and make further predictions. In particular we make a prediction for the anomalous dimensions of higher spin currents in the 3d Ising model.
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.)
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
Three Point Functions in Higher Spin AdS3 Holography with 1/N Corrections
Directory of Open Access Journals (Sweden)
Yasuaki Hikida
2017-10-01
Full Text Available We examine three point functions with two scalar operators and a higher spin current in 2d W N minimal model to the next non-trivial order in 1 / N expansion. The minimal model was proposed to be dual to a 3d higher spin gauge theory, and 1 / N corrections should be interpreted as quantum effects in the dual gravity theory. We develop a simple and systematic method to obtain three point functions by decomposing four point functions of scalar operators with Virasoro conformal blocks. Applying the method, we reproduce known results at the leading order in 1 / N and obtain new ones at the next leading order. As confirmation, we check that our results satisfy relations among three point functions conjectured before.
Extended Holomorphic Anomaly in Gauge Theory
Krefl, Daniel
2011-01-01
The partition function of an N=2 gauge theory in the Omega-background satisfies, for generic value of the parameter beta=-eps_1/eps_2, the, in general extended, but otherwise beta-independent, holomorphic anomaly equation of special geometry. Modularity together with the (beta-dependent) gap structure at the various singular loci in the moduli space completely fixes the holomorphic ambiguity, also when the extension is non-trivial. In some cases, the theory at the orbifold radius, corresponding to beta=2, can be identified with an "orientifold" of the theory at beta=1. The various connections give hints for embedding the structure into the topological string.
Improved thermodynamics of SU(2) gauge theory
Energy Technology Data Exchange (ETDEWEB)
Giudice, Pietro [University of Muenster, Institute for Theoretical Physics, Muenster (Germany); Piemonte, Stefano [University of Regensburg, Institute for Theoretical Physics, Regensburg (Germany)
2017-12-15
In this work we present the results of our investigation of the thermodynamics of SU(2) gauge theory. We employ a Symanzik improved action to reduce strongly the discretisations effects, and we use the scaling relations to take into account the finite volume effects close to the critical temperature. We determine the β-function for this particular theory and we use it in the determination of different thermodynamic observables. Finally we compare our results with previous work where only the standard Wilson action was considered. We confirm the relevance of using the improved action to access easily the correct continuum thermodynamics of the theory. (orig.)
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.
On Painlevé/gauge theory correspondence
Bonelli, Giulio; Lisovyy, Oleg; Maruyoshi, Kazunobu; Sciarappa, Antonio; Tanzini, Alessandro
2017-12-01
We elucidate the relation between Painlevé equations and four-dimensional rank one N = 2 theories by identifying the connection associated with Painlevé isomonodromic problems with the oper limit of the flat connection of the Hitchin system associated with gauge theories and by studying the corresponding renormalization group flow. Based on this correspondence, we provide long-distance expansions at various canonical rays for all Painlevé τ -functions in terms of magnetic and dyonic Nekrasov partition functions for N = 2 SQCD and Argyres-Douglas theories at self-dual Omega background ɛ _1 + ɛ _2 = 0 or equivalently in terms of c=1 irregular conformal blocks.
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.)
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)
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.
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.
Gravitational Goldstone fields from affine gauge theory
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.
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
Holographic entanglement in a noncommutative gauge theory
International Nuclear Information System (INIS)
Fischler, Willy; Kundu, Arnab; Kundu, Sandipan
2014-01-01
In this article we investigate aspects of entanglement entropy and mutual information in a large-N strongly coupled noncommutative gauge theory, both at zero and at finite temperature. Using the gauge-gravity duality and the Ryu-Takayanagi (RT) prescription, we adopt a scheme for defining spatial regions on such noncommutative geometries and subsequently compute the corresponding entanglement entropy. We observe that for regions which do not lie entirely in the noncommutative plane, the RT-prescription yields sensible results. In order to make sense of the divergence structure of the corresponding entanglement entropy, it is essential to introduce an additional cut-off in the theory. For regions which lie entirely in the noncommutative plane, the corresponding minimal area surfaces can only be defined at this cut-off and they have distinctly peculiar properties
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
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.
Microcanonical ensemble formulation of lattice gauge theory
International Nuclear Information System (INIS)
Callaway, D.J.E.; Rahman, A.
1982-01-01
A new formulation of lattice gauge theory without explicit path integrals or sums is obtained by using the microcanonical ensemble of statistical mechanics. Expectation values in the new formalism are calculated by solving a large set of coupled, nonlinear, ordinary differential equations. The average plaquette for compact electrodynamics calculated in this fashion agrees with standard Monte Carlo results. Possible advantages of the microcanonical method in applications to fermionic systems are discussed
Finite size scaling and lattice gauge theory
International Nuclear Information System (INIS)
Berg, B.A.
1986-01-01
Finite size (Fisher) scaling is investigated for four dimensional SU(2) and SU(3) lattice gauge theories without quarks. It allows to disentangle violations of (asymptotic) scaling and finite volume corrections. Mass spectrum, string tension, deconfinement temperature and lattice β-function are considered. For appropriate volumes, Monte Carlo investigations seem to be able to control the finite volume continuum limit. Contact is made with Luescher's small volume expansion and possibly also with the asymptotic large volume behavior. 41 refs., 19 figs
Comment on ''Topologically Massive Gauge Theories''
International Nuclear Information System (INIS)
Bezerra de Mello, E.R.
1988-01-01
In a recent paper by R. Pisarski and S. Rao concerning topologically massive quantum Yang--Mills theory, the expression of the P-even part of the non-Abelian gauge field self-energy at one-loop order is shown to obey a consistency condition, which is not fulfilled by the formula originally presented by S. Deser, R. Jackiw, and S. Templeton. In this comment, I present a recalculation which agress with Pisarski and Rao. copyright 1988 Academic Press, Inc
Some cosmological constraints on gauge theories
International Nuclear Information System (INIS)
Schramm, D.N.
1983-01-01
In these lectures, a review is made of various constraints cosmology may place on gauge theories. Particular emphasis is placed on those constraints obtainable from Big Bang Nucleosynthesis, with only brief mention made of Big Bang Baryosynthesis. There is also a considerable discussion of astrophysical constraints on masses and lifetimes of neutrinos with specific mention of the 'missing mass (light)' problem of galactic dynamics. (orig./HSI)
Symmetry behavior of the effective gauge theory
International Nuclear Information System (INIS)
Midorikawa, S.
1981-01-01
The restoration of spontaneously broken CP invariance is investigated by using the effective QED lagrangian obtained from the standard SU(2) x U(1) gauge theory with two Higgs doublets. It is shown that the large electromagnetic field may restore CP invariance by changing the relative phase angle of Higgs vacuum expectation values even before one of the vacuum expectation values of the two Higgs doublets disappears. Further large magnetic field may lead to the fine structure constant with discontinuous behavior. (orig.)
Abelian gauge symmetries in F-theory and dual theories
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
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
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.
Inflation and gauge mediation in supersymmetric gauge theory
International Nuclear Information System (INIS)
Nakai, Yuichiro; Sakai, Manabu
2011-01-01
We propose a simple high-scale inflationary scenario based on a phenomenologically viable model with direct gauge mediation of low-scale supersymmetry breaking. Hybrid inflation occurs in a hidden supersymmetry breaking sector. Two hierarchical mass scales to reconcile both high-scale inflation and gauge mediation are necessary for the stability of the metastable supersymmetry breaking vacuum. Our scenario is also natural in light of the Landau pole problem of direct gauge mediation. (author)
Higher spins and Yangian symmetries
Energy Technology Data Exchange (ETDEWEB)
Gaberdiel, Matthias R. [Institut für Theoretische Physik, ETH Zurich, CH-8093 Zurich (Switzerland); Gopakumar, Rajesh [International Centre for Theoretical Sciences-TIFR, Survey No. 151, Shivakote, Hesaraghatta Hobli, Bengaluru North 560 089 (India); Li, Wei [CAS Key Laboratory of Theoretical Physics,Institute of Theoretical Physics, Chinese Academy of Sciences,100190 Beijing (China); Peng, Cheng [Department of Physics, Brown University, 182 Hope Street, Providence, RI 02912 (United States)
2017-04-26
The relation between the bosonic higher spin W{sub ∞}[λ] algebra, the affine Yangian of gl{sub 1}, and the SH{sup c} algebra is established in detail. For generic λ we find explicit expressions for the low-lying W{sub ∞}[λ] modes in terms of the affine Yangian generators, and deduce from this the precise identification between λ and the parameters of the affine Yangian. Furthermore, for the free field cases corresponding to λ=0 and λ=1 we give closed-form expressions for the affine Yangian generators in terms of the free fields. Interestingly, the relation between the W{sub ∞} modes and those of the affine Yangian is a non-local one, in general. We also establish the explicit dictionary between the affine Yangian and the SH{sup c} generators. Given that Yangian algebras are the hallmark of integrability, these identifications should pave the way towards uncovering the relation between the integrable and the higher spin symmetries.
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
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
Noncommutative gauge theory without Lorentz violation
International Nuclear Information System (INIS)
Carlson, Carl E.; Carone, Christopher D.; Zobin, Nahum
2002-01-01
The most popular noncommutative field theories are characterized by a matrix parameter θ μν that violates Lorentz invariance. We consider the simplest algebra in which the θ parameter is promoted to an operator and Lorentz invariance is preserved. This algebra arises through the contraction of a larger one for which explicit representations are already known. We formulate a star product and construct the gauge-invariant Lagrangian for Lorentz-conserving noncommutative QED. Three-photon vertices are absent in the theory, while a four-photon coupling exists and leads to a distinctive phenomenology
Electron-positron scattering and gauge theories
International Nuclear Information System (INIS)
Davier, M.
1983-07-01
Recent results from high-energy e + e - colliding facilities are reviewed in the context of gauge theories. First QCD analyses are discussed and difficulties are seen to arise from the interplay between perturbative QCD and non-perturbative fragmentation processes. Many results have been recently obtained on weak electromagnetic interference, strengthening our faith in the standard SU(2) x U(1) theory: however some pieces are still missing and looked for. Finally, vigourous searches are pursued to find clues for physics beyond the SU(3) x SU(2) x U(1) framework: among those supersymmetric particles are being actively hunted in a large variety of situations
Gauge theory and defects in solids
Edelen, DGB
2012-01-01
This new series Mechanics and Physics of Discrete Systems aims to provide a coherent picture of the modern development of discrete physical systems. Each volume will offer an orderly perspective of disciplines such as molecular dynamics, crystal mechanics and/or physics, dislocation, etc. Emphasized in particular are the fundamentals of mechanics and physics that play an essential role in engineering applications.Volume 1, Gauge Theory and Defects in Solids, presents a detailed development of a rational theory of the dynamics of defects and damage in solids. Solutions to field e
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.)
M-Theory and Maximally Supersymmetric Gauge Theories
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.
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.)
Numerical studies of gauge field theories
International Nuclear Information System (INIS)
Creutz, M.
1981-06-01
Monte Carlo simulation of statistical systems is a well established technique of the condensed matter physicist. In the last few years, particle theorists have rediscovered this method and are having a marvelous time applying it to quantized gauge field theories. The main result has been strong numerical evidence that the standard SU(3) non-Abelian gauge theory of the strong interaction is capable of simultaneously confining quarks into the physical hadrons and exhibiting asymptotic freedom, the phenomenon of quark interactions being small at short distances. In four dimensions, confinement is a non-perturbative phenomenon. Essentially all models of confinement tie widely separated quarks together with strings of gauge field flux. This gives rise to a linear potential at long distances. A Monte Carlo program generates a sequence of field configuration by a series of random changes of the fields. The algorithm is so constructed that ultimately the probability density for finding any given configuration is proportional to the Boltzmann weighting. We bring our lattices into thermal equilibrium with a heat bath at a temperature specified by the coupling constant. Thus we do computer experiments with four-dimensional crystals stored in a computer memory. As the entire field configuration is stored, we have access to any correlation function desired. These lectures describe the kinds of experiments being done and the implications of these results for strong interaction physics
Lattice gauge theory in the microcanonical ensemble
International Nuclear Information System (INIS)
Callaway, D.J.E.; Rahman, A.
1983-01-01
The microcanonical-ensemble formulation of lattice gauge theory proposed recently is examined in detail. Expectation values in this new ensemble are determined by solving a large set of coupled ordinary differential equations, after the fashion of a molecular dynamics simulation. Following a brief review of the microcanonical ensemble, calculations are performed for the gauge groups U(1), SU(2), and SU(3). The results are compared and contrasted with standard methods of computation. Several advantages of the new formalism are noted. For example, no random numbers are required to update the system. Also, this update is performed in a simultaneous fashion. Thus the microcanonical method presumably adapts well to parallel processing techniques, especially when the p action is highly nonlocal (such as when fermions are included)
Status and future of lattice gauge theory
International Nuclear Information System (INIS)
Hoek, J.
1989-07-01
The current status of lattice Quantum Chromo Dynamics (QCD) calculations, the computer requirements to obtain physical results and the direction computing is taking are described. First of all, there is a lot of evidence that QCD is the correct theory of strong interactions. Since it is an asymptotically free theory we can use perturbation theory to solve it in the regime of very hard collisions. However even in the case of very hard parton collisions the end-results of the collisions are bound states of quarks and perturbation theory is not sufficient to calculate these final stages. The way to solve the theory in this regime was opened by Wilson. He contemplated replacing the space-time continuum by a discrete lattice, with a lattice spacing a. Continuum physics is then recovered in the limit where the correlation length of the theory, say ξ. is large with respect to the lattice spacing. This will be true if the lattice spacing becomes very small, which for asymptotically free theories also implies that the coupling g becomes small. The lattice approach to QCD is in many respects analogous to the use of finite element methods to solve classical field theories. These finite element methods are easy to apply in 2-dimensional simulations but are computationally demanding in the 3-dimensional case. Therefore it is not unexpected that the 4-dimensional simulations needed for lattice gauge theories have led to an explosion in demand for computing power by theorists. (author)
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
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
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.)
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.
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.
Global anomalies in chiral lattice gauge theories
International Nuclear Information System (INIS)
Baer, O.
2000-07-01
We study global anomalies in a new approach to chiral gauge theories on the lattice, which is based on the Ginsparg-Wilson relation. In this approach, global anomalies make it impossible to define consistently a fermionic measure for the functional integral. We show that a global anomaly occurs in an SU(2) theory if the fundamental representation is used for the fermion fields. The generalization to higher representations is also discussed. In addition we establish a close relation between global anomalies and the spectral flow of the Dirac operator and employ it in a numerical computation to prove the existence of the global SU(2) anomaly in a different way. This method is inspired by an earlier work of Witten who first discovered this type of anomalies in continuum field theory. (orig.)
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
Hadron masses in a gauge theory
International Nuclear Information System (INIS)
De Rujula, A.; Georgi, H.; Glashow, S.L.
1975-01-01
We explore the implications for hadron spectroscopy of the ''standard'' gauge model of weak, electromagnetic, and strong interactions. The model involves four types of fractionally charged quarks, each in three colors, coupling to massless gauge gluons. The quarks are confined within colorless hadrons by a long-range spin-independent force realizing infrared slavery. We use the asymptotic freedom of the model to argue that for the calculation of hadron masses, the short-range quark-quark interaction may be taken to be Coulomb-like. We rederive many successful quark-model mass relations for the low-lying hadrons. Because a specific interaction and symmetry-breaking mechanism are forced on us by the underlying renormalizable gauge field theory, we also obtain new mass relations. They are well satisfied. We develop a qualitative understanding of many features of the hadron mass spectrum, such as the origin and sign of the Σ-Λ mass splitting. Interpreting the newly discovered narrow boson resonances as states of charmonium, we use the model to predict the masses of charmed mesons and baryons
Lattice gauge theories and Monte Carlo simulations
International Nuclear Information System (INIS)
Rebbi, C.
1981-11-01
After some preliminary considerations, the discussion of quantum gauge theories on a Euclidean lattice takes up the definition of Euclidean quantum theory and treatment of the continuum limit; analogy is made with statistical mechanics. Perturbative methods can produce useful results for strong or weak coupling. In the attempts to investigate the properties of the systems for intermediate coupling, numerical methods known as Monte Carlo simulations have proved valuable. The bulk of this paper illustrates the basic ideas underlying the Monte Carlo numerical techniques and the major results achieved with them according to the following program: Monte Carlo simulations (general theory, practical considerations), phase structure of Abelian and non-Abelian models, the observables (coefficient of the linear term in the potential between two static sources at large separation, mass of the lowest excited state with the quantum numbers of the vacuum (the so-called glueball), the potential between two static sources at very small distance, the critical temperature at which sources become deconfined), gauge fields coupled to basonic matter (Higgs) fields, and systems with fermions
National software infrastructure for lattice gauge theory
International Nuclear Information System (INIS)
Brower, Richard C
2005-01-01
The current status of the SciDAC software infrastructure project for lattice gauge theory is summarized. This includes the the design of a QCD application programmers interface (API) that allows existing and future codes to be run efficiently on Terascale hardware facilities and to be rapidly ported to new dedicated or commercial platforms. The critical components of the API have been implemented and are in use on the US QCDOC hardware at BNL and on both the switched and mesh architecture Pentium 4 clusters at Fermi National Accelerator Laboratory (FNAL) and Thomas Jefferson National Accelerator Facility (JLab). Future software infrastructure requirements and research directions are also discussed
Lattice Gauge Field Theory and Prismatic Sets
DEFF Research Database (Denmark)
Akyar, Bedia; Dupont, Johan Louis
as and in particular the latter we use to study lattice gauge theory in the sense of Phillips and Stone. Thus for a Lie group and a set of parallel transport functions defining the transition over faces of the simplices, we define a classifying map from the prismatic star to a prismatic version of the classifying......We study prismatic sets analogously to simplicial sets except that realization involves prisms, i.e., products of simplices rather than just simplices. Particular examples are the prismatic subdivision of a simplicial set and the prismatic star of . Both have the same homotopy type...
Screening in two-dimensional gauge theories
International Nuclear Information System (INIS)
Korcyl, Piotr; Deutsches Elektronen-Synchrotron; Koren, Mateusz
2012-12-01
We analyze the problem of screening in 1+1 dimensional gauge theories. Using QED 2 as a warmup for the non-abelian models we show the mechanism of the string breaking, in particular the vanishing overlap of the Wilson loops to the broken-string ground state that has been conjectured in higher-dimensional analyses. We attempt to extend our analysis to non-integer charges in the quenched and unquenched cases, in pursuit of the numerical check of a renowned result for the string tension between arbitrarily-charged fermions in the massive Schwinger model.
Phase transition in SO(3) gauge theory
International Nuclear Information System (INIS)
Datta, Saumen; Gavai, Rajiv V.
1998-01-01
The phase transition in SO(3) lattice gauge theory is investigated by Monte Carlo techniques with a view (i) to understand the relationship between the bulk transition and the deconfinement transition, and (ii) to resolve the current ambiguity about the nature of the high temperature phase. By introduction of a magnetic field, it was shown that the +ve and -ve values of a > correspond to the same phase. Studies on different sized lattices lead to the conclusion that in SO(3), there is only one transition, which is deconfining in nature. (author)
The Lanczos method in lattice gauge theories
International Nuclear Information System (INIS)
Barbour, I.M.; Behilil, N.E.; Gibbs, P.E.; Teper, M.; Schierholz, G.
1984-09-01
We present a modified version of the Lanczos algorithm as a computational method for tridiagonalising large sparse matrices, which avoids the requirement for large amounts of storage space. It can be applied as a first step in calculating eigenvalues and eigenvectors or for obtaining the inverse of a matrix row by row. Here we describe the method and apply it to various problems in lattice gauge theories. We have found it to have excellent convergence properties. In particular it enables us to do lattice calculations at small and even zero quark mass. (orig.)
Monopole Solutions in Topologically Massive Gauge Theory
International Nuclear Information System (INIS)
Teh, Rosy; Wong, Khai-Ming; Koh, Pin-Wai
2010-01-01
Monopoles in topologically massive SU(2) Yang-Mils-Higgs gauge theory in 2+1 dimensions with a Chern-Simon mass term have been studied by Pisarski some years ago. He argued that there is a monopole solution that is regular everywhere, but found that it does not possess finite action. There were no exact or numerical solutions being presented by him. Hence it is our purpose to further investigate this solution in more detail. We obtained numerical regular solutions that smoothly interpolates between the behavior at small and large distances for different values of Chern-Simon term strength and for several fixed values of Higgs field strength.
Screening in two-dimensional gauge theories
Energy Technology Data Exchange (ETDEWEB)
Korcyl, Piotr [Uniwersytet Jagiellonski, Cracow (Poland). Inst. Fizyki; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Koren, Mateusz [Uniwersytet Jagiellonski, Cracow (Poland). Inst. Fizyki
2012-12-15
We analyze the problem of screening in 1+1 dimensional gauge theories. Using QED{sub 2} as a warmup for the non-abelian models we show the mechanism of the string breaking, in particular the vanishing overlap of the Wilson loops to the broken-string ground state that has been conjectured in higher-dimensional analyses. We attempt to extend our analysis to non-integer charges in the quenched and unquenched cases, in pursuit of the numerical check of a renowned result for the string tension between arbitrarily-charged fermions in the massive Schwinger model.
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.)
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.)
An infinite-dimensional calculus for gauge theories
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 ...
On the non-local obstruction to interacting higher spins in flat space
Energy Technology Data Exchange (ETDEWEB)
Taronna, Massimo [Physique Théorique et Mathématique,Université Libre de Bruxelles and International Solvay Institutes,ULB-Campus Plaine CP231, 1050 Brussels (Belgium)
2017-05-04
Owing to a renewed interest in flat space higher spin gauge theories, in this note we provide further details and clarifications on the results presented in arXiv:1107.5843 and arXiv: 1209.5755, which investigated their locality properties. Focusing, for simplicity, on quartic couplings with one of the external legs having non-zero integer spin (which can be considered as a prototype for Weinberg-type arguments), we review the appearance of 1/◻ non-localities. In particular, we emphasise that it appears to be not possible to eliminate all of the aforementioned non-localities in the general quartic Noether procedure solution with a judicious choice of coupling constants and spectrum. We also discuss the light-cone gauge fixing in d=4, and argue that the non-local obstruction discussed in the covariant language cannot be avoided using light-cone gauge formalism.
Non-Abelian Gauge Theory in the Lorentz Violating Background
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.
New results in topological field theory and Abelian gauge theory
International Nuclear Information System (INIS)
Thompson, G.
1995-10-01
These are the lecture notes of a set of lectures delivered at the 1995 Trieste summer school in June. I review some recent work on duality in four dimensional Maxwell theory on arbitrary four manifolds, as well as a new set of topological invariants known as the Seiberg-Witten invariants. Much of the necessary background material is given, including a crash course in topological field theory, cohomology of manifolds, topological gauge theory and the rudiments of four manifold theory. My main hope is to wet the readers appetite, so that he or she will wish to read the original works and perhaps to enter this field. (author). 41 refs, 5 figs
New results in topological field theory and Abelian gauge theory
Energy Technology Data Exchange (ETDEWEB)
Thompson, G
1995-10-01
These are the lecture notes of a set of lectures delivered at the 1995 Trieste summer school in June. I review some recent work on duality in four dimensional Maxwell theory on arbitrary four manifolds, as well as a new set of topological invariants known as the Seiberg-Witten invariants. Much of the necessary background material is given, including a crash course in topological field theory, cohomology of manifolds, topological gauge theory and the rudiments of four manifold theory. My main hope is to wet the readers appetite, so that he or she will wish to read the original works and perhaps to enter this field. (author). 41 refs, 5 figs.
Algebraic differential calculus for gauge theories
International Nuclear Information System (INIS)
Landi, G.; Marmo, G.
1990-01-01
The guiding idea in this paper is that, from the point of view of physics, functions and fields are more important than the (space time) manifold over which they are defined. The line pursued in these notes belongs to the general framework of ideas that replaces the space M by the ring of functions on it. Our essential observation, underlying this work, is that much of mathematical physics requires only a few differential operators (Lie derivative, d, δ) operating on modules of sections of suitable bundles. A connection (=gauge potential) can be described by a lift of vector fields from the base to the total space of a principal bundle. Much of the information can be encoded in the lift without reference to the bundle structures. In this manner, one arrives at an 'algebraic differential calculus' and its graded generalization that we are going to discuss. We are going to give an exposition of 'algebraic gauge theory' in both ungraded and graded versions. We show how to deal with the essential features of electromagnetism, Dirac, Kaluza-Klein and 't Hooft-Polyakov monopoles. We also show how to break the symmetry from SU(2) to U(1) without Higgs field. We briefly show how to deal with tests particles in external fields and with the Lagrangian formulation of field theories. (orig./HSI)
Path integral for gauge theories with fermions
International Nuclear Information System (INIS)
Fujikawa, K.
1980-01-01
The Atiyah-Singer index theorem indicates that a naive unitary transformation of basis vectors for fermions interacting with gauge fields is not allowed in general. On the basis of this observation, it was previously shown that the path-integral measure of a gauge-invariant fermion theory is transformed nontrivially under the chiral transformation, and thus leads to a simple derivation of ''anomalous'' chiral Ward-Takahashi identities. We here clarify some of the technical aspects associated with the discussion. It is shown that the Jacobian factor in the path-integral measure, which corresponds to the Adler-Bell-Jackiw anomaly, is independent of any smooth regularization procedure of large eigenvalues of D in Euclidean theory; this property holds in any even-dimensional space-time and also for the gravitational anomaly. The appearance of the anomaly and its connection with the index theorem are thus related to the fact that the primary importance is attached to the Lorentz-covariant ''energy'' operator D and that D and γ 5 do not commute. The abnormal behavior of the path-integral measure at the zero-frequency sector in the presence of instantons and its connection with spontaneous symmetry breaking is also clarified. We comment on several other problems associated with the anomaly and on the Pauli-Villars regularization method
Eternal higher spin black holes: a thermofield Interpretation
International Nuclear Information System (INIS)
Castro, Alejandra; Iqbal, Nabil; Llabrés, Eva
2016-01-01
We study Lorentzian eternal black holes in the Chern-Simons sector of AdS 3 higher spin gravity. We probe such black holes using bulk Wilson lines and motivate new regularity conditions that must be obeyed by the bulk connections in order for the geometry to be consistent with an interpretation as a thermofield state in the dual CFT 2 . We demonstrate that any higher spin black hole may be placed in a gauge that satisfies these conditions: this is the Chern-Simons analogue of the construction of Kruskal coordinates that permit passage through the black hole horizon. We also argue that the Wilson line provides a higher-spin notion of causality in higher spin gravity that can be used to associate a Penrose diagram with the black hole. We present some applications of the formalism, including a study of the time-dependent entanglement entropy arising from the higher spin black hole interior and evidence for an emergent AdS 2 region in the extremal limit.
RG cascades in hyperbolic quiver gauge theories
International Nuclear Information System (INIS)
Ahl Laamara, R.; Ait Ben Haddou, M.; Belhaj, A.; Drissi, L.B.; Saidi, E.H.
2004-01-01
In this paper, we provide a general classification of supersymmatric QFT4s into three basic sets: ordinary, affine and indefinite classes. The last class, which has not been enough explored in literature, is shown to share most of properties of ordinary and affine super-QFT4s. This includes, amongst others, its embedding in type II string on local Calabi-Yau threefolds. We give realizations of these supersymmetric QFT4s as D-brane world volume gauge theories. A special interest is devoted to hyperbolic subset for its peculiar features and for the role it plays in type IIB background with non-zero axion. We also study RG flows and duality cascades in case of hyperbolic quiver theories. Comments regarding the full indefinite sector are made
Semiclassical spinning strings and confining gauge theories
International Nuclear Information System (INIS)
Bigazzi, F.; Cotrone, A.L.; Martucci, L.
2004-03-01
We study multi-charged rotating string states on Type II B regular backgrounds dual to confining SU(N) gauge theories with (softly broken) N=1 supersymmetry, in the infra red regime. After exhibiting the classical energy/charge relations for the folded and circular two-charge strings, we compute in the latter case the one loop sigma-model quantum correction. The classical relation has an expansion in positive powers of the analogous of the BMN effective coupling, while the quantum corrections are non perturbative in nature and are not subleading in the limit of infinite charge. We comment about the dual field theory multi-charged hadrons and the implications of our computation for the AdS/N=4 duality. (author)
The Origins of Lattice Gauge Theory
International Nuclear Information System (INIS)
Wilson, Kenneth
2004-01-01
The main focus of this talk is an anecdotal account of the history underlying my 1974 article entitled 'Confinement of Quarks.' In preparing this talk, I will draw on a historical interview conducted by the project for History of Recent Science and Technology at the Dibner Institute for the History of Science and Technology at MIT, and on a theory of invention proposed by Peter Drucker in his book 'Innovation and Entrepreneurship.' I will explain this theory; no background is needed. The account will start with related work in the 1960's. I will end the talk with a plea for lattice gauge researchers to be alert for unexpected scalar or vector colored particles that are invisible to experimentalists yet could start to spoil the agreement of computations with experiment. Note: In association with the Symposium ' 'Lattice 2004,' June 21 to June 26, 2004.
CP nonconservation in dynamically broken gauge theories
International Nuclear Information System (INIS)
Lane, K.
1981-01-01
The recent proposal of Eichten, Lane, and Preskill for CP nonconservation in electroweak gauge theories with dynamical symmetry breaking is reviewed. Through the alignment of the vacuum with the explicit chiral symmetry breaking Hamiltonian, these theories provide a natural way to understand the dynamical origin of CP nonconservation. Special attention is paid to the problem of strong CP violation. Even through all vacuum angles are zero, this problem is not automatically avoided. In the absence of strong CP violation, the neutron electric dipole moment is expected to be 10 -24 -10 -26 e-cm. A new class of models is proposed in which both strong CP violation and large /ΔS/ = 2 effects may be avoided. In these models, /ΔC/ = 2 processes such as D/sup o/ D/sup -o/ mixing may be large enough to observe
Conformal higher spin scattering amplitudes from twistor space
Energy Technology Data Exchange (ETDEWEB)
Adamo, Tim [Blackett Laboratory, Imperial College, London, SW7 2AZ (United Kingdom); Hähnel, Philipp; McLoughlin, Tristan [School of Mathematics, Trinity College Dublin, College Green, Dublin 2 (Ireland)
2017-04-04
We use the formulation of conformal higher spin (CHS) theories in twistor space to study their tree-level scattering amplitudes, finding expressions for all three-point (MHV)-bar amplitudes and all MHV amplitudes involving positive helicity conformal gravity particles and two negative helicity higher spins. This provides the on-shell analogue for the covariant coupling of CHS fields to a conformal gravity background. We discuss the restriction of the theory to a ghost-free unitary subsector, analogous to restricting conformal gravity to general relativity with a cosmological constant. We study the flat-space limit and show that the restricted amplitudes vanish, supporting the conjecture that in the unitary sector the S-matrix of CHS theories is trivial. However, by appropriately rescaling the amplitudes we find non-vanishing results which we compare with chiral flat-space higher spin theories.
Conformal higher spin scattering amplitudes from twistor space
International Nuclear Information System (INIS)
Adamo, Tim; Hähnel, Philipp; McLoughlin, Tristan
2017-01-01
We use the formulation of conformal higher spin (CHS) theories in twistor space to study their tree-level scattering amplitudes, finding expressions for all three-point (MHV)-bar amplitudes and all MHV amplitudes involving positive helicity conformal gravity particles and two negative helicity higher spins. This provides the on-shell analogue for the covariant coupling of CHS fields to a conformal gravity background. We discuss the restriction of the theory to a ghost-free unitary subsector, analogous to restricting conformal gravity to general relativity with a cosmological constant. We study the flat-space limit and show that the restricted amplitudes vanish, supporting the conjecture that in the unitary sector the S-matrix of CHS theories is trivial. However, by appropriately rescaling the amplitudes we find non-vanishing results which we compare with chiral flat-space higher spin theories.
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.)
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
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.
Lattice gauge theory on a parallel computer
International Nuclear Information System (INIS)
Flower, J.W.
1987-01-01
The results of several numerical simulations of QCD by Monte Carlo lattice gauge theory are presented. Studying the mesonic potential on a 20 4 lattice, we conclude that asymptotic scaling does not hold over the range 6.1 ≤ β ≤ 6.7, although we are not able to quantify the discrepancies. The effect of discrete rotational symmetry on physical parameters is examined and seems to modify the string tension by 15% at β = 6.1, while at β = 6.3 the change was less than 1%. The potential between three charges is studied and yields a string tension of .18 GeV 2 , consistent with mesonic calculations and relativized potential models. Contributions to the potential from low-energy string vibrations appear small in the range x ≤ .5 fm. We perform energy density measurements in the color fields surrounding both mesons and baryons, which provide strong evidence in favor of the dual superconductor picture of confinement. It is also suggested that the confining strings in the baryon meet at a central point rather than joining the quarks pairwise. Several algorithms are explored in an attempt to develop simulation methods which are able to directly account for the currents generated by color sources. The extension of the Langevin equation to complex degrees of freedom is derived leading to a Fokker-Planck equation for a complex 'Probability distribution'. Using this technique we are then able to calculate energy densities in U(1) gauge theory at large charge separations. The extension of the method to non-Abelian theories comes up against an unresolved problem in segregation for certain types of observable. 145 refs., 36 figs
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.
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
Coset space dimension reduction of gauge theories
International Nuclear Information System (INIS)
Farakos, K.; Kapetanakis, D.; Koutsoumbas, G.; Zoupanos, G.
1989-01-01
A very interesting approach in the attempts to unify all the interactions is to consider that a unification takes place in higher than four dimensions. The most ambitious program based on the old Kaluza-Klein idea is not able to reproduce the low energy chiral nature of the weak interactions. A suggested way out was the introduction of Yang-Mills fields in the higher dimensional theory. From the particle physics point of view the most important question is how such a theory behaves in four dimensions and in particular in low energies. Therefore most of our efforts concern studies of the properties of an attractive scheme, the Coset-Space-Dimensional-Reduction (C.S.D.R.) scheme, which permits the study of the effective four dimensional theory coming from a gauge theory defined in higher dimensions. Here we summarize the C.S.D.R. procedure the main the rems which are obeyed and to present a realistic model which is the result of the model building efforts that take into account all the C.S.D.R. properties. (orig./HSI)
The Higgs sector of gravitational gauge theories
International Nuclear Information System (INIS)
Leclerc, M.
2006-01-01
Gravitational gauge theories with de Sitter, Poincare and affine symmetry group are investigated under the aspect of the breakdown of the initial symmetry group down to the Lorentz subgroup. As opposed to the nonlinear realization approach, in the dynamical symmetry breaking procedure, the structure subgroup is not chosen arbitrarily, but is dictated by the symmetry of the groundstate of a Higgs field. We review the theory of spontaneously broken de Sitter gravity by Stelle and West and apply a similar approach to the case of the Poincare and affine groups. We will find that the Poincare case is almost trivial. The translational Higgs field reveals itself as pure gauge, i.e., it is expressed entirely in terms of the Nambu-Goldstone bosons and does not appear in the Lagrangian after the symmetry breaking. The same holds for the translational part of the affine group. The Higgs field provoking the breakdown of the general linear group leads to the determination of the Lorentzian signature of the metric in the groundstate. We show that the Higgs field remains in its groundstate, i.e., that the metric will have Lorentzian signature, unless we introduce matter fields that explicitely couple to the symmetric part of the connection. Furthermore, we present arguments that the Lorentzian signature is actually the only possible choice for physical spacetime, since the symmetry breaking mechanism works only if the stability subgroup is taken to be the Lorentz group. The other four-dimensional rotation groups are therefore ruled out not only on physical, but also on theoretical grounds. Finally, we show that some features, like the necessity of the introduction of a dilaton field, that seem artificial in the context of the affine theory, appear most natural if the gauge group is taken to be the special linear group in five dimensions. We also present an alternative model which is based on the spinor representation of the Lorentz group and is especially adopted to the
The Hawking effect in abelian gauge theories
International Nuclear Information System (INIS)
Stephens, C.R.
1989-01-01
In an effort to compare and contrast gravity with other field theories an investigation is made into whether the Hawking effect is a peculiarly gravitational phenomenon. It is found that the effect exists for a particular background abelian gauge field configuration, as well as certain background gravitational field configurations. Specifically, pair production in a uniform electric field is shown to admit a thermal interpretation. In an effort to find out just what is singular about gravity it is found that the Hawking temperature characteristic of a particular gravitational field configuration is independent of the properties of the quantum fields propagating theorem, in direct contrast to the gauge field case. This implies that if the one loop approximation is to be valid the electric field must be ''cold'' relative to the energy scales set by the quantum fields. In gravity, however, because of the existence of a fundamental scale, the Planck length, the gravitational field can be ''hot'' or ''cold'' and a one loop approximation still remain valid. copyright 1989 Academic Press, Inc
Gauge hierarchy problem in grand unified theories
International Nuclear Information System (INIS)
Alhendi, H.A.A.
1982-01-01
In grand unification schemes, several mass scales are to be introduced, with some of them much larger than all the others, to cope with experimental observations, in which elementary particles of higher masses require higher energy to observe them than elementary particles of lower masses. There have been controversial arguments in the literature on such hierarchical scale structure, when radiative corrections are taken into account. It has been asserted that the gauge hierarchy depends on the choice of the subtraction point (in the classical field space), of the four-point function at zero external momentum. It also has been asserted that the gauge hierarchy problem whenever it is possible to be maintained in one sector of particles, it also is possible to be maintained in the other sectors. These two problems have been studied in a prototype model, namely an 0(3)-model with two triplets of real scalar Higgs fields. Our analysis shows that, within ordinary perturbation theory, none of these two problems is quite correct
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)
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.
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.
New Methods in Supersymmetric Theories and Emergent Gauge Symmetry
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.
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.)
Higher spin currents in orthogonal Wolf space
International Nuclear Information System (INIS)
Ahn, Changhyun; Paeng, Jinsub
2015-01-01
For the N=4 superconformal coset theory by ((SO(N+4))/(SO(N)×SU(2)))×U(1) (that contains an orthogonal Wolf space) with N = 4, the N=2 WZW affine current algebra is obtained. The 16 generators (or 11 generators) of the large N=4 linear (or nonlinear) superconformal algebra are described by these WZW affine currents explicitly. Along the line of large N=4 holography, the extra 16 currents with spins (2,(5/2),(5/2),3), ((5/2),3,3,(7/2)), ((5/2),3,3,(7/2)), and (3,(7/2),(7/2),4) are obtained in terms of the WZW affine currents. The lowest spin of this N=4 multiplet is two rather than one, which is for a unitary Wolf space. The operator product expansions between the above 11 currents and these extra 16 higher spin currents are found explicitly. (paper)
Off-shell superconformal higher spin multiplets in four dimensions
Kuzenko, Sergei M.; Manvelyan, Ruben; Theisen, Stefan
2017-07-01
We formulate off-shell N = 1 superconformal higher spin multiplets in four spacetime dimensions and briefly discuss their coupling to conformal supergravity. As an example, we explicitly work out the coupling of the superconformal gravitino multiplet to conformal supergravity. The corresponding action is super-Weyl invariant for arbitrary supergravity backgrounds. However, it is gauge invariant only if the supersymmetric Bach tensor vanishes. This is similar to linearised conformal supergravity in curved background.
Holographic repulsion and confinement in gauge theory
Husain, Viqar; Kothawala, Dawood
2013-02-01
We show that for asymptotically anti-de Sitter (AdS) backgrounds with negative energy, such as the AdS soliton and regulated negative-mass AdS-Schwarzshild metrics, the Wilson loop expectation value in the AdS/CFT conjecture exhibits a Coulomb to confinement transition. We also show that the quark-antiquark (q \\bar{q}) potential can be interpreted as affine time along null geodesics on the minimal string worldsheet and that its intrinsic curvature provides a signature of transition to confinement phase. Our results suggest a generic (holographic) relationship between confinement in gauge theory and repulsive gravity, which in turn is connected with singularity avoidance in quantum gravity. Communicated by P R L V Moniz
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
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
Cosmic strings in unified gauge theories
International Nuclear Information System (INIS)
Everett, A.E.
1981-01-01
Some spontaneously broken gauge theories can give rise to stringlike vacuum structures (vortices). It has been pointed out by Vilenkin that in grand unified theories these can be sufficiently massive to have cosmological implications, e.g., in explaining the formation of galaxies. The circumstances in which such structures occur are examined. They do not occur in the simplest grand unified theories, but can occur in some more elaborate models which have been proposed. The cross section for the scattering of elementary particles by strings is estimated. This is used to evaluate the effect of collisions on the dynamics of a collapsing circular string, with particular attention to the question of whether energy dissipation by collision can reduce the rate of formation of black holes by collapsed strings, which may be unacceptably large in models where strings occur. It is found that the effect of collisions is not important in the case of grand unified strings, although it can be important for lighter strings
Gauged supergravities from M-theory reductions
Katmadas, Stefanos; Tomasiello, Alessandro
2018-04-01
In supergravity compactifications, there is in general no clear prescription on how to select a finite-dimensional family of metrics on the internal space, and a family of forms on which to expand the various potentials, such that the lower-dimensional effective theory is supersymmetric. We propose a finite-dimensional family of deformations for regular Sasaki-Einstein seven-manifolds M 7, relevant for M-theory compactifications down to four dimensions. It consists of integrable Cauchy-Riemann structures, corresponding to complex deformations of the Calabi-Yau cone M 8 over M 7. The non-harmonic forms we propose are the ones contained in one of the Kohn-Rossi cohomology groups, which is finite-dimensional and naturally controls the deformations of Cauchy-Riemann structures. The same family of deformations can be also described in terms of twisted cohomology of the base M 6, or in terms of Milnor cycles arising in deformations of M 8. Using existing results on SU(3) structure compactifications, we briefly discuss the reduction of M-theory on our class of deformed Sasaki-Einstein manifolds to four-dimensional gauged supergravity.
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
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.
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
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
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
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)
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
On the WDVV equations in five-dimensional gauge theories
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
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$...
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
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
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.)
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
SO(2N) and SU(N) gauge theories
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) ...
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.)
Gravitation, gauge theories and differential geometry
International Nuclear Information System (INIS)
Eguchi, T.; Chicago Univ., IL; Chicago Univ., IL; Gilkey, P.B.; California Univ., Los Angeles; Hanson, A.J.
1980-01-01
The purpose of this article is to outline various mathematical ideas, methods, and results, primarily from differential geometry and topology, and to show where they can be applied to Yang-Mills gauge theories and Einstein's theory of gravitation.We have several goals in mind. The first is to convey to physicists the bases for many mathematical concepts by using intuitive arguments while avoiding the detailed formality of most textbooks. Although a variety of mathematical theorems will be stated, we will generally give simple examples motivating the results instead of presenting abstract proofs. Another goal is to list a wide variety of mathematical terminology and results in a format which allows easy reference. The reader then has the option of supplementing the descriptions given here by consulting standard mathematical references and articles such as those listed in the bibliography. Finally, we intend this article to serve the dual purpose of acquainting mathematicians with some basic physical concepts which have mathematical ramifications; physical problems have often stimuladed new directions in mathematical thought. (orig./WL)
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
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.)
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
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.)
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)
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)
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.
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.)
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
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)
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
Holism and structuralism in U(1) gauge theory
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.
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
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
Higher-spin algebras, holography and flat space
Energy Technology Data Exchange (ETDEWEB)
Sleight, C. [Max-Planck-Institut für Physik (Werner-Heisenberg-Institut),Föhringer Ring 6, D-80805 Munich (Germany); Université Libre de Bruxelles and International Solvay Institutes,ULB-Campus Plaine CP231, 1050 Brussels (Belgium); Taronna, M. [Université Libre de Bruxelles and International Solvay Institutes,ULB-Campus Plaine CP231, 1050 Brussels (Belgium)
2017-02-20
In this article we study the higher-spin algebra behind the type-A cubic couplings recently extracted from the free O(N) model in generic dimensions, demonstrating that they coincide with the known structure constants for the unique higher-spin algebra in generic dimensions. This provides an explicit check of the holographic reconstruction and of the duality between higher-spin theories and the free O(N) model in generic dimensions, generalising the result of Giombi and Yin in AdS{sub 4}. For completeness, we also address the same problem in the flat space for the cubic couplings derived by Metsaev in 1991, which are recovered from the flat limit of the AdS type-A cubic couplings. We observe that both flat and AdS{sub 4} higher-spin Lorentz subalgebras coincide, hinting towards the existence of a full higher-spin symmetry behind the flat-space cubic couplings of Metsaev.
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)
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
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
Spin chain and duality between string theory and gauge theories
International Nuclear Information System (INIS)
Gorskij, A.S.
2005-01-01
One discusses a string pattern hidden by the integrable spin chains describing the evolution equations in the Yang- Mills theory. It is shown that the single-loop correction to the dilatation operator in N = 4 theory may be expressed in terms of two-point correlation functions at two-dimensional world surface of a string. Correspondence between the Neumann integrable systems and the spin chains leads us to believe that passing to the finite values of the coupling constants in the gauge theory corresponds to the quantization of the world surface. The model of string bits for the digitized world surface is assumed to be in line with representation of the integrable spin chains in terms of the separable variables [ru
Nonlocal hidden variables and nonlocal gauge theories
International Nuclear Information System (INIS)
Boiteux, M.
1984-01-01
A possible unification of classical fundamental interactions together with quantum interactions is proposed, based on an extension of the concept of local gauge invariance to a nonlocal gauge invariance. As an example this new concept is developed for the particular case of the electromagnetic field. (Auth.)
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)
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
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)
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
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
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.)
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
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.)
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.)
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.
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.
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.
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.
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
An N=2 gauge theory and its supergravity dual
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.
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.
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
Gravitation SL(2,C) gauge theory and conservation laws
Carmeli, Moshe; Nissani, Noah
1990-01-01
This monograph gives a comprehensive presentation of the SL(2,C) Gauge Theory of Gravitation along with some recent developments in the problem of Conservation Laws in General Relativity. Emphasis is put on quadratic Lagrangians which yield the Einstein field equations, as compared with Hilbert's original linear Langrangian, thus gravitation follows the other Gauge Fields all of which are derived from nonlinear Lagrangians.
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)
Three-Dimensional Gauge Theories and ADE Monopoles
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.
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.
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
Canonical transformation path to gauge theories of gravity
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.
Exceptional gauge groups and quantum theory
International Nuclear Information System (INIS)
Horwitz, L.P.; Biedenharn, L.C.
1979-01-01
It is shown that a Hilbert space over the real Clifford algebra C 7 provides a mathematical framework, consistent with the structure of the usual quantum mechanical formalism, for models for the unification of weak, electromagnetic and strong interactions utilizing the exceptional Lie groups. In particular, in case no further structure is assumed beyond that of C 7 , the group of automorphisms leaving invariant a minimal subspace acts, in the ideal generated by that subspace, as G 2 , and the subgroup of this group leaving one generating element (e 7 ) fixed acts, in this ideal, as the color gauge group SU(3). A generalized phase algebra AcontainsC 7 is defined by the requirement that quantum mechanical states can be consistently constructed for a theory in which the smallest linear manifolds are closed over the subalgebra C(1,e 7 ) (isomorphic to the complex field) of C 7 . Eight solutions are found for the generalized phase algebra, corresponding (up to an overall sign), in effect, to the use of +- e 7 as imaginary unit in each of four superselection sectors. Operators linear over these alternative forms of imanary unit provide distinct types of ''lepton--quark'' and ''quark--quark'' transitions. The subgroup in A which leaves expectation values of operators linear over A invariant is its unitary subgroup U(4), and is a realization (explicitly constructed) of the U(4) invariance of the complex scalar product. An embedding of the algebraic Hilbert space into the complex space defined over C(1,e 7 ) is shown to lead to a decomposition into ''lepton and ''quark'' superselection subspaces. The color SU(3) subgroup of G 2 coincides with the SU(3) subgroup of the generalized phase U(4) which leaves the ''lepton'' space invariant. The problem of constructing tensor products is studied, and some remarks are made on observability and the role of nonassociativity
Higher spin black holes with soft hair
Energy Technology Data Exchange (ETDEWEB)
Grumiller, Daniel [Institute for Theoretical Physics, TU Wien,Wiedner Hauptstrasse 8-10/136, Vienna, A-1040 (Austria); Pérez, Alfredo [Centro de Estudios Científicos (CECs),Av. Arturo Prat 514, Valdivia (Chile); Prohazka, Stefan [Institute for Theoretical Physics, TU Wien,Wiedner Hauptstrasse 8-10/136, Vienna, A-1040 (Austria); Tempo, David; Troncoso, Ricardo [Centro de Estudios Científicos (CECs),Av. Arturo Prat 514, Valdivia (Chile)
2016-10-21
We construct a new set of boundary conditions for higher spin gravity, inspired by a recent “soft Heisenberg hair”-proposal for General Relativity on three-dimensional Anti-de Sitter space. The asymptotic symmetry algebra consists of a set of affine û(1) current algebras. Its associated canonical charges generate higher spin soft hair. We focus first on the spin-3 case and then extend some of our main results to spin-N, many of which resemble the spin-2 results: the generators of the asymptotic W{sub 3} algebra naturally emerge from composite operators of the û(1) charges through a twisted Sugawara construction; our boundary conditions ensure regularity of the Euclidean solutions space independently of the values of the charges; solutions, which we call “higher spin black flowers”, are stationary but not necessarily spherically symmetric. Finally, we derive the entropy of higher spin black flowers, and find that for the branch that is continuously connected to the BTZ black hole, it depends only on the affine purely gravitational zero modes. Using our map to W-algebra currents we recover well-known expressions for higher spin entropy. We also address higher spin black flowers in the metric formalism and achieve full consistency with previous results.
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.)
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
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.
Extended Nambu models: Their relation to gauge theories
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.
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
A quantization scheme for scale-invariant pure gauge theories
International Nuclear Information System (INIS)
Hortacsu, M.
1988-01-01
A scheme is suggested for the quantization of the recently proposed scale-invariant gauge theories in higher dimensions. The model is minimally coupled to a spinor field. Regularization algorithms are proposed. (orig.)
Classical confining solutions of a tensor gauge theory incorporating colour
International Nuclear Information System (INIS)
Salam, A.; Strathdee, J.
1977-04-01
A mass-modified Einstein-Weyl gauge theory of colour carrying spin-two mesons is formulated. A classical solution is exhibited for the case of internal SU(2) symmetry which may confine quarks in colour singlets
On the Generalized Geometry Origin of Noncommutative Gauge Theory
Jurco, Branislav; Vysoky, Jan
2013-01-01
We discuss noncommutative gauge theory from the generalized geometry point of view. We argue that the equivalence between the commutative and semiclassically noncommutative DBI actions is naturally encoded in the generalized geometry of D-branes.
Standard model and chiral gauge theories on the lattice
International Nuclear Information System (INIS)
Smit, J.
1990-01-01
A review is given of developments in lattice formulations of chiral gauge theories. There is now evidence that the unwanted fermion doublers can be decoupled satisfactorily by giving them masses of the order of the cutoff. (orig.)
New solutions of euclidean SU(2) gauge theory
International Nuclear Information System (INIS)
Khan, I.
1983-08-01
New solutions of the Euclidean SU(2) gauge theory having finite field strength everywhere are presented. The solutions are self dual or antidual and constitute a two-parameter family which includes the instantons. (author)
Effective average action for gauge theories and exact evolution equations
International Nuclear Information System (INIS)
Reuter, M.; Wetterich, C.
1993-11-01
We propose a new nonperturbative evolution equation for Yang-Mills theories. It describes the scale dependence of an effective action. The running of the nonabelian gauge coupling in arbitrary dimension is computed. (orig.)
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.
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
Chiral symmetry breaking in gauge theories from Reggeon diagram analysis
International Nuclear Information System (INIS)
White, A.R.
1991-01-01
It is argued that reggeon diagrams can be used to study dynamical properties of gauge theories containing a large number of massless fermions. SU(2) gauge theory is studied in detail and it is argued that there is a high energy solution which is analogous to the solution of the massless Schwinger model. A generalized winding-number condensate produces the massless pseudoscalar spectrum associated with chiral symmetry breaking and a ''trivial'' S-Matrix
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
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.)
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)
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.
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
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
Cosmology in Gauge Field Theory and String Theory
International Nuclear Information System (INIS)
Garcia Compean, H
2005-01-01
This new book is intended for students and researchers who want to go into the interplay between cosmology and high-energy physics. It assumes a prior knowledge of these subjects such as some of the topics contained in the previous books by the authors, Introduction to Gauge Field Theory (1993 Bristol: Institute of Physics Publishing) and Supersymmetric Gauge Field Theory and String Theory (1994 Bristol: Institute of Physics Publishing). However, the book is intended to be self-contained, explaining, from a modern perspective, some background material mainly in standard cosmology, topological defects, baryogenesis, inflationary cosmology and, at the end of the book, some of the basics of string theory. What is distinctively new about this book is that it lies in the interplay between cosmology and high-energy physics typically above 100 GeV (10 15 K). Often these subjects are presented in regular textbooks in a disconnected way, or in research papers, proceedings and review papers but usually not in a pedagogical style. Thus, in this sense, the book is unique and deserves a special place in the recent literature. The book starts by reviewing the standard material of the early universe. The standard model of cosmology from a modern perspective is revised in chapter 1. In chapter 2, phase transitions in different models are discussed, Higgs, electroweak, GUTs, supersymmetric GUTs and supergravity, by using quantum field theory at finite temperature. Chapter 3 is devoted to a general account of topological defects and discusses how they arise as possible remnants of these phase transitions in GUTs. Other relics, such as neutrinos and axions, are introduced in chapter 5 and their impact in cosmology is assessed. In chapter 4, some of the most relevant mechanisms of baryogenesis are discussed in the context of the different GUTs and the minimal supersymmetric standard model (MSSM). Inflation is also discussed in the context of GUTs. In chapter 6, the authors introduce
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)
Phenomenology of strongly coupled chiral gauge theories
International Nuclear Information System (INIS)
Bai, Yang; Berger, Joshua; Osborne, James; Stefanek, Ben A.
2016-01-01
A sector with QCD-like strong dynamics is common in models of non-standard physics. Such a model could be accessible in LHC searches if both confinement and big-quarks charged under the confining group are at the TeV scale. Big-quark masses at this scale can be explained if the new fermions are chiral under a new U(1) ′ gauge symmetry such that their bare masses are related to the U(1) ′ -breaking and new confinement scales. Here we present a study of a minimal GUT-motivated and gauge anomaly-free model with implications for the LHC Run 2 searches. We find that the first signatures of such models could appear as two gauge boson resonances. The chiral nature of the model could be confirmed by observation of a Z ′ γ resonance, where the Z ′ naturally has a large leptonic branching ratio because of its kinetic mixing with the hypercharge gauge boson.
Loop calculus for lattice gauge theories
International Nuclear Information System (INIS)
Gambini, R.; Leal, L.; Trias, A.; Departamento de Fisica Aplicada, Facultad de Ingenieria, Universidad Central de Venezuela, Apartado 47724, Caracas 1051, Venezuela; Departament de Matematiques, Universitat Politecnica de Catalunya, Escuela Tecnica Superior de Enginyers de Telecomunicaciones, Barcelona 08034, Spain)
1989-01-01
Hamiltonian calculations are performed using a loop-labeled basis where the full set of identities for the SU(N) gauge models has been incorporated. The loops are classified as clusterlike structures and the eigenvalue problem leads to a linear set of finite-difference equations easily amenable to numerical treatment. Encouraging results are reported for SU(2) at spatial dimension 2
Monte Carlo simulations of lattice gauge theories
International Nuclear Information System (INIS)
Forcrand, P. de; Minnesota Univ., Minneapolis, MN
1989-01-01
Lattice gauge simulations are presented in layman's terms. The need for large computer resources is justified. The main aspects of implementations on vector and parallel machines are explained. An overview of state of the art simulations and dedicated hardware projects is presented. 8 refs.; 1 figure; 1 table
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
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.
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
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
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
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
Perturbative quantum gravity as a double copy of gauge theory.
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.
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.
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
Noncommutative gauge field theories: A no-go theorem
International Nuclear Information System (INIS)
Chaichian, M.; Tureanu, A.; Presnajder, P.; Sheikh-Jabbari, M.M.
2001-06-01
Studying the mathematical structure of the noncommutative groups in more detail, we prove a no-go theorem for the noncommutative gauge theories. According to this theorem, the closure condition of the gauge algebra implies that: 1) the local noncommutative u(n) algebra only admits the irreducible nxn matrix-representation. Hence the gauge fields, as elements of the algebra, are in nxn matrix form, while the matter fields can only be either in fundamental, adjoint or singlet states; 2) for any gauge group consisting of several simple group factors, the matter fields can transform nontrivially under at most two noncommutative group factors. In other words, the matter fields cannot carry more than two simple noncommutative gauge group charges. This no-go theorem imposes strong restrictions on the construction of the noncommutative version of the Standard Model and in resolving the standing problem of charge quantization in noncommutative QED. (author)
U(1) Wilson lattice gauge theories in digital quantum simulators
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.
Analytic stochastic regularization and gauge theories
International Nuclear Information System (INIS)
Abdalla, E.; Gomes, M.; Lima-Santos, A.
1987-04-01
We prove that analytic stochatic regularization braks gauge invariance. This is done by an explicit one loop calculation of the two three and four point vertex functions of the gluon field in scalar chromodynamics, which turns out not to be geuge invariant. We analyse the counter term structure, Langevin equations and the construction of composite operators in the general framework of stochastic quantization. (author) [pt
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
Minimal local Lagrangians for higher-spin geometry
International Nuclear Information System (INIS)
Francia, Dario; Sagnotti, Augusto
2005-01-01
The Fronsdal Lagrangians for free totally symmetric rank-s tensors φ μ 1 ...μ s rest on suitable trace constraints for their gauge parameters and gauge fields. Only when these constraints are removed, however, the resulting equations reflect the expected free higher-spin geometry. We show that geometric equations, in both their local and non-local forms, can be simply recovered from local Lagrangians with only two additional fields, a rank-(s-3) compensator α μ 1 ...μ s-3 and a rank-(s-4) Lagrange multiplier β μ 1 ...μ s-4 . In a similar fashion, we show that geometric equations for unconstrained rank-n totally symmetric spinor-tensors ψ μ 1 ...μ n can be simply recovered from local Lagrangians with only two additional spinor-tensors, a rank-(n-2) compensator ξ μ 1 ...μ n-2 and a rank-(n-3) Lagrange multiplier λ μ 1 ...μ n-3
Supergravity duals of supersymmetric four dimensional gauge theories
Energy Technology Data Exchange (ETDEWEB)
Bigazzi, F [Abdus Salam International Centre for Theoretical Physics, Trieste (Italy); Cotrone, A L [Centre de Physique Theorique, Ecole Polytechnique, Palaiseau Cedex (France); [INFN, Rome (Italy); Petrini, M [Centre de Physique Theorique, Ecole Polytechnique, Palaiseau (France); Zaffaroni, A [Universita di Milano-Bicocca and INFN, Milan (Italy)
2002-03-01
This article contains an overview of some recent attempts of understanding supergravity and string duals of four dimensional gauge theories using the AdS/CFT correspondence. We discuss the general philosophy underlying the various ways to realize Super Yang-Mills theories in terms of systems of branes. We then review some of the existing duals for N=2 and N=1 theories. We also discuss differences and similarities with realistic theories. (author)
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
On the zero mode of the Poisson gauge theory
International Nuclear Information System (INIS)
Saidi, E.H.
1990-09-01
The fundamentals of the Diff(S 2 ) and the SDiff(S 2 ) gauge theories are developed. It is shown that the adjoint representation of SU(∞) is described by a divergentless two dimensional vector field defined on the sphere. The SU(∞) Yang-Mills gauge action obtained earlier by Floratos et al. is reviewed. The problem of the zero modes is solved without need of any constraint. The fundamental representations of SU(∞) and the gauge matter couplings are discussed. (author). 6 refs
Quantum Link Models and Quantum Simulation of Gauge Theories
International Nuclear Information System (INIS)
Wiese, U.J.
2015-01-01
This lecture is about Quantum Link Models and Quantum Simulation of Gauge Theories. The lecture consists out of 4 parts. The first part gives a brief history of Computing and Pioneers of Quantum Computing and Quantum Simulations of Quantum Spin Systems are introduced. The 2nd lecture is about High-Temperature Superconductors versus QCD, Wilson’s Lattice QCD and Abelian Quantum Link Models. The 3rd lecture deals with Quantum Simulators for Abelian Lattice Gauge Theories and Non-Abelian Quantum Link Models. The last part of the lecture discusses Quantum Simulators mimicking ‘Nuclear’ physics and the continuum limit of D-Theorie models. (nowak)
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
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)
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)
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)
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.
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.
Ambiguities of the natural gauge in Yang-Mills theories
International Nuclear Information System (INIS)
Lazarides, G.
1978-01-01
We study the ambiguities of the natural gauge condition for the Euclidean SU(2) Yang-Mills theory in four dimensions. Then, we show that, in the stationary-phase approximation, these ambiguities do not affect the contribution of the sector with Pontryagin index q = 1 to the correlation functions of gauge-invariant operators. They affect only the higher-order corrections to this contribution
Renormalization of an abelian gauge theory in stochastic quantization
International Nuclear Information System (INIS)
Chaturvedi, S.; Kapoor, A.K.; Srinivasan, V.
1987-01-01
The renormalization of an abelian gauge field coupled to a complex scalar field is discussed in the stochastic quantization method. The super space formulation of the stochastic quantization method is used to derive the Ward Takahashi identities associated with supersymmetry. These Ward Takahashi identities together with previously derived Ward Takahashi identities associated with gauge invariance are shown to be sufficient to fix all the renormalization constants in terms of scaling of the fields and of the parameters appearing in the stochastic theory. (orig.)
Geometrodynamics of gauge fields on the geometry of Yang-Mills and gravitational gauge theories
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...
Introduction to gauge theories and the Standard Model
de Wit, Bernard
1995-01-01
The conceptual basis of gauge theories is introduced to enable the construction of generic models.Spontaneous symmetry breaking is dicussed and its relevance for the renormalization of theories with massive vector field is explained. Subsequently a d standard model. When time permits we will address more practical questions that arise in the evaluation of quantum corrections.
Instantons and the vacuum condensates of SUSY-gauge theories
International Nuclear Information System (INIS)
Schmidt, M.G.
1987-01-01
In the supersymmetric gauge theories the ''non-renormalization'' theorem guarantees that some quantities which are zero in lowest order remain zero in higher orders of perturbation theory. I show that such quantities get nonvanishing contributions from instanton-induced interactions. Also, no cut-off in the size of instantons is needed. 28 refs., 12 figs. (author)
One-instanton calculations in N=2 supersymmetric gauge theories
International Nuclear Information System (INIS)
Ito, Katsushi
1998-01-01
We study the low-energy effective action of N=2 supersymmetric gauge theories in the Coulomb branch. Using microscopic instanton calculus, we compute the one-instanton contribution to the pre potential for N=2 supersymmetric SU(N c ) Yang-Mills theory. We show that the microscopic result agrees with the exact solution. (Author). 23 refs
Five-dimensional gauge theory and compactification on a torus
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.
Another scheme for quantization of scale invariant gauge theories
International Nuclear Information System (INIS)
Hortacsu, M.
1987-10-01
A new scheme is proposed for the quantization of scale invariant gauge theories for all even dimensions when they are minimally coupled to a spinor field. A cut-off procedure suggests an algorithm which may regularize the theory. (author). 10 refs
Gauge theories, black hole evaporation and cosmic censorship
International Nuclear Information System (INIS)
Davies, P.C.W.
1981-01-01
Recent work of Linde, which suggests that gauge theories modify the effective gravitational constant, are applied to the theory of black hole evaporation. Considerable modification of the late stages of evaporation are predicted. Contrary to expectations, the black hole never attains a sufficient temperature to enter the antigravity regime, which would represent a failure of cosmic censorship. (orig.)
Tumbling and complementarity in a chiral gauge theory
International Nuclear Information System (INIS)
Goity, J.; Peccei, R.D.; Zeppenfeld, D.
1985-06-01
We consider in detail a chiral SU(N) gauge theory which undergoes multiple tumbling. An extension of the notion of complementarity is used which allows us to deduce the set of massless fermions, in the confining phase of the theory, which we needed for anomaly matching. The likelyhood of this confining phase ever being realized in practice is discussed. (orig.)
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)
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.)
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.)
Hyperunified field theory and gravitational gauge-geometry duality
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.
Effective potentials in gauge field theories
International Nuclear Information System (INIS)
Caldas, P.S.S.; Fleming, H.; Garcia, R.L.
An elementary and very efficient method for computing the effective potential of any theory containing scalar bosons is described. Examples include massless scalar electrodynamics and Yang-Mills theories [pt
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
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.)
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
Constant self-dual Abelian gauge fields and fermions in SU(2) gauge theory
International Nuclear Information System (INIS)
Kay, D.; Parthasarathy, R.; Viswanathan, K.S.
1983-01-01
Fermion one-loop corrections to the effective action in a self-dual Abelian background field are calculated for an SU(2) gauge theory. It is found that these corrections for massless fermions tend to destabilize the vacuum. The quantitative and qualitative features of such corrections for the case of massive fermions are discussed
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.
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.)
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