Non commutative geometry and super Yang-Mills theory
International Nuclear Information System (INIS)
Bigatti, D.
1999-01-01
We aim to connect the non commutative geometry 'quotient space' viewpoint with the standard super Yang Mills theory approach in the spirit of Connes-Douglas-Schwartz and Douglas-Hull description of application of noncommutative geometry to matrix theory. This will result in a relation between the parameters of a rational foliation of the torus and the dimension of the group U(N). Namely, we will be provided with a prescription which allows to study a noncommutative geometry with rational parameter p/N by means of a U(N) gauge theory on a torus of size Σ/N with the boundary conditions given by a system with p units of magnetic flux. The transition to irrational parameter can be obtained by letting N and p tend to infinity with fixed ratio. The precise meaning of the limiting process will presumably allow better clarification. (Copyright (c) 1999 Elsevier Science B.V., Amsterdam. All rights reserved.)
International Nuclear Information System (INIS)
Thierry-Mieg, Jean
2006-01-01
In Yang-Mills theory, the charges of the left and right massless Fermions are independent of each other. We propose a new paradigm where we remove this freedom and densify the algebraic structure of Yang-Mills theory by integrating the scalar Higgs field into a new gauge-chiral 1-form which connects Fermions of opposite chiralities. Using the Bianchi identity, we prove that the corresponding covariant differential is associative if and only if we gauge a Lie-Kac super-algebra. In this model, spontaneous symmetry breakdown naturally occurs along an odd generator of the super-algebra and induces a representation of the Connes-Lott non commutative differential geometry of the 2-point finite space
Monopoles and vortices in Yang-Mills plasma
International Nuclear Information System (INIS)
Chernodub, M. N.; Zakharov, V. I.
2009-01-01
We discuss the role of magnetic degrees of freedom in Yang-Mills plasma at temperatures above and of order of the critical temperature T c . While at zero temperature the magnetic degrees of freedom are condensed and electric degrees of freedom are confined, at the point of the phase transition both magnetic and electric degrees of freedom are released into the thermal vacuum. This phenomenon might explain the observed unusual properties of the plasma.
The shear viscosity of the non-commutative plasma
International Nuclear Information System (INIS)
Landsteiner, Karl; Mas, Javier
2007-01-01
We compute the shear viscosity of the non-commutative N = 4 super Yang-Mills quantum field theory at strong coupling using the dual supergravity background. Special interest derives from the fact that the background presents an intrinsic anisotropy in space through the distinction of commutative and non-commutative directions. Despite this anisotropy the analysis exhibits the ubiquitous result η/s = 1/4π for two different shear channels. In order to derive this result, we show that the boundary energy momentum tensor must couple to the open string metric. As a byproduct we compute the renormalised holographic energy momentum tensor and show that it coincides with one in the commutative theory
Chakraborty, Somdeb; Roy, Shibaji
2012-02-01
A particular decoupling limit of the nonextremal (D1, D3) brane bound state system of type IIB string theory is known to give the gravity dual of space-space noncommutative Yang-Mills theory at finite temperature. We use a string probe in this background to compute the jet quenching parameter in a strongly coupled plasma of hot noncommutative Yang-Mills theory in (3+1) dimensions from gauge/gravity duality. We give expressions for the jet quenching parameter for both small and large noncommutativity. For small noncommutativity, we find that the value of the jet quenching parameter gets reduced from its commutative value. The reduction is enhanced with temperature as T7 for fixed noncommutativity and fixed ’t Hooft coupling. We also give an estimate of the correction due to noncommutativity at the present collider energies like in RHIC or in LHC and find it too small to be detected. We further generalize the results for noncommutative Yang-Mills theories in diverse dimensions.
Non-commutative geometry and supersymmetry 2
International Nuclear Information System (INIS)
Hussain, F.; Thompson, G.
1991-05-01
Following the general construction of supersymmetric models, the model based on the idea of non-commutative geometry is formulated as a Yang-Mills theory of the graded Lie algebra U(2/1) over a graded space-time manifold. 4 refs
International Nuclear Information System (INIS)
Chesler, Paul M.; Yaffe, Laurence G.
2008-01-01
The stress-energy tensor of a quark moving through a strongly-coupled N=4 supersymmetric Yang-Mills plasma, at large N c , is evaluated using gauge/string duality. The accuracy with which the resulting wake, in position space, is reproduced by hydrodynamics is examined. Remarkable agreement is found between hydrodynamics and the complete result down to distances less than 2/T away from the quark. In performing the gravitational analysis, we use a relatively simple formulation of the bulk to boundary problem in which the linearized Einstein field equations are fully decoupled. Our analysis easily generalizes to other sources in the bulk.
Yang-Mills-Vlasov system in the temporal gauge
International Nuclear Information System (INIS)
Choquet-Bruhat, Y.; Noutchegueme, N.
1991-01-01
We prove a local in time existence theorem of a solution of the Cauchy problem for the Yang-Mills-Vlasov integrodifferential system. Such equations govern the evolution of plasmas, for instance of quarks and gluons (quagmas), where non abelian gauge fields and Yang-Mills charges replace the usual electromagnetic field and electric charge. We work with the temporal gauge and use functional spaces with appropriate weight on the momenta, but no fall off is required in the space direction [fr
Einstein-Yang-Mills from pure Yang-Mills amplitudes
Energy Technology Data Exchange (ETDEWEB)
Nandan, Dhritiman; Plefka, Jan [Institut für Physik and IRIS Adlershof, Humboldt-Universität zu Berlin,Zum Großen Windkanal 6, D-12489 Berlin (Germany); Schlotterer, Oliver [Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut,Am Mühlenberg 1, D-14476 Potsdam (Germany); Wen, Congkao [I.N.F.N. Sezione di Roma Tor Vergata,Via della Ricerca Scientifica, 00133 Roma (Italy)
2016-10-14
We present new relations for scattering amplitudes of color ordered gluons and gravitons in Einstein-Yang-Mills theory. Tree-level amplitudes of arbitrary multiplicities and polarizations involving up to three gravitons and up to two color traces are reduced to partial amplitudes of pure Yang-Mills theory. In fact, the double-trace identities apply to Einstein-Yang-Mills extended by a dilaton and a B-field. Our results generalize recent work of Stieberger and Taylor for the single graviton case with a single color trace. As the derivation is made in the dimension-agnostic Cachazo-He-Yuan formalism, our results are valid for external bosons in any number of spacetime dimensions. Moreover, they generalize to the superamplitudes in theories with 16 supercharges.
International Nuclear Information System (INIS)
Crooks, David E.; Evans, Nick
2003-01-01
We describe a ten dimensional supergravity geometry which is dual to a gauge theory that is non-supersymmetric Yang Mills in the infra-red but reverts to N=4 super Yang Mills in the ultra-violet. A brane probe of the geometry shows that the scalar potential of the gauge theory is stable. We discuss the infra-red behaviour of the solution. The geometry describes a Schroedinger equation potential that determines the glueball spectrum of the theory; there is a mass gap and a discrete spectrum. The glueball mass predictions match previous AdS/CFT Correspondence computations in the non-supersymmetric Yang Mills theory, and lattice data, at the 10% level. (author)
International Nuclear Information System (INIS)
Bagchi, Arjun; Basu, Rudranil; Kakkar, Ashish; Mehra, Aditya
2016-01-01
We investigate the symmetry structure of the non-relativistic limit of Yang-Mills theories. Generalising previous results in the Galilean limit of electrodynamics, we discover that for Yang-Mills theories there are a variety of limits inside the Galilean regime. We first explicitly work with the SU(2) theory and then generalise to SU(N) for all N, systematising our notation and analysis. We discover that the whole family of limits lead to different sectors of Galilean Yang-Mills theories and the equations of motion in each sector exhibit hitherto undiscovered infinite dimensional symmetries, viz. infinite Galilean Conformal symmetries in D=4. These provide the first examples of interacting Galilean Conformal Field Theories (GCFTs) in D>2.
Energy Technology Data Exchange (ETDEWEB)
Bagchi, Arjun [Center for Theoretical Physics, Massachusetts Institute of Technology,77 Massachusetts Avenue, Cambridge, MA 02139 (United States); Basu, Rudranil [Saha Institute of Nuclear Physics,Block AF, Sector 1, Bidhannagar, Kolkata 700068 (India); Kakkar, Ashish [Indian Institute of Science Education and Research,Dr Homi Bhabha Road, Pashan. Pune 411008 (India); Mehra, Aditya [Indian Institute of Science Education and Research,Dr Homi Bhabha Road, Pashan. Pune 411008 (India); Van Swinderen Institute for Particle Physics and Gravity, University of Groningen, Nijenborgh 4, 9747 AG Groningen (Netherlands)
2016-04-11
We investigate the symmetry structure of the non-relativistic limit of Yang-Mills theories. Generalising previous results in the Galilean limit of electrodynamics, we discover that for Yang-Mills theories there are a variety of limits inside the Galilean regime. We first explicitly work with the SU(2) theory and then generalise to SU(N) for all N, systematising our notation and analysis. We discover that the whole family of limits lead to different sectors of Galilean Yang-Mills theories and the equations of motion in each sector exhibit hitherto undiscovered infinite dimensional symmetries, viz. infinite Galilean Conformal symmetries in D=4. These provide the first examples of interacting Galilean Conformal Field Theories (GCFTs) in D>2.
Introduction to Dubois-Violette's non-commutative differential geometry
International Nuclear Information System (INIS)
Djemai, A.E.F.
1994-07-01
In this work, one presents a detailed review of Dubois-Violette et al. approach to non-commutative differential calculus. The non-commutative differential geometry of matrix algebras and the non-commutative Poisson structures are treated in some details. We also present the analog of the Maxwell's theory and the new models of Yang-Mills-Higgs theories that can be constructed in this framework. In particular, some simple models are compared with the standard model. Finally, we discuss some perspectives and open questions. (author). 32 refs
Veltman, M.J.G.; Reiff, J.
1969-01-01
Two problems are studied in the paper: (i) the relation between Lagrangian and Feynman rules if the Lagrangian contains derivative couplings and/or vector meson fields and (ii) the behaviour of certain two closed loop diagrams in the perturbation theory of Yang-Mills fields. With respect to ( i ) .
Yang-Mills gravity in biconformal space
International Nuclear Information System (INIS)
Anderson, Lara B; Wheeler, James T
2007-01-01
We write a gravity theory with Yang-Mills-type action using the biconformal gauging of the conformal group. We show that the resulting biconformal Yang-Mills gravity theories describe 4-dim, scale-invariant general relativity in the case of slowly changing fields. In addition, we systematically extend arbitrary 4-dim Yang-Mills theories to biconformal space, providing a new arena for studying flat-space Yang-Mills theories. By applying the biconformal extension to a 4-dim pure Yang-Mills theory with conformal symmetry, we establish a 1-1, onto mapping between a set of gravitational gauge theories and 4-dim, flat-space gauge theories
Analogy between spin glasses and Yang--Mills fluids
International Nuclear Information System (INIS)
Holm, D.D.; Kupershmidt, B.A.
1988-01-01
A dictionary of correspondence is established between the dynamical variables for spin-glass fluid and Yang-Mills plasma. The Lie-algebraic interpretation of these variables is presented for the two theories. The noncanonical Poisson bracket for the Hamiltonian dynamics of an ideal spin glass is shown to be identical to that for the dynamics of a Yang--Mills fluid plasma, although the Hamiltonians differ for the two theories. This Poisson bracket is associated to the dual space of an infinite-dimensional Lie algebra of semidirect-product type
Black holes with Yang-Mills hair
International Nuclear Information System (INIS)
Kleihaus, B.; Kunz, J.; Sood, A.; Wirschins, M.
1998-01-01
In Einstein-Maxwell theory black holes are uniquely determined by their mass, their charge and their angular momentum. This is no longer true in Einstein-Yang-Mills theory. We discuss sequences of neutral and charged SU(N) Einstein-Yang-Mills black holes, which are static spherically symmetric and asymptotically flat, and which carry Yang-Mills hair. Furthermore, in Einstein-Maxwell theory static black holes are spherically symmetric. We demonstrate that, in contrast, SU(2) Einstein-Yang-Mills theory possesses a sequence of black holes, which are static and only axially symmetric
An extended topological Yang-Mills theory
International Nuclear Information System (INIS)
Deguchi, Shinichi
1992-01-01
Introducing infinite number of fields, we construct an extended version of the topological Yang-Mills theory. The properties of the extended topological Yang-Mills theory (ETYMT) are discussed from standpoint of the covariant canonical quantization. It is shown that the ETYMT becomes a cohomological topological field theory or a theory equivalent to a quantum Yang-Mills theory with anti-self-dual constraint according to subsidiary conditions imposed on state-vector space. On the basis of the ETYMT, we may understand a transition from an unbroken phase to a physical phase (broken phase). (author)
Two loop diagrams in Yang Mills theory
International Nuclear Information System (INIS)
Jones, D.R.T.
1974-01-01
A calculation of the renormalization constants of the Yang Mills field to 0(g 4 ) is presented. The function β(g) is hence evaluated to 0(g 5 ) and possible implications for gauge theories of the strong interactions discussed
Yang Mills instantons, geometrical aspects
International Nuclear Information System (INIS)
Stora, R.
1977-09-01
The word instanton has been coined by analogy with the word soliton. They both refer to solutions of elliptic non linear field equations with boundary conditions at infinity (of euclidean space time in the first case, euclidean space in the second case) lying on the set of classical vacua in such a way that stable topological properties emerge, susceptible to survive quantum effects, if those are small. Under this assumption, instantons are believed to be relevant to the description of tunnelling effects between classical vacua and signal some characteristics of the vacuum at the quantum level, whereas solitons should be associated with particles, i.e. discrete points in the mass spectrum. In one case the euclidean action is finite, in the other case, the energy is finite. From the mathematical point of view, the geometrical phenomena associated with the existence of solitons have forced physicists to learn rudiments of algebraic topology. The study of euclidean classical Yang Mills fields involves naturally mathematical items falling under the headings: differential geometry (fibre bundles, connections); differential topology (characteristic classes, index theory) and more recently algebraic geometry. These notes are divided as follows: a first section is devoted to a description of the physicist's views; a second section is devoted to the mathematician's vie
A Note on UV/IR Mixing and Non-Commutative Instanton Calculus
Bichl, A A
2003-01-01
We estimate the instanton-induced vacuum energy in non-commutative U(1) Yang-Mills theory in four dimensions. In the dilute gas approximation, it is found to be plagued by infrared divergences, as a result of UV/IR mixing.
Infrared finiteness in Yang--Mills theories
International Nuclear Information System (INIS)
Appelquist, T.; Carazzone, J.; Kluberg-Stern, H.; Roth, M.
1976-01-01
The infrared divergences of renormalizable theories with coupled massless fields (in particular, the Yang--Mills theory) are shown to cancel for transition probabilities corresponding to finite-energy-resolution detectors, just as in quantum electrodynamics. This result is established through lowest nontrivial order in perturbation theory for the detection of massive muons in a quantum electrodynamic theory containing massless electrons or the detection of massive quarks in a Yang--Mills theory
Higher derivative super Yang-Mills theories
International Nuclear Information System (INIS)
Bergshoeff, E.; Rakowski, M.; Sezgin, E.
1986-11-01
The most general higher derivative Yang-Mills actions of the type (F 2 +α2F 4 ) which are globally supersymmetric up to order α 2 in six and ten dimensional spacetimes are given. The F 4 -terms turn out to occur in the combination α 2 (tr F 4 - 1/4(tr F 2 ) 2 ), where the trace is over the Lorentz indices. This result agrees with the low energy limit of the open superstring in ten dimensions, where α is the string tension. Surprisingly, the transformation rules of the Yang-Mills multiplet receive order α 2 corrections even in the off-shell formulation. For the case of Abelian Yang-Mills group, the action is expressed in Born-Infeld form with a metric generically given by (1+α 2 F 2 +...). (author)
Einstein-Yang-Mills-Lorentz black holes
Energy Technology Data Exchange (ETDEWEB)
Cembranos, Jose A.R.; Gigante Valcarcel, Jorge [Universidad Complutense de Madrid, Departamento de Fisica Teorica I, Madrid (Spain)
2017-12-15
Different black hole solutions of the coupled Einstein-Yang-Mills equations have been well known for a long time. They have attracted much attention from mathematicians and physicists since their discovery. In this work, we analyze black holes associated with the gauge Lorentz group. In particular, we study solutions which identify the gauge connection with the spin connection. This ansatz allows one to find exact solutions to the complete system of equations. By using this procedure, we show the equivalence between the Yang-Mills-Lorentz model in curved space-time and a particular set of extended gravitational theories. (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.
Nonperturbative Results for Yang-Mills Theories
DEFF Research Database (Denmark)
Sannino, Francesco; Schechter, Joseph
2010-01-01
Some non perturbative aspects of the pure SU(3) Yang-Mills theory are investigated assuming a specific form of the beta function, based on a recent modification by Ryttov and Sannino of the known one for supersymmetric gauge theories. The characteristic feature is a pole at a particular value....... Assuming the usual QCD value one finds it to be 1.67 GeV, which is in surprisingly good agreement with a quenched lattice calculation. A similar calculation is made for the supersymmetric Yang-Mills theory where the corresponding beta function is considered to be exact....
Yang-Mills formulation of interacting strings
International Nuclear Information System (INIS)
Chan Hongmo; Tsou Sheungtsun
1988-06-01
A suggestion that the theory of interacting open bosonic string be reformulated as a generalised Yang-Mills theory is further elucidated. Moreover, a serious reservation regarding the ordering of operators in the earlier 'proof' of equivalence between the new and standard formulations is now removed. (author)
Unique specification of Yang-Mills solutions
International Nuclear Information System (INIS)
Campbell, W.B.; Joseph, D.W.; Morgan, T.A.
1980-01-01
Screened time-independent cylindrically-symmetric solutions of Yang-Mills equations are given which show that the source does not uniquely determine the field. However, these particular solutions suggest a natural way of uniquely specifying solutions in terms of a physical realization of a symmetry group. (orig.)
Random geometry and Yang-Mills theory
International Nuclear Information System (INIS)
Froehlich, J.
1981-01-01
The author states various problems and discusses a very few preliminary rigorous results in a branch of mathematics and mathematical physics which one might call random (or stochastic) geometry. Furthermore, he points out why random geometry is important in the quantization of Yang-Mills theory. (Auth.)
A class of Yang-Mills solutions
International Nuclear Information System (INIS)
Castillejo, L.; Kugler, M.
1980-09-01
We investigate a class of solutions of the classical SU(2) Yang-Mills equations. The symmetry of this class prescribes a natural set of gauge invariant degrees of freedom. Using these degrees of freedom we obtain a simple set of equations which enables us to find all the solutions belonging to the class under discussion. (Author)
Fate of Yang-Mills black hole in early Universe
Energy Technology Data Exchange (ETDEWEB)
Nakonieczny, Lukasz; Rogatko, Marek [Institute of Physics Maria Curie-Sklodowska University 20-031 Lublin, pl. Marii Curie-Sklodowskiej 1 (Poland)
2013-02-21
According to the Big Bang Theory as we go back in time the Universe becomes progressively hotter and denser. This leads us to believe that the early Universe was filled with hot plasma of elementary particles. Among many questions concerning this phase of history of the Universe there are questions of existence and fate of magnetic monopoles and primordial black holes. Static solution of Einstein-Yang-Mills system may be used as a toy model for such a black hole. Using methods of field theory we will show that its existence and regularity depend crucially on the presence of fermions around it.
Yang-Mills theory for non-semisimple groups
Nuyts, J; Nuyts, Jean; Wu, Tai Tsun
2003-01-01
For semisimple groups, possibly multiplied by U(1)'s, the number of Yang-Mills gauge fields is equal to the number of generators of the group. In this paper, it is shown that, for non-semisimple groups, the number of Yang-Mills fields can be larger. These additional Yang-Mills fields are not irrelevant because they appear in the gauge transformations of the original Yang-Mills fields. Such non-semisimple Yang-Mills theories may lead to physical consequences worth studying. The non-semisimple group with only two generators that do not commute is studied in detail.
Loop quantum corrected Einstein Yang-Mills black holes
Protter, Mason; DeBenedictis, Andrew
2018-05-01
In this paper, we study the homogeneous interiors of black holes possessing SU(2) Yang-Mills fields subject to corrections inspired by loop quantum gravity. The systems studied possess both magnetic and induced electric Yang-Mills fields. We consider the system of equations both with and without Wilson loop corrections to the Yang-Mills potential. The structure of the Yang-Mills Hamiltonian, along with the restriction to homogeneity, allows for an anomaly-free effective quantization. In particular, we study the bounce which replaces the classical singularity and the behavior of the Yang-Mills fields in the quantum corrected interior, which possesses topology R ×S2 . Beyond the bounce, the magnitude of the Yang-Mills electric field asymptotically grows monotonically. This results in an ever-expanding R sector even though the two-sphere volume is asymptotically constant. The results are similar with and without Wilson loop corrections on the Yang-Mills potential.
An ambitwistor Yang-Mills Lagrangian
International Nuclear Information System (INIS)
Mason, L.J.; Skinner, D.
2006-01-01
We introduce a Chern-Simons Lagrangian for Yang-Mills theory as formulated on ambitwistor space via the Ward, Isenberg, Yasskin, Green, Witten construction. The Lagrangian requires the selection of a codimension-2 Cauchy-Riemann submanifold which is naturally picked out by the choice of space-time reality structure and we focus on the choice of Euclidean signature. The action is shown to give rise to a space-time action that is equivalent to the standard one, but has just cubic vertices. We identify the ambitwistor propagators and vertices and work out their corresponding expressions on space-time and momentum space. It is proposed that this formulation of Yang-Mills theory underlies the recursion relations of Britto, Cachazo, Feng and Witten and provides the generating principle for twistor diagrams for gauge theory
Yang--Mills vacua in Landau gauge
International Nuclear Information System (INIS)
Frampton, P.H.; Hagiwara, T.; Palmer, W.F.; Pinsky, S.S.
1977-01-01
A vacuum gauge field A/sub μ//sup a/ for Yang-Mills theory is constructed; this field is pure vacuum (A/sub μ//sup a/ = 0) at the origin, approaches at large distances, the Belavin-Polyakov-Schwartz-Tyupkin pseudo-particle, and satisfies delta/sub μ/A/sub μ//sup a/ = 0 everywhere. The net topological charge is zero, and there is a Dirac-like string terminating at the origin
International Nuclear Information System (INIS)
Atiyah, M.F.
1978-01-01
In this talk I shall explain how information about classical solutions of Yang-Mills equations can be obtained, rather surprisingly, from algebraic geometry. Although direct physical interest is restricted to the case of four dimensions I shall begin by discussing the two-dimensional case. Besides preparing the ground for the four-dimensional problem this has independent mathematical (and possible physical) interest, and very complete results can be obtained. (orig.) [de
Continuum regularized Yang-Mills theory
International Nuclear Information System (INIS)
Sadun, L.A.
1987-01-01
Using the machinery of stochastic quantization, Z. Bern, M. B. Halpern, C. Taubes and I recently proposed a continuum regularization technique for quantum field theory. This regularization may be implemented by applying a regulator to either the (d + 1)-dimensional Parisi-Wu Langevin equation or, equivalently, to the d-dimensional second order Schwinger-Dyson (SD) equations. This technique is non-perturbative, respects all gauge and Lorentz symmetries, and is consistent with a ghost-free gauge fixing (Zwanziger's). This thesis is a detailed study of this regulator, and of regularized Yang-Mills theory, using both perturbative and non-perturbative techniques. The perturbative analysis comes first. The mechanism of stochastic quantization is reviewed, and a perturbative expansion based on second-order SD equations is developed. A diagrammatic method (SD diagrams) for evaluating terms of this expansion is developed. We apply the continuum regulator to a scalar field theory. Using SD diagrams, we show that all Green functions can be rendered finite to all orders in perturbation theory. Even non-renormalizable theories can be regularized. The continuum regulator is then applied to Yang-Mills theory, in conjunction with Zwanziger's gauge fixing. A perturbative expansion of the regulator is incorporated into the diagrammatic method. It is hoped that the techniques discussed in this thesis will contribute to the construction of a renormalized Yang-Mills theory is 3 and 4 dimensions
Area-preserving diffeomorphisms in gauge theory on a non-commutative plane. A lattice study
International Nuclear Information System (INIS)
Bietenholz, W.; Bigarini, A.; INFN, Sezione di Perugia; Humboldt-Universitaet, Berlin; Torrielli, A.
2007-06-01
We consider Yang-Mills theory with the U(1) gauge group on a non-commutative plane. Perturbatively it was observed that the invariance of this theory under area-preserving diffeomorphisms (APDs) breaks down to a rigid subgroup SL(2,R). Here we present explicit results for the APD symmetry breaking at finite gauge coupling and finite non-commutativity. They are based on lattice simulations and measurements of Wilson loops with the same area but with a variety of different shapes. Our results confirm the expected loss of invariance under APDs. Moreover, they strongly suggest that non-perturbatively the SL(2,R) symmetry does not persist either. (orig.)
Jorgensen, Palle
2017-01-01
The book features new directions in analysis, with an emphasis on Hilbert space, mathematical physics, and stochastic processes. We interpret 'non-commutative analysis' broadly to include representations of non-Abelian groups, and non-Abelian algebras; emphasis on Lie groups and operator algebras (C* algebras and von Neumann algebras.)A second theme is commutative and non-commutative harmonic analysis, spectral theory, operator theory and their applications. The list of topics includes shift invariant spaces, group action in differential geometry, and frame theory (over-complete bases) and their applications to engineering (signal processing and multiplexing), projective multi-resolutions, and free probability algebras.The book serves as an accessible introduction, offering a timeless presentation, attractive and accessible to students, both in mathematics and in neighboring fields.
Marginal and non-commutative deformations via non-abelian T-duality
Energy Technology Data Exchange (ETDEWEB)
Hoare, Ben [Institut für Theoretische Physik, ETH Zürich,Wolfgang-Pauli-Strasse 27, 8093 Zürich (Switzerland); Thompson, Daniel C. [Theoretische Natuurkunde, Vrije Universiteit Brussel & The International Solvay Institutes, Pleinlaan 2, B-1050 Brussels (Belgium)
2017-02-10
In this short article we develop recent proposals to relate Yang-Baxter sigma-models and non-abelian T-duality. We demonstrate explicitly that the holographic space-times associated to both (multi-parameter)-β-deformations and non-commutative deformations of N=4 super Yang-Mills gauge theory including the RR fluxes can be obtained via the machinery of non-abelian T-duality in Type II supergravity.
Duality in supersymmetric Yang-Mills theory
Energy Technology Data Exchange (ETDEWEB)
Peskin, M.E.
1997-02-01
These lectures provide an introduction to the behavior of strongly-coupled supersymmetric gauge theories. After a discussion of the effective Lagrangian in nonsupersymmetric and supersymmetric field theories, the author analyzes the qualitative behavior of the simplest illustrative models. These include supersymmetric QCD for N{sub f} < N{sub c}, in which the superpotential is generated nonperturbatively, N = 2 SU(2) Yang-Mills theory (the Seiberg-Witten model), in which the nonperturbative behavior of the effect coupling is described geometrically, and supersymmetric QCD for N{sub f} large, in which the theory illustrates a non-Abelian generalization of electric-magnetic duality. 75 refs., 12 figs.
YANG-MILLS FIELDS AND THE LATTICE.
Energy Technology Data Exchange (ETDEWEB)
CREUTZ,M.
2004-05-18
The Yang-Mills theory lies at the heart of our understanding of elementary particle interactions. For the strong nuclear forces, we must understand this theory in the strong coupling regime. The primary technique for this is the lattice. While basically an ultraviolet regulator, the lattice avoids the use of a perturbative expansion. I discuss some of the historical circumstances that drove us to this approach, which has had immense success, convincingly demonstrating quark confinement and obtaining crucial properties of the strong interactions from first principles.
Duality in supersymmetric Yang-Mills theory
International Nuclear Information System (INIS)
Peskin, M.E.
1997-02-01
These lectures provide an introduction to the behavior of strongly-coupled supersymmetric gauge theories. After a discussion of the effective Lagrangian in nonsupersymmetric and supersymmetric field theories, the author analyzes the qualitative behavior of the simplest illustrative models. These include supersymmetric QCD for N f c , in which the superpotential is generated nonperturbatively, N = 2 SU(2) Yang-Mills theory (the Seiberg-Witten model), in which the nonperturbative behavior of the effect coupling is described geometrically, and supersymmetric QCD for N f large, in which the theory illustrates a non-Abelian generalization of electric-magnetic duality. 75 refs., 12 figs
Perturbative spacetimes from Yang-Mills theory
Energy Technology Data Exchange (ETDEWEB)
Luna, Andrés [School of Physics and Astronomy, University of Glasgow,Glasgow G12 8QQ, Scotland (United Kingdom); Monteiro, Ricardo [Theoretical Physics Department, CERN,Geneva (Switzerland); Nicholson, Isobel; Ochirov, Alexander; O’Connell, Donal [Higgs Centre for Theoretical Physics,School of Physics and Astronomy, The University of Edinburgh,Edinburgh EH9 3JZ, Scotland (United Kingdom); Westerberg, Niclas [Institute of Photonics and Quantum Sciences,School of Engineering and Physical Sciences, Heriot-Watt University,Edinburgh (United Kingdom); Higgs Centre for Theoretical Physics,School of Physics and Astronomy, The University of Edinburgh,Edinburgh EH9 3JZ, Scotland (United Kingdom); White, Chris D. [Centre for Research in String Theory,School of Physics and Astronomy, Queen Mary University of London,327 Mile End Road, London E1 4NS (United Kingdom)
2017-04-12
The double copy relates scattering amplitudes in gauge and gravity theories. In this paper, we expand the scope of the double copy to construct spacetime metrics through a systematic perturbative expansion. The perturbative procedure is based on direct calculation in Yang-Mills theory, followed by squaring the numerator of certain perturbative diagrams as specified by the double-copy algorithm. The simplest spherically symmetric, stationary spacetime from the point of view of this procedure is a particular member of the Janis-Newman-Winicour family of naked singularities. Our work paves the way for applications of the double copy to physically interesting problems such as perturbative black-hole scattering.
Yang-Mills theory in Coulomb gauge; Yang-Mills-theorie in Coulombeichung
Energy Technology Data Exchange (ETDEWEB)
Feuchter, C.
2006-07-01
In this thesis we study the Yang-Mills vacuum structure by using the functional Schroedinger picture in Coulomb gauge. In particular we discuss the scenario of colour confinement, which was originally formulated by Gribov. After a short introduction, we recall some basic aspects of Yang-Mills theories, its canonical quantization in the Weyl gauge and the functional Schroedinger picture. We then consider the minimal Coulomb gauge and the Gribov problem of the gauge theory. The gauge fixing of the Coulomb gauge is done by using the Faddeev-Popov method, which enables the resolution of the Gauss law - the constraint on physical states. In the third chapter, we variationally solve the stationary Yang-Mills Schroedinger equation in Coulomb gauge for the vacuum state. Therefor we use a vacuum wave functional, which is strongly peaked at the Gribov horizon. The vacuum energy functional is calculated and minimized resulting in a set of coupled Schwinger-Dyson equations for the gluon energy, the ghost and Coulomb form factors and the curvature in gauge orbit space. Using the angular approximation these integral equations have been solved analytically in both the infrared and the ultraviolet regime. The asymptotic analytic solutions in the infrared and ultraviolet regime are reasonably well reproduced by the full numerical solutions of the coupled Schwinger-Dyson equations. In the fourth chapter, we investigate the dependence of the Yang-Mills wave functional in Coulomb gauge on the Faddeev-Popov determinant. (orig.)
Yang-Mills-Chern-Simons supergravity
International Nuclear Information System (INIS)
Lue, H; Pope, C N; Sezgin, E
2004-01-01
N = (1, 0) supergravity in six dimensions admits AdS 3 x S 3 as a vacuum solution. We extend our recent results presented in Lue et al (2002 Preprint hep-th/0212323), by obtaining the complete N = 4 Yang-Mills-Chern-Simons supergravity in D = 3, up to quartic fermion terms, by S 3 group manifold reduction of the six-dimensional theory. The SU(2) gauge fields have Yang-Mills kinetic terms as well as topological Chern-Simons mass terms. There is in addition a triplet of matter vectors. After diagonalization, these fields describe two triplets of topologically-massive vector fields of opposite helicities. The model also contains six scalars, described by a GL(3, R)/SO(3) sigma model. It provides the first example of a three-dimensional gauged supergravity that can be obtained by a consistent reduction of string theory or M-theory and that admits AdS 3 as a vacuum solution. There are unusual features in the reduction from six-dimensional supergravity, owing to the self-duality condition on the 3-form field. The structure of the full equations of motion in N = (1, 0) supergravity in D = 6 is also elucidated, and the role of the self-dual field strength as torsion is exhibited
Semiclassical scattering in Yang-Mills theory
International Nuclear Information System (INIS)
Gould, T.M.; Poppitz, E.R.
1994-01-01
A classical solution to the Yang-Mills theory is given a semiclassical interpretation. The boundary value problem on a complex time contour which arises from the semiclassical approximation to multiparticle scattering amplitudes is reviewed and applied to the case of Yang-Mills theory. The solution describes a classically forbidden transition between states with a large average number of particles in the limit g→0. It dominates a transition probability with a semiclassical suppression factor equal to twice the action of the well-known BPST instanton. Hence, it is relevant to the problem of high-energy tunnelling. It describes transitions of unit topological charge for an appropriate time contour. Therefore, it may have a direct interpretation in terms of fermion-number violating processes in electroweak theory. The solution describes a transition between an initial state with parametrically fewer particles than the final state. Thus, it may be relevant to the study of semiclassical initial-state corrections in the limit of a small number of initial particles. The implications of these results for multiparticle production in electroweak theory are also discussed. (orig.)
Some global charges in classical Yang-Mills theory
International Nuclear Information System (INIS)
Chrus'ciel, P.T.; Kondracki, W.
1987-01-01
Three classes of boundary conditions allowing the definition of a global field strength (''global color'') are presented. A definition of global color of the sources and of the Yang-Mills field is proposed. Some exact solutions of Yang-Mills equations with point sources and with ''topologically nontrivial electric color'' are presented
A QCD Model Using Generalized Yang-Mills Theory
International Nuclear Information System (INIS)
Wang Dianfu; Song Heshan; Kou Lina
2007-01-01
Generalized Yang-Mills theory has a covariant derivative, which contains both vector and scalar gauge bosons. Based on this theory, we construct a strong interaction model by using the group U(4). By using this U(4) generalized Yang-Mills model, we also obtain a gauge potential solution, which can be used to explain the asymptotic behavior and color confinement.
Chaotic behavior of the lattice Yang-Mills on CUDA
Directory of Open Access Journals (Sweden)
Forster Richárd
2015-12-01
Full Text Available The Yang-Mills fields plays important role in the strong interaction, which describes the quark gluon plasma. The non-Abelian gauge theory provides the theoretical background understanding of this topic. The real time evolution of the classical fields is derived by the Hamiltonian for SU(2 gauge field tensor. The microcanonical equations of motion is solved on 3 dimensional lattice and chaotic dynamics was searched by the monodromy matrix. The entropy-energy relation was presented by Kolmogorov-Sinai entropy. We used block Hessenberg reduction to compute the eigenvalues of the current matrix. While the purely CPU based algorithm can handle effectively only a small amount of values, the GPUs provide enough performance to give more computing power to solve the problem.
Nonperturbative aspects of Yang-Mills theory
International Nuclear Information System (INIS)
Schleifenbaum, Wolfgang
2008-01-01
The subject of this thesis is the theory of strong interactions of quarks and gluons, with particular emphasis on nonperturbative aspects of the gluon sector. Continuum methods are used to investigate in particular the confinement phenomenon. Confinement which states that the elementary quarks and gluons cannot be detected as free particles requires an understanding of large-scale correlations. In perturbation theory, only short-range correlations can be reliably described. A nonperturbative approach is given by the set of integral Dyson Schwinger equations involving all Green functions of the theory. A solution for the gluon propagator is obtained in the infrared and ultraviolet asymptotic limits. In chapter 1, redundant degrees of freedom of the Yang Mills gauge theory are removed by fixing the Weyl and Coulomb gauge prior to quantization. The constrained quantization in the Dirac bracket formalism is then performed explicitly to produce the quantized Yang Mills Hamiltonian. The asymptotic infrared limits of Coulomb gauge correlation functions are studied analytically in chapter 2 in the framework of the Gribov Zwanziger confinement scenario. The Coulomb potential between heavy quarks as part of the Yang Mills Hamiltonian is calculated in this limit. A connection between the infrared limits of Coulomb and Landau gauge is established. The Hamiltonian derived paves the way in chapter 3 for finding the Coulomb gauge vacuum wave functional by means of the variational principle. Numerical solutions for the propagators in this vacuum state are discussed and seen to reproduce the anticipated infrared limit. The discussion is extended to the vertex functions. The effect of the approximations on the results is examined. Chapter 4 is mainly devoted to the ultraviolet behavior of the propagators. The discussion is issued in both Coulomb and Landau gauge. A nonperturbative running coupling is defined and calculated. The ultraviolet tails of the variational solutions from
Nonperturbative aspects of Yang-Mills theory
Energy Technology Data Exchange (ETDEWEB)
Schleifenbaum, Wolfgang
2008-07-01
The subject of this thesis is the theory of strong interactions of quarks and gluons, with particular emphasis on nonperturbative aspects of the gluon sector. Continuum methods are used to investigate in particular the confinement phenomenon. Confinement which states that the elementary quarks and gluons cannot be detected as free particles requires an understanding of large-scale correlations. In perturbation theory, only short-range correlations can be reliably described. A nonperturbative approach is given by the set of integral Dyson Schwinger equations involving all Green functions of the theory. A solution for the gluon propagator is obtained in the infrared and ultraviolet asymptotic limits. In chapter 1, redundant degrees of freedom of the Yang Mills gauge theory are removed by fixing the Weyl and Coulomb gauge prior to quantization. The constrained quantization in the Dirac bracket formalism is then performed explicitly to produce the quantized Yang Mills Hamiltonian. The asymptotic infrared limits of Coulomb gauge correlation functions are studied analytically in chapter 2 in the framework of the Gribov Zwanziger confinement scenario. The Coulomb potential between heavy quarks as part of the Yang Mills Hamiltonian is calculated in this limit. A connection between the infrared limits of Coulomb and Landau gauge is established. The Hamiltonian derived paves the way in chapter 3 for finding the Coulomb gauge vacuum wave functional by means of the variational principle. Numerical solutions for the propagators in this vacuum state are discussed and seen to reproduce the anticipated infrared limit. The discussion is extended to the vertex functions. The effect of the approximations on the results is examined. Chapter 4 is mainly devoted to the ultraviolet behavior of the propagators. The discussion is issued in both Coulomb and Landau gauge. A nonperturbative running coupling is defined and calculated. The ultraviolet tails of the variational solutions from
Massive Yang-Mills fields in the Kemmer's formulation
International Nuclear Information System (INIS)
Santana Cordolino, L.A. de.
1984-01-01
The Kemmer's equation, which describes the meson, is presented in the field theory formalism. Conservated, quantities are found through the Noether's identity. This formalism is used for masive Yang-Mills fields and two equations, similar to the Kemmer's equation, are obtained, although of different formates, both containing quadratic terms. In consequence two Lagrangians are defined, formally distint, for the Yang-Mills fields. The Schroedinger-like Hamiltonian is calculated for the first wave equations. This Hamiltonian presentes one spin-Yang-Mills field interaction term, PHI jk . (L.C.) [pt
Yang-Mills analogs of general-relativistic solutions
International Nuclear Information System (INIS)
Singlton, D.
1998-01-01
Some solutions of Yang-Mills equations, which can be found with the use of the general relativistic theory and Yang-Mills theory, are discussed. Some notes concerning possible physical sense of these solutions are made. Arguments showing that some of such solutions in the Yang-Mills theory (similar to the general relativistic ones) may be connected with the confinement phenomenon are given in particular. The motion of probe particles located into the phonon potential similar to the Schwarz-Child one is briefly discussed for this purpose [ru
Conformally flat spaces and solutions to Yang-Mills equations
International Nuclear Information System (INIS)
Chaohao, G.
1980-01-01
Using the conformal invariance of Yang-Mills equations in four-dimensional manifolds, it is proved that in a simply connected space of negative constant curvature Yang-Mills equations admit solutions with any real number as their Pontryagin number. It is also shown that the space S 3 x S 1 which is the regular counterpart of the meron solution is one example of a class of solutions to Yang-Mills equations on compact manifolds that are neither self-dual nor anti-self-dual
Testing Non-commutative QED, Constructing Non-commutative MHD
Guralnik, Z.; Jackiw, R.; Pi, S. Y.; Polychronakos, A. P.
2001-01-01
The effect of non-commutativity on electromagnetic waves violates Lorentz invariance: in the presence of a background magnetic induction field b, the velocity for propagation transverse to b differs from c, while propagation along b is unchanged. In principle, this allows a test by the Michelson-Morley interference method. We also study non-commutativity in another context, by constructing the theory describing a charged fluid in a strong magnetic field, which forces the fluid particles into ...
Noncommutative Yang-Mills from equivalence of star products
International Nuclear Information System (INIS)
Jurco, B.; Schupp, P.
2000-01-01
It is shown that the transformation between ordinary and noncommutative Yang-Mills theory as formulated by Seiberg and Witten is due to the equivalence of certain star products on the D-brane world-volume. (orig.)
Noncommutative Yang-Mills from equivalence of star products
Energy Technology Data Exchange (ETDEWEB)
Jurco, B. [Max-Planck-Institut fuer Mathematik, Bonn (Germany); Schupp, P. [Sektion Physik, Universitaet Muenchen, Theresienstrasse 37, 80333 Muenchen (Germany)
2000-05-01
It is shown that the transformation between ordinary and noncommutative Yang-Mills theory as formulated by Seiberg and Witten is due to the equivalence of certain star products on the D-brane world-volume. (orig.)
Yang-Mills theory - a string theory in disguise
International Nuclear Information System (INIS)
Foerster, D.
1979-01-01
An examination of the Schwinger-Dyson equations of U(N) lattice Yang-Mills theory shows that this theory is exactly equivalent to a theory of strings that interact with one another only through their topology. (Auth.)
Cosmological coevolution of Yang-Mills fields and perfect fluids
International Nuclear Information System (INIS)
Barrow, John D.; Jin, Yoshida; Maeda, Kei-ichi
2005-01-01
We study the coevolution of Yang-Mills fields and perfect fluids in Bianchi type I universes. We investigate numerically the evolution of the universe and the Yang-Mills fields during the radiation and dust eras of a universe that is almost isotropic. The Yang-Mills field undergoes small amplitude chaotic oscillations, as do the three expansion scale factors which are also displayed by the expansion scale factors of the universe. The results of the numerical simulations are interpreted analytically and compared with past studies of the cosmological evolution of magnetic fields in radiation and dust universes. We find that, whereas magnetic universes are strongly constrained by the microwave background anisotropy, Yang-Mills universes are principally constrained by primordial nucleosynthesis but the bound is comparatively weak with Ω YM rad
Auxiliary fields for super Yang-Mills from division algebras
Evans, Jonathan M.
1994-01-01
Division algebras are used to explain the existence and symmetries of various sets of auxiliary fields for super Yang-Mills in dimensions d=3,4,6,10. (Contribution to G\\"ursey Memorial Conference I: Strings and Symmetries)
Homotopy Lie superalgebra in Yang-Mills theory
International Nuclear Information System (INIS)
Zeitlin, Anton M.
2007-01-01
The Yang-Mills equations are formulated in the form of generalized Maurer-Cartan equations, such that the corresponding algebraic operations are shown to satisfy the defining relations of homotopy Lie superalgebra
Null solution of the Yang-Mills equations
International Nuclear Information System (INIS)
Tafel, J.
1986-05-01
We investigate the correspondence between null solutions of the Yang-Mills equations and shearfree geodesic null congruences. We give an example of a non-Abelian null solution with twisting rays. (orig.)
Electric vortex lines from the Yang-Mills theory
International Nuclear Information System (INIS)
Nielsen, N.K.; Olesen, P.
1978-08-01
The dynamics of an unstable Yang-Mills field mode previously found by the authors is developed. It is argued that this unstable mode corresponds to the transition to a state where electric vortex lines are created. (Auth.)
Integrability of N=3 super Yang-Mills equations
International Nuclear Information System (INIS)
Devchand, C.; Ogievetsky, V.
1993-10-01
We describe the harmonic superspace formulation of the Witten-Manin supertwistor correspondence for N=3 extended super Yang-Mills theories. The essence in that on being sufficiently supersymmetrised (up to the N=3 extension), the Yang-Mills equations of motion can be recast in the form of Cauchy-Riemann-like holomorphicity conditions for a pair of prepotentials in the appropriate harmonic superspace. This formulation makes the explicit construction of solutions a rather more tractable proposition than previous attempts. (orig.)
Superlocalization formulas and supersymmetric Yang-Mills theories
International Nuclear Information System (INIS)
Bruzzo, U.; Fucito, F.
2004-01-01
By using supermanifolds techniques we prove a generalization of the localization formula in equivariant cohomology which is suitable for studying supersymmetric Yang-Mills theories in terms of ADHM data. With these techniques one can compute the reduced partition functions of topological super-Yang-Mills theory with 4, 8 or 16 supercharges. More generally, the superlocalization formula can be applied to any topological field theory in any number of dimensions
Towards the general solution of the Yang-Mills equations
International Nuclear Information System (INIS)
Helfer, A.D.
1985-01-01
The author presents a new non-perturbative technique for finding arbitrary self-dual solutions to the Yang-Mills equations, and of describing massless fields minimally coupled to them. The approach uses techniques of complex analysis in several variables, and is complementary to Ward's: it is expected that a combination of the two techniques will yield general, non-self-dual solutions to the Yang-Mills equations. This has been verified to first order in perturbation theory
Instability of higher dimensional Yang-Mills systems
International Nuclear Information System (INIS)
Randjbar-Daemi, S.; Strathdee, J.
1983-01-01
We investigate the stability of Poincare xO(3) invariant solutions for a pure semi-simple Yang-Mills, as well as Yang-Mills coupled to gravity in 6-dimensional space-time compactified over M 4 xS 2 . In contrast to the Maxwell U(1) theory (IC-82/208) in six dimensions coupled with gravity and investigated previously, the present theory exhibits tachyonic excitations and is unstable. (author)
Dynamical CP violation of the generalized Yang-Mills model
International Nuclear Information System (INIS)
Wang Dianfu; Chang Xiaojing; Sun Xiaoyu
2011-01-01
Starting from the generalized Yang-Mills model which contains, besides the vector part V μ , also a scalar part S and a pseudoscalar part P . It is shown, in terms of the Nambu-Jona-Lasinio (NJL) mechanism, that CP violation can be realized dynamically. The combination of the generalized Yang-Mills model and the NJL mechanism provides a new way to explain CP violation. (authors)
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.)
On maximally supersymmetric Yang-Mills theories
International Nuclear Information System (INIS)
Movshev, M.; Schwarz, A.
2004-01-01
We consider ten-dimensional supersymmetric Yang-Mills theory (10D SUSY YM theory) and its dimensional reductions, in particular, BFSS and IKKT models. We formulate these theories using algebraic techniques based on application of differential graded Lie algebras and associative algebras as well as of more general objects, L ∞ - and A ∞ -algebras. We show that using pure spinor formulation of 10D SUSY YM theory equations of motion and isotwistor formalism one can interpret these equations as Maurer-Cartan equations for some differential Lie algebra. This statement can be used to write BV action functional of 10D SUSY YM theory in Chern-Simons form. The differential Lie algebra we constructed is closely related to differential associative algebra (Ω,∂) of (0,k)-forms on some supermanifold; the Lie algebra is tensor product of (Ω,) and matrix algebra. We construct several other algebras that are quasiisomorphic to (Ω,∂) and, therefore, also can be used to give BV formulation of 10D SUSY YM theory and its reductions. In particular, (Ω,∂) is quasiisomorphic to the algebra (B,d), constructed by Berkovits. The algebras (Ω 0 ,∂) and (B 0 ,d) obtained from (Ω,∂) and (B,d) by means of reduction to a point can be used to give a BV-formulation of IKKT model. We introduce associative algebra SYM as algebra where relations are defined as equations of motion of IKKT model and show that Koszul dual to the algebra (B 0 ,d) is quasiisomorphic to SYM
Bootstrapping non-commutative gauge theories from L∞ algebras
Blumenhagen, Ralph; Brunner, Ilka; Kupriyanov, Vladislav; Lüst, Dieter
2018-05-01
Non-commutative gauge theories with a non-constant NC-parameter are investigated. As a novel approach, we propose that such theories should admit an underlying L∞ algebra, that governs not only the action of the symmetries but also the dynamics of the theory. Our approach is well motivated from string theory. We recall that such field theories arise in the context of branes in WZW models and briefly comment on its appearance for integrable deformations of AdS5 sigma models. For the SU(2) WZW model, we show that the earlier proposed matrix valued gauge theory on the fuzzy 2-sphere can be bootstrapped via an L∞ algebra. We then apply this approach to the construction of non-commutative Chern-Simons and Yang-Mills theories on flat and curved backgrounds with non-constant NC-structure. More concretely, up to the second order, we demonstrate how derivative and curvature corrections to the equations of motion can be bootstrapped in an algebraic way from the L∞ algebra. The appearance of a non-trivial A∞ algebra is discussed, as well.
Full colour for loop amplitudes in Yang-Mills theory
Energy Technology Data Exchange (ETDEWEB)
Ochirov, Alexander [Higgs Centre for Theoretical Physics, School of Physics and Astronomy,The University of Edinburgh,Edinburgh EH9 3JZ, Scotland (United Kingdom); Page, Ben [Albert-Ludwigs-Universität Freiburg, Physikalisches Institut,D-79104 Freiburg (Germany)
2017-02-20
We present a general method to account for full colour dependence Yang-Mills amplitudes at loop level. The method fits most naturally into the framework of multi-loop integrand reduction and in a nutshell amounts to consistently retaining the colour structures of the unitarity cuts from which the integrand is gradually constructed. This technique has already been used in the recent calculation of the two-loop five-gluon amplitude in pure Yang-Mills theory with all positive helicities, (DOI: 10.1007/JHEP10(2015)064). In this note, we give a careful exposition of the method and discuss its connection to loop-level Kleiss-Kuijf relations. We also explore its implications for cancellation of nontrivial symmetry factors at two loops. As an example of its generality, we show how it applies to the three-loop case in supersymmetric Yang-Mills case.
A connection between the Einstein and Yang-Mills equations
International Nuclear Information System (INIS)
Mason, L.J.; Newman, E.T.
1989-01-01
It is our purpose here to show an unusual relationship between the Einstein equations and the Yang-Mills equations. We give a correspondence between solutions of the self-dual Einstein vacuum equations and the self-dual Yang-Mills equations with a special choice of gauge group. The extension of the argument to the full Yang-Mills equations yields Einstein's unified equations. We try to incorporate the full Einstein vacuum equations, but the approach is incomplete. We first consider Yang-Mills theory for an arbitrary Lie-algebra with the condition that the connection 1-form and curvature are constant on Minkowski space. This leads to a set of algebraic equations on the connection components. We then specialize the Lie-algebra to be the (infinite dimensional) Lie algebra of a group of diffeomorphisms of some manifold. The algebraic equations then become differential equations for four vector fields on the manifold on which the diffeomorphisms act. In the self-dual case, if we choose the connection components from the Lie-algebra of the volume preserving 4-dimensional diffeomorphism group, the resulting equations are the same as those obtained by Ashtekar, Jacobsen and Smolin, in their remarkable simplification of the self-dual Einstein vacuum equations. (An alternative derivation of the same equations begins with the self-dual Yang-Mills connection now depending only on the time, then choosing the Lie-algebra as that of the volume preserving 3-dimensional diffeomorphisms). When the reduced full Yang-Mills equations are used in the same context, we get Einstein's equations for his unified theory based on absolute parallelism. To incorporate the full Einstein vacuum equations we use as the Lie group the semi-direct product of the diffeomorphism group of a 4-dimensional manifold with the group of frame rotations of an SO(1, 3) bundle over the 4-manifold. This last approach, however, yields equations more general than the vacuum equations. (orig.)
β-function in a noncovariant Yang-Mills theory
International Nuclear Information System (INIS)
Nielsen, H.B.; Ninomiya, M.
1978-05-01
The betafunction for a noncovariant pure Yang-Mills theory is calculated in perturbation theory to lowest order in the coupling constant and in the deviation from covariance. The authors use the methods developed by DeWitt, Hawking and Dowker. The β-function shows that Lorentz invariance becomes more and more accurate as one goes toward smaller mass scales. The relative deviation of the coupling constant set from covariance diminishes towards lower mass scales as αsub(s)sup(-7/11), where αsub(s) is the QCD 'fine structure constant', for a pure (noncovariant) Yang-Mills theory. (Auth.)
On tree amplitudes of supersymmetric Einstein-Yang-Mills theory
Energy Technology Data Exchange (ETDEWEB)
Adamo, Tim; Casali, Eduardo; Roehrig, Kai A.; Skinner, David [Department of Applied Mathematics & Theoretical Physics, University of Cambridge,Wilberforce Road, Cambridge, CB3 0WA United Kingdom (United Kingdom)
2015-12-29
We present a new formula for all single trace tree amplitudes in four dimensional super Yang-Mills coupled to Einstein supergravity. Like the Cachazo-He-Yuan formula, our expression is supported on solutions of the scattering equations, but with momenta written in terms of spinor helicity variables. Supersymmetry and parity are both manifest. In the pure gravity and pure Yang-Mills sectors, it reduces to the known twistor-string formulae. We show that the formula behaves correctly under factorization and sketch how these amplitudes may be obtained from a four-dimensional (ambi)twistor string.
Yang-Mills theory on the mass shell
International Nuclear Information System (INIS)
Cvitanovic, P.
1976-01-01
Gauge-invariant mass-shell amplitudes for quantum electrodynamics (QED) and Yang-Mills theory are defined by dimensional regularization. Gauge invariance of the mass-shell renormalization constants is maintained through interplay of ultraviolet and infrared divergences. Quark renormalizations obey the same simple Ward identity as do the electron renormalizations in QED, while the gluon contributions to gluon renormalizations are identically zero. The simplest amplitude finite in QED, the magnetic moment, is gauge-invariant but divergent in Yang-Mills theory for both external gluon and external photon
Ultraviolet divergences in higher dimensional supersymmetric Yang-Mills theories
International Nuclear Information System (INIS)
Howe, P.S.; Stelle, K.S.
1984-01-01
We determine the loop orders for the onset of allowed ultra-violet divergences in higher dimensional supersymmetric Yang-Mills theories. Cancellations are controlled by the non-renormalization theorems for the linearly realizable supersymmetries and by the requirement that counterterms display the full non-linear supersymmetries when the classical equations of motion are imposed. The first allowed divergences in the maximal super Yang-Mills theories occur at four loops in five dimensions, three loops in six dimensions and two loops in seven dimensions. (orig.)
Yang-Mills correlation functions from integrable spin chains
International Nuclear Information System (INIS)
Roiban, Radu; Volovich, Anastasia
2004-01-01
The relation between the dilatation operator of N = 4 Yang-Mills theory and integrable spin chains makes it possible to compute the one-loop anomalous dimensions of all operators in the theory. In this paper we show how to apply the technology of integrable spin chains to the calculation of Yang-Mills correlation functions by expressing them in terms of matrix elements of spin operators on the corresponding spin chain. We illustrate this method with several examples in the SU(2) sector described by the XXX 1/2 chain. (author)
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)
Supersymmetric sigma models and composite Yang-Mills theory
International Nuclear Information System (INIS)
Lukierski, J.
1980-04-01
We describe two types of supersymmetric sigma models: with field values in supercoset space and with superfields. The notion of Riemannian symmetric pair (H,G/H) is generalized to supergroups. Using the supercoset approach the superconformal-invariant model of composite U(n) Yang-Mills fields in introduced. In the framework of the superfield approach we present with some details two versions of the composite N=1 supersymmetric Yang-Mills theory in four dimensions with U(n) and U(m) x U(n) local invariance. We argue that especially the superfield sigma models can be used for the description of pre-QCD supersymmetric dynamics. (author)
Global symmetries of Yang-Mills squared in various dimensions
Energy Technology Data Exchange (ETDEWEB)
Anastasiou, A. [Theoretical Physics, Blackett Laboratory, Imperial College London,London SW7 2AZ (United Kingdom); Borsten, L. [Theoretical Physics, Blackett Laboratory, Imperial College London,London SW7 2AZ (United Kingdom); School of Theoretical Physics, Dublin Institute for Advanced Studies,10 Burlington Road, Dublin 4 (Ireland); Hughes, M.J. [Theoretical Physics, Blackett Laboratory, Imperial College London,London SW7 2AZ (United Kingdom); Nagy, S. [Theoretical Physics, Blackett Laboratory, Imperial College London,London SW7 2AZ (United Kingdom); Department of Mathematics, Instituto Superior Técnico,Av. Rovisco Pais, 1049-001 Lisbon (Portugal)
2016-01-25
Tensoring two on-shell super Yang-Mills multiplets in dimensions D≤10 yields an on-shell supergravity multiplet, possibly with additional matter multiplets. Associating a (direct sum of) division algebra(s) D with each dimension 3≤D≤10 we obtain a formula for the supergravity U-duality G and its maximal compact subgroup H in terms of the internal global symmetry algebras of each super Yang-Mills theory. We extend our analysis to include supergravities coupled to an arbitrary number of matter multiplets by allowing for non-supersymmetric multiplets in the tensor product.
Analysis of Ward identities in supersymmetric Yang-Mills theory
Ali, Sajid; Bergner, Georg; Gerber, Henning; Montvay, Istvan; Münster, Gernot; Piemonte, Stefano; Scior, Philipp
2018-05-01
In numerical investigations of supersymmetric Yang-Mills theory on a lattice, the supersymmetric Ward identities are valuable for finding the critical value of the hopping parameter and for examining the size of supersymmetry breaking by the lattice discretisation. In this article we present an improved method for the numerical analysis of supersymmetric Ward identities, which takes into account the correlations between the various observables involved. We present the first complete analysis of supersymmetric Ward identities in N=1 supersymmetric Yang-Mills theory with gauge group SU(3). The results indicate that lattice artefacts scale to zero as O(a^2) towards the continuum limit in agreement with theoretical expectations.
5D Yang-Mills instantons from ABJM Monopoles
Lambert, N.; Papageorgakis, C.
2012-01-01
In the presence of a background supergravity flux, N M2-branes will expand via the Myers effect into M5-branes wrapped on a fuzzy three-sphere. In previous work the fluctuations of the M2-branes were shown to be described by the five-dimensional Yang-Mills gauge theory associated to D4-branes. We show that the ABJM prescription for eleven-dimensional momentum in terms of magnetic flux lifts to an instanton flux of the effective five-dimensional Yang-Mills theory on the sphere, giving an M-theory interpretation for these instantons.
Stochastic variables in N=1 supersymmetric Yang-Mills theory
International Nuclear Information System (INIS)
Lechtenfeld, O.
1984-06-01
The stochastic structure of N=1 supersymmetric Yang-Mills theory is rederived by using a previously developed method for the construction of the (nonlocal) Nicolai map. The stochastic variables correspond to the fixed points of this mapping. The relations are derived in a light cone gauge and in general covariant gauges. (orig.)
Euclidean self-dual Yang-Mills field configurations
International Nuclear Information System (INIS)
Sartori, G.
1980-01-01
The determination of a large class of regular and singular Euclidean self-dual Yang-Mills field configurations is reduced to the solution of a set of linear algebraic equations. The matrix of the coefficients is a polynomial functions of x and the rules for its construction are elementary. (author)
Quantum Yang-Mills theory on arbitrary surfaces
International Nuclear Information System (INIS)
Blau, Matthias; Thompson, George
1991-05-01
Quantum Yang-Mills theory on 2-dimensional surfaces is studied. Using path integral methods general and explicit expressions are derived for the partition function and expectation values of homologically trivial and non-trivial Wilson loops on closed surfaces of any genus, as well as for the kernels on manifolds with handles and boundaries. (author). 15 refs
Bifurcation and stability in Yang-Mills theory with sources
International Nuclear Information System (INIS)
Jackiw, R.
1979-06-01
A lecture is presented in which some recent work on solutions to classical Yang-Mills theory is discussed. The investigations summarized include the field equations with static, external sources. A pattern allowing a comprehensive description of the solutions and stability in dynamical systems are covered. A list of open questions and problems for further research is given. 20 references
Quantization of the topological Yang-Mills theory
International Nuclear Information System (INIS)
Dahmen, H.D.; Marculescu, S.; Szymanowski, L.
1990-01-01
The structure of the conserved or partially conserved currents of the topological Yang-Mills theory is discussed. These currents are then used to show that at the one-loop level the β-function reproduces the N=2 supersymmetry value. The result holds even if N=2 supersymmetry is broken down to a singlet supersymmetry. (orig.)
Hamiltonian reduction of SU(2) Yang-Mills field theory
International Nuclear Information System (INIS)
Khvedelidze, A.M.; Pavel, H.-P.
1998-01-01
The unconstrained system equivalent to SU (2) Yang-Mills field theory is obtained in the framework of the generalized Hamiltonian formalism using the method of Hamiltonian reduction. The reduced system is expressed in terms of fields with 'nonrelativistic' spin-0 and spin-2
Perturbation Theory of Massive Yang-Mills Fields
Veltman, M.
1968-08-01
Perturbation theory of massive Yang-Mills fields is investigated with the help of the Bell-Treiman transformation. Diagrams containing one closed loop are shown to be convergent if there are more than four external vector boson lines. The investigation presented does not exclude the possibility that the theory is renormalizable.
Massive Yang-Mills theory: Renormalizability versus unitarity
International Nuclear Information System (INIS)
Delbourgo, R.; Twisk, S.; Thompson, G.
1987-06-01
Various massive Yang-Mills theories not based on the Higgs mechanism are investigated. They are subject to conflicting demands in the twin requirements of unitarity and perturbative renormalizability. Either one or other of these requirements is violated. Unitarity is considered in some detail. (author). 18 refs, 5 figs
On the infrared behaviour of Yang-Mills Greens functions
International Nuclear Information System (INIS)
Olesen, P.
1976-01-01
Making certain assumptions (valid to any finite order of perturbation theory), it is shown that non-perturbatively pure Yang-Mills Greens functions are power behaved in the momenta in a limit related to the infrared limit. It is also shown that the fundamental vertices have a more singular behaviour than indicated by perturbation theory. (Auth.)
The zero mass limit in Yang-Mills theory
International Nuclear Information System (INIS)
Dombey, N.
1976-01-01
The zero mass limit of massive Yang-Mills theory is investigated and it is shown that there is a conflict between Lorentz invariance and the internal symmetry group in the theory. A necessary but not sufficient condition for the resolution of this conflict is the introduction of zero mass scalar fields. (author)
Topological susceptibility for the SU(3) Yang--Mills theory
DEFF Research Database (Denmark)
Del Debbio, Luigi; Giusti, Leonardo; Pica, Claudio
2004-01-01
We present the results of a computation of the topological susceptibility in the SU(3) Yang--Mills theory performed by employing the expression of the topological charge density operator suggested by Neuberger's fermions. In the continuum limit we find r_0^4 chi = 0.059(3), which corresponds to chi...
Solvable Relativistic Hydrogenlike System in Supersymmetric Yang-Mills Theory
DEFF Research Database (Denmark)
Caron-Huot, Simon; Henn, Johannes M.
2014-01-01
this symmetry? In this Letter we show that the answer is positive: in the nonrelativistic limit, we identify the dual conformal symmetry of planar N=4 super Yang-Mills theory with the well-known symmetries of the hydrogen atom. We point out that the dual conformal symmetry offers a novel way to compute...
Quantum theory of massive Yang-Mills fields, 2
International Nuclear Information System (INIS)
Fukuda, Takashi; Monda, Minoru; Takeda, Minoru; Yokoyama, Kan-ichi.
1981-06-01
By generalization of a basic formulation presented in a preceding part of the same series, a massive Yang-Mills field theory with gauge covariance is formulated within one-parameter invariant gauge families. It is consequently concluded that all cases of different gauges belonging to the same gauge family are equivalent to one another in a rigorous field-theoretical sense. (author)
Propagation of field disturbances in Yang-Mills theory
International Nuclear Information System (INIS)
De Lorenci, Vitorio A.; Li Shiyuan
2008-01-01
The propagation of field disturbances is examined in the context of the effective Yang-Mills Lagrangian, which is intended to be applied to QCD systems. It is shown that birefringence phenomena can occur in such systems provided some restrictive conditions, as causality, are fulfilled. Possible applications to phenomenology are addressed.
Einstein equation and Yang-Mills theory of gravitation
International Nuclear Information System (INIS)
Stedile, E.
1988-01-01
The possibility of Yang Mills theory of gravitation being a candidate as a gauge model for the Poincare group is pointed out. If the arguments favoring this theory are accepted then Einstein's equations can be derived by a different method in which they arise from a dynamical equation for the torsion field, in a particular case. (author) [pt
Classical Yang-Mills mechanics. Nonlinear colour oscillations
International Nuclear Information System (INIS)
Matinyan, S.G.; Savvidi, G.K.; Ter-Arutyunyan-Savvidi, N.G.
1981-01-01
A novel class of solutions of the classical Yang-Mills equations in the Minkowsky space which leads to nonlinear colour oscillations is studied. The system discribing these oscillations is apparently stochastic. Periodic trajectories corresponding to the solutions are found and studied and it is demonstrated that they constitute at least an enumerable set [ru
S-duality, deconstruction and confinement for a marginal deformation of N=4 SUSY Yang-Mills
International Nuclear Information System (INIS)
Dorey, Nick
2004-01-01
We study an exactly marginal deformation of N=4 SUSY Yang-Mills with gauge group U(N) using field theory and string theory methods. The classical theory has a Higgs branch for rational values of the deformation parameter. We argue that the quantum theory also has an S-dual confining branch which cannot be seen classically. The low-energy effective theory on these branches is a six-dimensional non-commutative gauge theory with sixteen supercharges. Confinement of magnetic and electric charges, on the Higgs and confining branches respectively, occurs due to the formation of BPS-saturated strings in the low energy theory. The results also suggest a new way of deconstructing Little String Theory as a large-N limit of a confining gauge theory in four dimensions. (author)
Non-commutative Nash inequalities
International Nuclear Information System (INIS)
Kastoryano, Michael; Temme, Kristan
2016-01-01
A set of functional inequalities—called Nash inequalities—are introduced and analyzed in the context of quantum Markov process mixing. The basic theory of Nash inequalities is extended to the setting of non-commutative L p spaces, where their relationship to Poincaré and log-Sobolev inequalities is fleshed out. We prove Nash inequalities for a number of unital reversible semigroups
Saddle point solutions in Yang-Mills-dilaton theory
International Nuclear Information System (INIS)
Bizon, P.
1992-01-01
The coupling of a dilaton to the SU(2)-Yang-Mills field leads to interesting non-perturbative static spherically symmetric solutions which are studied by mixed analytical and numerical methods. In the abelian sector of the theory there are finite-energy magnetic and electric monopole solutions which saturate the Bogomol'nyi bound. In the nonabelian sector there exist a countable family of globally regular solutions which are purely magnetic but have zero Yang-Mills magnetic charge. Their discrete spectrum of energies is bounded from above by the energy of the abelian magnetic monopole with unit magnetic charge. The stability analysis demonstrates that the solutions are saddle points of the energy functional with increasing number of unstable modes. The existence and instability of these solutions are 'explained' by the Morse-theory argument recently proposed by Sudarsky and Wald. (author)
Non self-dual Yang-Mills fields
International Nuclear Information System (INIS)
Bor, G.
1991-01-01
The purpose of the thesis is to prove the existence of a new family of non self-dual finite-energy solutions to the Yang-Mills equations on Euclidean four-space, with SU(2) as a gauge group. The approach is that of equivalent geometry: attention is restricted to a special class of fields, those that satisfy a certain kind of rotational symmetry which it is proved that (1) a solution to the Yang-Mills equations exists for among them, and (2) no solution to the self-duality equations exists among them. The first assertion is proved by an application of the direct method of the calculus of variations (existence and regularity of minimizers), and the second assertion by showing that the self-duality equations, linearized at a symmetric self-dual solution, cannot possess the required symmetry
Yang-Mills fields which are not self-dual
International Nuclear Information System (INIS)
Bor, G.
1992-01-01
The purpose of this paper is to prove the existence of a new family of non-self-dual finite-energy solutions to the Yang-Mills equations on Euclidean four-space, with SU(2) as a gauge group. The approach is that of 'equivariant geometry': Attention is restricted to a special class of fields, those that satisfy a certain kind of rotational symmetry, for which it is proved that (1) a solution to the Yang-Mills equations exists among them; and (2) no solution to the self-duality equations exists among them. The first assertion is proved by an application of the direct method of the calculus of variations (existence and regularity of minimizers), and the second assertion by studying the symmetry properties of the linearized-self-duality equations. The same technique yields a new family of non-self-dual solutions on the complex projective plane. (orig.)
Loop groups and Yang-Mills theory in dimension two
DEFF Research Database (Denmark)
Gravesen, Jens
1990-01-01
Given a connection ω in a G-bundle over S2, then a process called radial trivialization from the poles gives a unique clutching function, i.e., an element γ of the loop group ΩG. Up to gauge equivalence, ω is completely determined by γ and a map f:S2 →g into the Lie algebra. Moreover, the Yang......-Mills function of ω is the sum of the energy of γ and the square of a certain norm of f. In particular, the Yang-Mills functional has the same Morse theory as the energy functional on ΩG. There is a similar description of connections in a G-bundle over an arbitrary Riemann surface, but so far not of the Yang...
On N = 4 supersymmetric Yang-Mills in harmonic superspace
International Nuclear Information System (INIS)
Ahmed, E.; Bedding, S.; Card, C.T.; Dumbrell, M.; Nouri-Moghadam, M.; Taylor, J.G.
1985-01-01
An analysis of N=4 supersymmetric Yang-Mills theory is presented using a construction involving additional bosonic variables in the coset space SU(4)/H. No choice of H can be shown to lead to an analytic formulation of the theory. by introducing an analysis on dual planes the theory is reduced (including the reality constraint) to one involving N=2 symmetry. This approach has to be extended to include truly harmonic derivatives. For the typical case of SU(4)/SU(2)xU(1) prepotentials are introduced which solve the constraints. It has not been possible, however, to construct an action which leads to the equation of motion for the original N=4 supersymmetric Yang-Mills theory (at the linearised level). (author)
Fiber spaces, connections and Yang-Mills fields
International Nuclear Information System (INIS)
Hermann, R.
1982-01-01
From the point of view of a differential geometer, Yang-Mills Fields are connections on principal fiber bundles whose curvature satisfies certain first-order differential equations. These lectures notes assume a knowledge of the formalism of calculus on manifolds, i.e., the theory of differential forms and vector fields, and are based on the theory of connections in fiber spaces, developed primarily by E. Cartan and C. Ehresmann in the period 1920-1955. To make the material more readily accessible to someone familiar with classical physics, the emphasis will be on Maxwell electromagnetic theory, considered as a Yang-Mills with an abelian structure group. Some of the material is from Interdisciplinary Mathematics, some is new. (orig.)
YANG-MILLS Theory in, Beyond, and Behind Observed Reality
Wilczek, Frank
The primary interactions of Yang-Mills theory [1] are visibly embodied in hard processes, most directly in jets. The character of jets also reflects the deep structure of effective charge, which is dominated by the influence of intrinsically non-Abelian gauge dynamics. These proven insights into fundamental physics ramify in many directions, and are far from being exhausted. I will discuss three rewarding explorations from my own experience, whose point of departure is the hard Yang-Mills interaction, and whose end is not yet in sight. Given an insight so profound and fruitful as Yang and Mills brought us, it is in order to try to consider its broadest implications, which I attempt at the end.
Real and virtual infrared behaviour in Yang-Mills theory
International Nuclear Information System (INIS)
Frenkel, J.; Meuldermans, R.; Mohammad, I.; Taylor, J.C.
1977-01-01
The leading infrared divergences, up to fourth order, from both virtual and from real soft gluon corrections to massive quark scattering have been calculated in an external colourless potential. In the combined corrections, the infrared divergences cancel, as expected. The form of the correction is very simple, and can be expressed in terms of the effective coupling constant of the pure Yang-Mills theory. (Auth.)
Quantum theory of massive Yang-Mills fields, 3
International Nuclear Information System (INIS)
Fukuda, Takashi; Matsuda, Hiroaki; Seki, Yoshinori; Yokoyama, Kan-ichi
1983-01-01
The renormalizable structure of a massive Yang-Mills field theory proposed previously is revealed in view of nonpolynomial Lagrangian theories. Analytic properties of several relevant superpropagators are elucidated in the sense of distributions. It is shown that these regularized superpropagators exhibit a strong infinity-suppression mechanism making the theory renormalizable. There appears a divergence-free model as a subcase of the present theory. (author)
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
Loop Amplitudes in Pure Yang-Mills from Generalised Unitarity
Brandhuber, Andreas; McNamara, Simon; Spence, Bill; Travaglini, Gabriele
2005-01-01
We show how generalised unitarity cuts in D = 4 - 2 epsilon dimensions can be used to calculate efficiently complete one-loop scattering amplitudes in non-supersymmetric Yang-Mills theory. This approach naturally generates the rational terms in the amplitudes, as well as the cut-constructible parts. We test the validity of our method by re-deriving the one-loop ++++, -+++, --++, -+-+ and +++++ gluon scattering amplitudes using generalised quadruple cuts and triple cuts in D dimensions.
Loop amplitudes in pure Yang-Mills from generalised unitarity
International Nuclear Information System (INIS)
Brandhuber, Andreas; McNamara, Simon; Spence, Bill; Travaglini, Gabriele
2005-01-01
We show how generalised unitarity cuts in D = 4-2ε dimensions can be used to calculate efficiently complete one-loop scattering amplitudes in non-supersymmetric Yang-Mills theory. This approach naturally generates the rational terms in the amplitudes, as well as the cut-constructible parts. We test the validity of our method by re-deriving the one-loop ++++, -+++, --++, -+-+ and +++++ gluon scattering amplitudes using generalised quadruple cuts and triple cuts in D dimensions
Loop amplitudes in pure Yang-Mills from generalised unitarity
Energy Technology Data Exchange (ETDEWEB)
Brandhuber, Andreas [Department of Physics, Queen Mary, University of London, Mile End Road, London, E1 4NS (United Kingdom); McNamara, Simon [Department of Physics, Queen Mary, University of London, Mile End Road, London, E1 4NS (United Kingdom); Spence, Bill [Department of Physics, Queen Mary, University of London, Mile End Road, London, E1 4NS (United Kingdom); Travaglini, Gabriele [Department of Physics, Queen Mary, University of London, Mile End Road, London, E1 4NS (United Kingdom)
2005-10-15
We show how generalised unitarity cuts in D = 4-2{epsilon} dimensions can be used to calculate efficiently complete one-loop scattering amplitudes in non-supersymmetric Yang-Mills theory. This approach naturally generates the rational terms in the amplitudes, as well as the cut-constructible parts. We test the validity of our method by re-deriving the one-loop ++++, -+++, --++, -+-+ and +++++ gluon scattering amplitudes using generalised quadruple cuts and triple cuts in D dimensions.
Solving pure yang-mills theory in dimensions.
Leigh, Robert G; Minic, Djordje; Yelnikov, Alexandr
2006-06-09
We analytically compute the spectrum of the spin zero glueballs in the planar limit of pure Yang-Mills theory in 2 + 1 dimensions. The new ingredient is provided by our computation of a new nontrivial form of the ground state wave functional. The mass spectrum of the theory is determined by the zeroes of Bessel functions, and the agreement with large lattice data is excellent.
Regular behaviors in SU(2) Yang-Mills classical mechanics
International Nuclear Information System (INIS)
Xu Xiaoming
1997-01-01
In order to study regular behaviors in high-energy nucleon-nucleon collisions, a representation of the vector potential A i a is defined with respect to the (a,i)-dependence in the SU(2) Yang-Mills classical mechanics. Equations of the classical infrared field as well as effective potentials are derived for the elastic or inelastic collision of two plane wave in a three-mode model and the decay of an excited spherically-symmetric field
Wormhole instanton solution in the Einstein-Yang-Mills system
International Nuclear Information System (INIS)
Hosoya, Akio; Ogura, Waichi.
1989-01-01
A spherical symmetric classical solution of the Einstein and the SU(2) Yang-Mills equations is found in the four dimensional Euclidean space-time with the cosmological constant. The isospinor fermion has zero modes. Their cosmological implications are also discussed with an emphasis on the fact that wormhole instantons in general can be found not only in the sub-Planck physics but also in almost all the stages in lower energy physics. (author)
Dirac equations for generalised Yang-Mills systems
International Nuclear Information System (INIS)
Lechtenfeld, O.; Nahm, W.; Tchrakian, D.H.
1985-06-01
We present Dirac equations in 4p dimensions for the generalised Yang-Mills (GYM) theories introduced earlier. These Dirac equations are related to the self-duality equations of the GYM and are checked to be elliptic in a 'BPST' background. In this background these Dirac equations are integrated exactly. The possibility of imposing supersymmetry in the GYM-Dirac system is investigated, with negative results. (orig.)
The Yang-Mills vacuum wave functional in Coulomb gauge
International Nuclear Information System (INIS)
Campagnari, Davide R.
2011-01-01
Yang-Mills theories are the building blocks of today's Standard Model of elementary particle physics. Besides methods based on a discretization of space-time (lattice gauge theory), also analytic methods are feasible, either in the Lagrangian or in the Hamiltonian formulation of the theory. This thesis focuses on the Hamiltonian approach to Yang-Mills theories in Coulomb gauge. The thesis is presented in cumulative form. After an introduction into the general formulation of Yang-Mills theories, the Hamilton operator in Coulomb gauge is derived. Chap. 1 deals with the heat-kernel expansion of the Faddeev-Popov determinant. In Chapters 2 and 3, the high-energy behaviour of the theory is investigated. To this purpose, perturbative methods are applied, and the results are compared with the ones stemming from functional methods in Coulomb and Landau gauge. Chap. 4 is devoted to the variational approach. Variational ansatzes going beyond the Gaussian form for the vacuum wave functional are considered and treated using Dyson-Schwinger techniques. Equations for the higher-order variational kernels are derived and their effects are estimated. Chap. 5 presents an application of the previously obtained propagators, namely the evaluation of the topological susceptibility, which is related to the mass of the η meson. Finally, a short overview of the perturbative treatment of dynamical fermion fields is presented.
Introduction to instantons in Yang-Mills theory
International Nuclear Information System (INIS)
Pak, N.K.
1980-02-01
The Yang-Mills theory is outlined; the classical formalism is discussed first, and then the difficulties related to gauge invariance in the canonical quantization of the theory are taken up. Next, the task of finding and studying Euclidean gauge field configurations of finite action as solutions to the equation of motion is addressed. It is found that configurations which contribute the most in the semi-classical approximation are those which minimize the action. The question of a lower bound for the Euclidean action is considered. Properties of topological charge and the behavior of topological charge under gauge transformation are discussed. Then instanton solutions to the field equations are produced. Finally, the physical interpretation of the instanton is considered. It is found that the instanton, the Euclidean gauge field configuration which minimizes the action, induces tunneling among the infinitely degenerate vacua of the Yang-Mills theory by lifting the degeneracy and creating new distinct inequivalent (invariant under topologically nontrivial gauge transformations) vacua labelled by a superselection index theta. The angle theta is shown not to be a gauge artifact. In conclusion, the tunneling Hamiltonian and effective Lagrangian for the Yang-Mills theory are discussed
Higgs Amplitudes from N=4 Supersymmetric Yang-Mills Theory.
Brandhuber, Andreas; Kostacińska, Martyna; Penante, Brenda; Travaglini, Gabriele
2017-10-20
Higgs plus multigluon amplitudes in QCD can be computed in an effective Lagrangian description. In the infinite top-mass limit, an amplitude with a Higgs boson and n gluons is computed by the form factor of the operator TrF^{2}. Up to two loops and for three gluons, its maximally transcendental part is captured entirely by the form factor of the protected stress tensor multiplet operator T_{2} in N=4 supersymmetric Yang-Mills theory. The next order correction involves the calculation of the form factor of the higher-dimensional, trilinear operator TrF^{3}. We present explicit results at two loops for three gluons, including the subleading transcendental terms derived from a particular descendant of the Konishi operator that contains TrF^{3}. These are expressed in terms of a few universal building blocks already identified in earlier calculations. We show that the maximally transcendental part of this quantity, computed in nonsupersymmetric Yang-Mills theory, is identical to the form factor of another protected operator, T_{3}, in the maximally supersymmetric theory. Our results suggest that the maximally transcendental part of Higgs amplitudes in QCD can be entirely computed through N=4 super Yang-Mills theory.
SU(2) Yang-Mills solitons in R2 gravity
Perapechka, I.; Shnir, Ya.
2018-05-01
We construct new family of spherically symmetric regular solutions of SU (2) Yang-Mills theory coupled to pure R2 gravity. The particle-like field configurations possess non-integer non-Abelian magnetic charge. A discussion of the main properties of the solutions and their differences from the usual Bartnik-McKinnon solitons in the asymptotically flat case is presented. It is shown that there is continuous family of linearly stable non-trivial solutions in which the gauge field has no nodes.
On self-dual Yang-Mills hierarchy
International Nuclear Information System (INIS)
Nakamura, Yoshimasa
1989-01-01
In this note, motivated by the Kadomtsev-Petviashvili (KP) hierarchy of integrable nonlinear evolution equations, a GL(n,C) self-dual Yang-Mills (SDYM) hierarchy is presented; it is an infinite system of SDYM equations having an infinite number of independent variables and being outside of the KP hierarchy. A relationship between the KP hierarchy and the SDYM hierarchy is discussed. It is also shown that GL(∞) SDYM equations introduced in this note are reduced to the GL(n,C) SDYM hierarchy by imposing an algebraic constraint. (orig.)
N=1 supersymmetric Yang-Mills theory on the lattice
Energy Technology Data Exchange (ETDEWEB)
Piemonte, Stefano
2015-04-08
Supersymmetry (SUSY) relates two classes of particles of our universe, bosons and fermions. SUSY is considered nowadays a fundamental development to explain many open questions about high energy physics. The N=1 super Yang-Mills (SYM) theory is a SUSY model that describes the interaction between gluons and their fermion superpartners called ''gluinos''. Monte Carlo simulations on the lattice are a powerful tool to explore the non-perturbative dynamics of this theory and to understand how supersymmetry emerges at low energy. This thesis presents new results and new simulations about the properties of N=1 SYM, in particular about the phase diagram at finite temperature.
Infrared divergence cancellation in pure Yang-Mills theory
International Nuclear Information System (INIS)
Alvarez, A.G.
1977-01-01
Virtual and real corrections to massless external lines in pure Yang-Mills theory are considered in order to look for general features of the infrared divergence cancellation. Use of the Ward identities and sums over transverse polarization states give rise to terms formally corresponding to real ghost emission, cancelling ghost loop singularities, and to a factorisation of the hard narrow single gauge boson emission. Other virtual corrections are examined in the soft region and a graph by graph cancellation is also found. An illustrative explicit calculation of scattering of a gauge particle in an external scalar potential, including hard narrow angle emission is presented. (Auth.)
A gluon cluster solution of effective Yang-Mills theory
Pavlovsky, O V
2001-01-01
A classical solution of the effective Yang-Mills (YM) theory with a finite energy and nonstandard Lagrangian was obtained. Influence of vacuum polarization on gluon cluster formation was discussed. Appearance of cluster solutions in the theory of non-Abelian fields can take place only if the result goes beyond the framework of pure YM theory. It is shown that account of quantum effects of polarized vacuum in the presence of a classical gluon field can also result in formation of the solutions. Solutions with the finite intrinsic energy are provided. Besides, fields of colour groups SU(2) were studied
Polyakov lines in Yang-Mills matrix models
International Nuclear Information System (INIS)
Austing, Peter; Wheater, John F.; Vernizzi, Graziano
2003-01-01
We study the Polyakov line in Yang-Mills matrix models, which include the IKKT model of IIB string theory. For the gauge group SU(2) we give the exact formulae in the form of integral representations which are convenient for finding the asymptotic behaviour. For the SU(N) bosonic models we prove upper bounds which decay as a power law at large momentum p. We argue that these capture the full asymptotic behaviour. We also indicate how to extend the results to some correlation functions of Polyakov lines. (author)
Two-dimensional N = 2 Super-Yang-Mills Theory
August, Daniel; Wellegehausen, Björn; Wipf, Andreas
2018-03-01
Supersymmetry is one of the possible scenarios for physics beyond the standard model. The building blocks of this scenario are supersymmetric gauge theories. In our work we study the N = 1 Super-Yang-Mills (SYM) theory with gauge group SU(2) dimensionally reduced to two-dimensional N = 2 SYM theory. In our lattice formulation we break supersymmetry and chiral symmetry explicitly while preserving R symmetry. By fine tuning the bar-mass of the fermions in the Lagrangian we construct a supersymmetric continuum theory. To this aim we carefully investigate mass spectra and Ward identities, which both show a clear signal of supersymmetry restoration in the continuum limit.
Supersymmetric self-dual Yang-Mills fields
International Nuclear Information System (INIS)
Zhao Liu
1994-01-01
A new four dimensional (4d) N = 1 supersymmetric integrable model, i.e. the supersymmetric self-dual Yang-Mills model is constructed. The equations of motion for this model are shown to be equivalent to the zero curvature condition on some superplane in the 4d superspace, the superplane being characterized by a point in the project space CP 3,4 . The linear systems are established according to this geometrical interpretation, and the effective action is also proposed in order to explain the dynamical content of the model
Einstein constraints in the Yang-Mills form
International Nuclear Information System (INIS)
Ashtekar, A.
1987-01-01
It is pointed out that constraints of Einstein's theory play a powerful role in both classical and quantum theory because they generate motions in spacetime, rather than in an internal space. New variables are then introduced on the Einstein phase space in terms of which constraints simplify considerably. In particular, the use of these variables enables one to imbed the constraint surface of Einstein's theory into that of Yang-Mills. The imbedding suggests new lines of attack to a number of problems in classical and quantum gravity and provides new concepts and tools to investigate the microscopic structure of space-time geometry
Is the ground state of Yang-Mills theory Coulombic?
Heinzl, Thomas; Ilderton, Anton; Langfeld, Kurt; Lavelle, Martin; Lutz, Wolfgang; McMullan, David
2008-01-01
We study trial states modelling the heavy quark-antiquark ground state in SU(2) Yang-Mills theory. A state describing the flux tube between quarks as a thin string of glue is found to be a poor description of the continuum ground state; the infinitesimal thickness of the string leads to UV artifacts which suppress the overlap with the ground state. Contrastingly, a state which surrounds the quarks with non-abelian Coulomb fields is found to have a good overlap with the ground state for all ch...
Strong coupling effects in non-commutative spaces from OM theory and supergravity
International Nuclear Information System (INIS)
Russo, J.G.; Sheikh-Jabbari, M.M.
2000-11-01
We show that a four-parameter class of 3+1 dimensional NCOS theories can be obtained by dimensional reduction on a general 2-torus from OM theory. Compactifying two spatial directions of NCOS theory on a 2-torus, we study the transformation properties under the SO(2,2; Z) T-duality group. We then discuss non-perturbative configurations of non-commutative super Yang-Mills theory. In particular, we calculate the tension for magnetic monopoles and (p,q) dyons and exhibit their six-dimensional origin, and construct a supergravity solution representing an instanton in the gauge theory. We also compute the potential for a monopole-antimonopole in the supergravity approximation. (author)
Holographic thermalization in N = 4 super Yang-Mills theory at finite coupling
Energy Technology Data Exchange (ETDEWEB)
Stricker, Stefan A. [Technische Universitaet Wien, Institut fuer Theoretische Physik, Vienna (Austria)
2014-02-15
We investigate the behavior of energy-momentum tensor correlators in holographic N = 4 super Yang-Mills plasma, taking finite coupling corrections into account. In the thermal limit we determine the flow of quasinormal modes as a function of the 't Hooft coupling. Then we use a specific model of holographic thermalization to study the deviation of the spectral densities from their thermal limit in an out-of-equilibrium situation. The main focus lies on the thermalization pattern with which the plasma constituents approach their thermal distribution as the coupling constant decreases from the infinite coupling limit. All obtained results point towards the weakening of the usual top-down thermalization pattern. (orig.)
Self-dual solutions to Euclidean Yang-Mills equations
International Nuclear Information System (INIS)
Corrigan, E.
1979-01-01
The paper provides an introduction to two approaches towards understanding the classical Yang-Mills field equations. On the one hand, the work of Atiyah and Ward showed that the self-dual equations, which are non-linear, could be regarded as a set of linear equations which turned out to be related to each other by Baecklund transformations. Fundamental to their procedure was the observation that the information carried by the vector potential could be coded into the structure of certain analytic vector bundles over a three dimensional projective space. The classification of these bundles and the subsequent recovery of the gauge field led to the infinite set of ansaetze, corresponding to the sets of linear equation mentioned already. On the other hand, Atiyah, Hitchin, Drinfeld and Manin have recently constructed, completely algebraically, the bundles of interest and indicated how the Yang-Mills potential may be obtained. Remarkably, their construction differs very little as the gauge group is changed (to any of the classical compact groups) and, uses only the elementary operations of linear algebra to yield potentials as rational functions of the spatial coordinates. (Auth.)
The Massive Yang-Mills Model and Diffractive Scattering
Forshaw, J R; Parrinello, C
1999-01-01
We argue that the massive Yang-Mills model of Kunimasa and Goto, Slavnov, and Cornwall, in which massive gauge vector bosons are introduced in a gauge-invariant way without resorting to the Higgs mechanism, may be useful for studying diffractive scattering of strongly interacting particles. With this motivation, we perform in this model explicit calculations of S-matrix elements between quark states, at tree level, one loop, and two loops, and discuss issues of renormalisability and unitarity. In particular, it is shown that the S-matrix element for quark scattering is renormalisable at one-loop order and is only logarithmically non-renormalisable at two loops. The discrepancies in the ultraviolet regime between the one-loop predictions of this model and those of massless QCD are discussed in detail. In addition, some of the similarities and differences between the massive Yang-Mills model and theories with a Higgs mechanism are analysed at the level of the S-matrix. As an elementary application of the model ...
Spinning higher dimensional Einstein-Yang-Mills black holes
International Nuclear Information System (INIS)
Ghosh, Sushant G.; Papnoi, Uma
2014-01-01
We construct a Kerr-Newman-like spacetime starting from higher dimensional (HD) Einstein-Yang-Mills black holes via complex transformations suggested by Newman-Janis. The new metrics are a HD generalization of Kerr-Newman spacetimes which has a geometry that is precisely that of Kerr-Newman in 4D corresponding to a Yang-Mills (YM) gauge charge, but the sign of the charge term gets flipped in the HD spacetimes. It is interesting to note that the gravitational contribution of the YM gauge charge, in HD, is indeed opposite (attractive rather than repulsive) to that of the Maxwell charge. The effect of the YM gauge charge on the structure and location of static limit surface and apparent horizon is discussed. We find that static limit surfaces become less prolate with increase in dimensions and are also sensitive to the YM gauge charge, thereby affecting the shape of the ergosphere. We also analyze some thermodynamical properties of these BHs. (orig.)
Spinning higher dimensional Einstein-Yang-Mills black holes
Energy Technology Data Exchange (ETDEWEB)
Ghosh, Sushant G. [Jamia Millia Islamia, Centre for Theoretical Physics, New Delhi (India); University of Kwa-Zulu-Natal, Astrophysics and Cosmology Research Unit, School of Mathematical Sciences, Private Bag 54001, Durban (South Africa); Papnoi, Uma [Jamia Millia Islamia, Centre for Theoretical Physics, New Delhi (India)
2014-08-15
We construct a Kerr-Newman-like spacetime starting from higher dimensional (HD) Einstein-Yang-Mills black holes via complex transformations suggested by Newman-Janis. The new metrics are a HD generalization of Kerr-Newman spacetimes which has a geometry that is precisely that of Kerr-Newman in 4D corresponding to a Yang-Mills (YM) gauge charge, but the sign of the charge term gets flipped in the HD spacetimes. It is interesting to note that the gravitational contribution of the YM gauge charge, in HD, is indeed opposite (attractive rather than repulsive) to that of the Maxwell charge. The effect of the YM gauge charge on the structure and location of static limit surface and apparent horizon is discussed. We find that static limit surfaces become less prolate with increase in dimensions and are also sensitive to the YM gauge charge, thereby affecting the shape of the ergosphere. We also analyze some thermodynamical properties of these BHs. (orig.)
Nonexistence theorems for Yang-Mills fields and harmonic maps in the Schwarzschild spacetime
International Nuclear Information System (INIS)
Hu Hesheng
1987-01-01
The nonexistence of static solutions to pure Yang-Mills equations and nonconstant harmonic maps defined on the Schwarzschild spacetime outside the black hole (r>2M) is considered. Nonexistence theorems for pure Yang-Mills equations and harmonic maps in the region r≥5M and r≥3M are obtained, respectively. (orig.)
Quantum Yang-Mills theory of Riemann surfaces and conformal field theory
International Nuclear Information System (INIS)
Killingback, T.P.
1989-01-01
It is shown that Yang-Mills theory on a smooth surface, when suitably quantized, is a topological quantum field theory. This topological gauge theory is intimately related to two-dimensional conformal field theory. It is conjectured that all conformal field theories may be obtained from Yang-Mills theory on smooth surfaces. (orig.)
On the exponentiation of leading infrared divergences in massless Yang-Mills theories
International Nuclear Information System (INIS)
Frenkel, J.; Garcia, R.L.
1977-01-01
We derive, in the axial gauge, the effective U-matrix which governs the behaviour of leading infrared singularities in the self-energy functions of Yang-Mills particles. We then show in a very simple manner, that these divergences, which determine the leading singularities in massless Yang-Mills theories, exponentiate [pt
Light Dilaton at Fixed Points and Ultra Light Scale Super Yang Mills
DEFF Research Database (Denmark)
Antipin, Oleg; Mojaza, Matin; Sannino, Francesco
2012-01-01
of pure supersymmetric Yang-Mills. We can therefore determine the exact nonperturbative fermion condensate and deduce relevant properties of the nonperturbative spectrum of the theory. We also show that the intrinsic scale of super Yang-Mills is exponentially smaller than the scale associated...
5D black hole solution in Einstein-Yang-Mills-Gauss-Bonnet theory
International Nuclear Information System (INIS)
Mazharimousavi, S. Habib; Halilsoy, M.
2007-01-01
By adopting the 5D version of the Wu-Yang ansatz we present in closed form a black hole solution in the Einstein-Yang-Mills-Gauss-Bonnet theory. In the Einstein-Yang-Mills limit, we recover the 5D black hole solution already known
A Static Solution of Yang-Mills Equation on Anti-de Sitter Space
International Nuclear Information System (INIS)
Chen Li; Ren Xinan
2009-01-01
Since product metric on AdS space has played a very important role in Lorentz version of AdS/CFT correspondence, the Yang-Mills equation on AdS space with this metric is considered and a static solution is obtained in this paper, which helps to understand the AdS/CFT correspondence of Yang-Mills fields. (general)
Covariant non-commutative space–time
Directory of Open Access Journals (Sweden)
Jonathan J. Heckman
2015-05-01
Full Text Available We introduce a covariant non-commutative deformation of 3+1-dimensional conformal field theory. The deformation introduces a short-distance scale ℓp, and thus breaks scale invariance, but preserves all space–time isometries. The non-commutative algebra is defined on space–times with non-zero constant curvature, i.e. dS4 or AdS4. The construction makes essential use of the representation of CFT tensor operators as polynomials in an auxiliary polarization tensor. The polarization tensor takes active part in the non-commutative algebra, which for dS4 takes the form of so(5,1, while for AdS4 it assembles into so(4,2. The structure of the non-commutative correlation functions hints that the deformed theory contains gravitational interactions and a Regge-like trajectory of higher spin excitations.
Non-commutative tomography and signal processing
International Nuclear Information System (INIS)
Mendes, R Vilela
2015-01-01
Non-commutative tomography is a technique originally developed and extensively used by Professors M A Man’ko and V I Man’ko in quantum mechanics. Because signal processing deals with operators that, in general, do not commute with time, the same technique has a natural extension to this domain. Here, a review is presented of the theory and some applications of non-commutative tomography for time series as well as some new results on signal processing on graphs. (paper)
Non-commutative standard model: model building
Chaichian, Masud; Presnajder, P
2003-01-01
A non-commutative version of the usual electro-weak theory is constructed. We discuss how to overcome the two major problems: (1) although we can have non-commutative U(n) (which we denote by U sub * (n)) gauge theory we cannot have non-commutative SU(n) and (2) the charges in non-commutative QED are quantized to just 0,+-1. We show how the latter problem with charge quantization, as well as with the gauge group, can be resolved by taking the U sub * (3) x U sub * (2) x U sub * (1) gauge group and reducing the extra U(1) factors in an appropriate way. Then we proceed with building the non-commutative version of the standard model by specifying the proper representations for the entire particle content of the theory, the gauge bosons, the fermions and Higgs. We also present the full action for the non-commutative standard model (NCSM). In addition, among several peculiar features of our model, we address the inherentCP violation and new neutrino interactions. (orig.)
Boundary effects in super-Yang-Mills theory
Energy Technology Data Exchange (ETDEWEB)
Shah, Mushtaq B.; Ganai, Prince A. [National Institute of Technology, Department of Physics, Srinagar, Kashmir (India); Faizal, Mir [University of British Columbia-Okanagan, Irving K. Barber School of Arts and Sciences, Kelowna, BC (Canada); University of Lethbridge, Department of Physics and Astronomy, Alberta (Canada); Zaz, Zaid [University of Kashmir, Department of Electronics and Communication Engineering, Srinagar, Kashmir (India); Bhat, Anha [National Institute of Technology, Department of Metallurgical and Materials Engineering, Srinagar, Kashmir (India); Masood, Syed [International Islamic University, Department of Physics, Islamabad (Pakistan)
2017-05-15
In this paper, we shall analyze a three dimensional supersymmetry theory with N = 2 supersymmetry. We will analyze the quantization of this theory, in the presence of a boundary. The effective Lagrangian used in the path integral quantization of this theory, will be given by the sum of the gauge fixing term and the ghost term with the original classical Lagrangian. Even though the supersymmetry of this effective Lagrangian will also be broken due to the presence of a boundary, it will be demonstrated that half of the supersymmetry of this theory can be preserved by adding a boundary Lagrangian to the effective bulk Lagrangian. The supersymmetric transformation of this new boundary Lagrangian will exactly cancel the boundary term generated from the supersymmetric transformation of the effective bulk Lagrangian. We will analyze the Slavnov-Taylor identity for this N = 2 Yang-Mills theory with a boundary. (orig.)
Gravitational catalysis of merons in Einstein-Yang-Mills theory
Canfora, Fabrizio; Oh, Seung Hun; Salgado-Rebolledo, Patricio
2017-10-01
We construct regular configurations of the Einstein-Yang-Mills theory in various dimensions. The gauge field is of meron-type: it is proportional to a pure gauge (with a suitable parameter λ determined by the field equations). The corresponding smooth gauge transformation cannot be deformed continuously to the identity. In the three-dimensional case we consider the inclusion of a Chern-Simons term into the analysis, allowing λ to be different from its usual value of 1 /2 . In four dimensions, the gravitating meron is a smooth Euclidean wormhole interpolating between different vacua of the theory. In five and higher dimensions smooth meron-like configurations can also be constructed by considering warped products of the three-sphere and lower-dimensional Einstein manifolds. In all cases merons (which on flat spaces would be singular) become regular due to the coupling with general relativity. This effect is named "gravitational catalysis of merons".
Confinement in a three-dimensional Yang-Mills theory
Energy Technology Data Exchange (ETDEWEB)
Frasca, Marco
2017-04-15
We show that, starting from known exact classical solutions of the Yang-Mills theory in three dimensions, the string tension is obtained and the potential is consistent with a marginally confining theory. The potential we obtain agrees fairly well with preceding findings in the literature but here we derive it analytically from the theory without further assumptions. The string tension is in strict agreement with lattice results and the well-known theoretical result by Karabali-Kim-Nair analysis. Classical solutions depend on a dimensionless numerical factor arising from integration. This factor enters into the determination of the spectrum and has been arbitrarily introduced in some theoretical models. We derive it directly from the solutions of the theory and is now fully justified. The agreement obtained with the lattice results for the ground state of the theory is well below 1% at any value of the degree of the group. (orig.)
Step scaling and the Yang-Mills gradient flow
International Nuclear Information System (INIS)
Lüscher, Martin
2014-01-01
The use of the Yang-Mills gradient flow in step-scaling studies of lattice QCD is expected to lead to results of unprecedented precision. Step scaling is usually based on the Schrödinger functional, where time ranges over an interval [0,T] and all fields satisfy Dirichlet boundary conditions at time 0 and T. In these calculations, potentially important sources of systematic errors are boundary lattice effects and the infamous topology-freezing problem. The latter is here shown to be absent if Neumann instead of Dirichlet boundary conditions are imposed on the gauge field at time 0. Moreover, the expectation values of gauge-invariant local fields at positive flow time (and of other well localized observables) that reside in the center of the space-time volume are found to be largely insensitive to the boundary lattice effects.
Is the ground state of Yang-Mills theory Coulombic?
Heinzl, T.; Ilderton, A.; Langfeld, K.; Lavelle, M.; Lutz, W.; McMullan, D.
2008-08-01
We study trial states modelling the heavy quark-antiquark ground state in SU(2) Yang-Mills theory. A state describing the flux tube between quarks as a thin string of glue is found to be a poor description of the continuum ground state; the infinitesimal thickness of the string leads to UV artifacts which suppress the overlap with the ground state. Contrastingly, a state which surrounds the quarks with non-Abelian Coulomb fields is found to have a good overlap with the ground state for all charge separations. In fact, the overlap increases as the lattice regulator is removed. This opens up the possibility that the Coulomb state is the true ground state in the continuum limit.
Boundary effects in super-Yang-Mills theory
International Nuclear Information System (INIS)
Shah, Mushtaq B.; Ganai, Prince A.; Faizal, Mir; Zaz, Zaid; Bhat, Anha; Masood, Syed
2017-01-01
In this paper, we shall analyze a three dimensional supersymmetry theory with N = 2 supersymmetry. We will analyze the quantization of this theory, in the presence of a boundary. The effective Lagrangian used in the path integral quantization of this theory, will be given by the sum of the gauge fixing term and the ghost term with the original classical Lagrangian. Even though the supersymmetry of this effective Lagrangian will also be broken due to the presence of a boundary, it will be demonstrated that half of the supersymmetry of this theory can be preserved by adding a boundary Lagrangian to the effective bulk Lagrangian. The supersymmetric transformation of this new boundary Lagrangian will exactly cancel the boundary term generated from the supersymmetric transformation of the effective bulk Lagrangian. We will analyze the Slavnov-Taylor identity for this N = 2 Yang-Mills theory with a boundary. (orig.)
Yang-Mills fields due to an infinite charge cylinder
International Nuclear Information System (INIS)
Campbell, W.B.; Joseph, D.W.; Morgan, T.A.; Nebraska Univ., Lincoln
1981-01-01
The problem of determining time-independent solutions of the classical Yang-Mills equations for infinitely long charge cylinders is studied. A useful expression for the total energy in the field in terms of just the sources is derived. Numerical solutions have been found in the special cases of a small charge cylinder with a magnetic field B that either lies along the axis of symmetry or encircles the axis. It is as if these two solutions were due to currents encircling the axis or parallelling it, respectively. The condition that the solutions behave well at infinity implies an exponential fall off for the fields in the azimuthal B field case and a fall off more rapid than 1/R in the axial B field case, so that in both cases the existence of a B field requires the charge on the axis to be shieled. Consequently, these solutions do not behave at infinity at all like the Maxwell solution for a charge cylinder, and they have a lower energy per unit length. They show that in Yang-Mills theories the source does not determine a unique field. A classical interpretation of this is that the field remembers how the charges were transported during the construction of the cylinder. It also suggests that a quantum mechanical version of this problem would exhibit a spontaneous symmetry breaking to a less symmetric, lower energy vacuum. These solutions exhibit a twofold degeneracy, as the magnetic field may be either left- or right-handed in the azimuthal B field case, or point along the +z or -z axis in the axial B field case. (orig.)
Yang-Mills theory in null path space
International Nuclear Information System (INIS)
Kent, S.L.
1982-01-01
A reformulation of classical GL(n,c) Yang-Mills theory is presented. The reformulation is in terms of a single matrix-valued function G on a six-dimensional subspace of the space of paths in Minkowski space, M. This subspace is defined as the null paths beginning at each point, (X/sup a/), of M and ending at future null infinity. A convenient parametrization of these paths is to give the Minkowski coordinates x/sup a/ of the starting point and the (complex) stereographic coordinates (xi, antixi) on S 2 which label the light cone generators of x/sup a/. A path is thus labeled by (x/sup a/,xi, antixi). The function G(x/sup a/,xi, antixi) is defined by the parallel propagation (with a given connection) of n linearly independent fiber vectors from x/sup a/ to null infinity along the (xi, antixi) generator. From knowledge of G(x/sup a/,xi, antixi) the connection one-form γ/sub a/ at the point x/sup a/ can be obtained is shown. Furthermore how the vacuum Yang-Mills equations can be imposed on the G is shown. This results in a rather complicated integro-differential equation for G which involves the characteristic initial data (essentially the radiation field) acting as the driving term. Two simple special cases are immediately obtainable; in the case of self-dual (or anti-self dual) fields the author obtains a simple derivation of the Sparling equation, namely delta G = -GA, while for Abelian (Maxwell) theories obtained the equation delta anti delta log G = -anti delta A-anti delta A, where A and its conjugate anti A are the characteristic free data given on null infinity. The latter equation is equivalent to the vacuum Maxwell equations
Renormalizability aspects of massive Yang--Mills field models
International Nuclear Information System (INIS)
Ktorides, C.N.
1976-01-01
We confront the problem concerning the renormalizability of massive Yang--Mills theories in which the mass term for the vector fields has been inserted by hand. Our starting Lagrangians are of a type in the past found to be nonrenormalizable. The massive Yang--Mills fields are split into transverse and longitudinal components. The latter carry all the nonrenormalizability pathologies which manifest themselves in terms of certain nonpolynomial factors involving the longtitudinal fields. The removal of the bad nonpolynomial terms (Boulware's problem) is studied within the context of the adjoint representation of the gauge group SU(2). A necessary condition for solving Boulware's problem is the introduction of extra fields. We find an explicit solution which requires the introduction of a triplet of scalar fields belonging to the adjoint representation of SU(2). We interpret the additional fields as ghost, or superfluous, fields, most probably corresponding to the ghost fields of spontaneously broken gauge theories in the R gauge. Out interpretation of the fields which combine with the longitudinal ones in order to remove the nonpolymomial factors as ghost fields is not evident in the treatment of Cornwall et al. Unlike the case of Cornwall et al., we do not just show the existence of the trnasformation which removes the undesirable terms, but also give the explicit conditions which bring about this result in the case of SU(2). A proposition relating the models under consideration to spontaneously broken gauge ones is also presented. We argue, without explicit proof, that the combination of this proposition with out main theorem corresponds to building a spontaneously broken gauge theory in the R gauge, having started from a non-Abelian theory with mass inserted by hand
Towards a 'pointless' generalisation of Yang-Mills theory
International Nuclear Information System (INIS)
Chan Hongmo; Tsou Sheungtsun
1989-05-01
We examine some generalisations in physical concepts of gauge theories, leading towards a scenario corresponding to non-commutative geometry, where the concept of locality loses its usual meaning of being associated with points on a base manifold and becomes intertwined with the concept of internal symmetry, suggesting thereby a gauge theory of extended objects. Examples are given where such generalised gauge structures can be realised, in particular that of string theory. (author)
4-dimensional General Relativity from the instrinsic spatial geometry of SO(3) Yang-Mills theory
International Nuclear Information System (INIS)
Ita, Eyo Eyo
2011-01-01
In this paper we derive 4-dimensional General Relativity from three dimensions, using the intrinsic spatial geometry inherent in Yang-Mills theory which has been exposed by previous authors as well as some properties of the Ashtekar variables. We provide various interesting relations, including the fact that General Relativity can be written as a Yang-Mills theory where the antiself-dual Weyl curvature replaces the Yang-Mills coupling constant. We have generalized the results of some previous authors, covering Einstein's spaces, to include more general spacetime geometries.
A new approach to the self-dual Yang-Mills equations
International Nuclear Information System (INIS)
Takasaki, K.
1984-01-01
Inspired by Sato's new theory for soliton equations, we find a new approach to the self-dual Yang-Mills equations. We first establish a correspondence of solutions between the self-dual Yang-Mills equations and a new system of equations with infinitely many unknown functions. It then turns out that the latter equations can be easily solved by a simple explicit procedure. This leads to an explicit description of a very broad class of solutions to the self-dual Yang-Mills equations, and also to a construction of transformations acting on these solutions. (orig.)
A Generalized Yang-Mills Model and Dynamical Breaking of Gauge Symmetry
International Nuclear Information System (INIS)
Wang Dianfu; Song Heshan
2005-01-01
A generalized Yang-Mills model, which contains, besides the vector part V μ , also a scalar part S, is constructed and the dynamical breaking of gauge symmetry in the model is also discussed. It is shown, in terms of Nambu-Jona-Lasinio (NJL) mechanism, that the gauge symmetry breaking can be realized dynamically in the generalized Yang-Mills model. The combination of the generalized Yang-Mills model and the NJL mechanism provides a way to overcome the difficulties related to the Higgs field and the Higgs mechanism in the usual spontaneous symmetry breaking theory.
Non-commutativity in polar coordinates
Energy Technology Data Exchange (ETDEWEB)
Edwards, James P. [Universidad Michoacana de San Nicolas de Hidalgo, Ciudad Universitaria, Instituto de Fisica y Matematicas, Morelia, Michoacan (Mexico)
2017-05-15
We reconsider the fundamental commutation relations for non-commutative R{sup 2} described in polar coordinates with non-commutativity parameter θ. Previous analysis found that the natural transition from Cartesian coordinates to the traditional polar system led to a representation of [r, φ] as an everywhere diverging series. In this article we compute the Borel resummation of this series, showing that it can subsequently be extended throughout parameter space and hence provide an interpretation of this commutator. Our analysis provides a complete solution for arbitrary r and θ that reproduces the earlier calculations at lowest order and benefits from being generally applicable to problems in a two-dimensional non-commutative space. We compare our results to previous literature in the (pseudo-)commuting limit, finding a surprising spatial dependence for the coordinate commutator when θ >> r{sup 2}. Finally, we raise some questions for future study in light of this progress. (orig.)
Investigations on the renormalizability of a non-commutative u(1) gauge theory
International Nuclear Information System (INIS)
Rofner, A.
2009-01-01
standard model is formulated via gauge field theories. It is therefore crucial to find their non-commutative, renormalizable counterparts. Having said this we have already addressed the goal and content of this dissertation, which consists in finding a potentially renormalizable theta-deformed u(1) gauge theory. In a first step, we studied in detail a localized version of a model, which represents an extension of ordinary u(1) gauge theory (formulated on Euclidean space) to the non-commutative setting, and is based on adding a term similar to the one of Gurau et. al., leading to an IR-damped gauge boson propagator. In the course of one-loop calculations, we have shown that it implements additional degrees of freedom and hence modifies the original physical content of the theory. A way out was found by implementing the modification of the IR sector through the introduction of a soft breaking term similar to the approach of Gribov and Zwanziger known from commutative Yang Mills theory. However, when trying to show renormalizability at one-loop level, it turned out that the action does not contain the appropriate terms for absorbing the IR divergences. usually, in such cases one constructs an effective renormalizable action via application of renormalization schemes such as Algebraic Renormalization, which in this case fails, due to the inherent non-locality of the star product. As a consequence, some ideas regarding the applicability and possible extension of traditional renormalization schemes to non-commutative GFTs have been discussed. Finally a new action (the BRSW model) was constructed. It could be shown to be renormalizable to one-loop order. Although a rigorous proof is still missing, we expect it to be a very promising candidate for the first fully renormalizable non-commutative gauge field theory.(author) [de
Zeta-function regularization of the quantum fluctuations around the Yang-Mills pseudoparticle
International Nuclear Information System (INIS)
Chadha, S.; Di Vecchia, P.; D'Adda, A.; Nicodemi, F.
1977-01-01
The hypersphere stereographic projection and the zeta-function regularization procedure are used to compute the one loop correction around the Yang-Mills pseudoparticle with scalars and fermions in an arbitrary representation of the SU(2) gauge group. (Auth.)
International Nuclear Information System (INIS)
Thierry-Mieg, J.
1985-01-01
This paper discusses the reinterpretation of the BRS equations of Quantum Field Theory as the Maurer Cartan equation of a classical principal fiber bundle leads to a simple gauge invariant classification of the anomalies in Yang Mills theory and gravity
International Nuclear Information System (INIS)
Thierry-Mieg, J.
1985-01-01
The reinterpretation of the BRS equations of Quantum Field Theory as the Maurer Cartan equation of a classical principal fiber bundle leads to a simple gauge invariant classification of the anomalies in Yang Mills theory and gravity
International Nuclear Information System (INIS)
Johansen, A.A.
1992-01-01
It is shown, that under the certain constraints the generating functional for the Donaldson invariants in the D=4 topological Yang-Mills theory can be interpreted as a partition function for the renormalizable theory. 20 refs
Finite Yang-Mills theories and the Bjorken--Johnson--Low limit
International Nuclear Information System (INIS)
Ali, A.; Bernstein, J.
1975-01-01
We consider the Bjorken-Johnson-Low limit for the propagator in massless Yang-Mills theories. The significance of our result in terms of imposing an eigenvalue on the theory so as to render it finite is discussed
Gauge invariant frequency splitting of the continuum Yang-Mills field
International Nuclear Information System (INIS)
Mitter, P.K.; Valent, G.
1977-01-01
Frequency splitting plays an important role in Wilson's theory of critical phenomena. Here the authors give a theory of gauge invariant frequency splitting of the Yang-Mills field in 4 dimensions. (Auth.)
Liouville and Painleve equations and Yang--Mills strings
International Nuclear Information System (INIS)
Saclioglu, C.K.
1984-01-01
Stringlike solutions of the self-dual Yang--Mills equations (dimensionally reduced to R 2 ) are sought. A multistring Ansatz results in the sinh--Gordon and Liouville equations. According to a general theorem, the solutions must be either real and singular and have infinite action, or complex and nonsingular, with zero action. In the Liouville case, explicit arbitrarily separated n-string solutions of both classes are given. The magnetic flux for these solutions is found to be the Chern class of a Kaehler manifold, and it consequently assumes quantized values 4πn/e. The axisymmetric version of the sinh--Gordon is solved by the third Painleve transcendent P 3 , using the results on P 3 by Wu et al. [Phys. Rev. B 13, 316 (1976)] and McCoy et al. [J. Math. Phys. 18, 10 (1977)]. The axisymmetric case can be cast into the Ernst equation framework for the generation of further solutions. In the Appendix, the Euclideanized Ernst equation is shown to give self-dual Gibbons--Hawking gravitational instantons
Singular points in moduli spaces of Yang-Mills fields
International Nuclear Information System (INIS)
Ticciati, R.
1984-01-01
This thesis investigates the metric dependence of the moduli spaces of Yang-Mills fields of an SU(2) principal bundle P with chern number -1 over a four-dimensional, simply-connected, oriented, compact smooth manifold M with positive definite intersection form. The purpose of this investigation is to suggest that the surgery class of the moduli space of irreducible connections is, for a generic metric, a Z 2 topological invariant of the smooth structure on M. There are three main parts. The first two parts are local analysis of singular points in the moduli spaces. The last part is global. The first part shows that the set of metrics for which the moduli space of irreducible connections has only non-degenerate singularities has codimension at least one in the space of all metrics. The second part shows that, for a one-parameter family of moduli spaces in a direction transverse to the set of metrics for which the moduli spaces have singularities, passing through a non-degenerate singularity of the simplest type changes the moduli space by a cobordism. The third part shows that generic one-parameter families of metrics give rise to six-dimensional manifolds, the corresponding family of moduli spaces of irreducible connections. It is shown that when M is homeomorphic to S 4 the six-dimensional manifold is a proper cobordism, thus establishing the independence of the surgery class of the moduli space on the metric on M
N=1 supersymmetric yang-mills theory in Ito Calculus
International Nuclear Information System (INIS)
Nakazawa, Naohito
2003-01-01
The stochastic quantization method is applied to N = 1 supersymmetric Yang-Mills theory, in particular in 4 and 10 dimensions. In the 4 dimensional case, based on Ito calculus, the Langevin equation is formulated in terms of the superfield formalism. The stochastic process manifestly preserves both the global N = 1 supersymmetry and the local gauge symmetry. The expectation values of the local gauge invariant observables in SYM 4 are reproduced in the equilibrium limit. In the superfield formalism, it is impossible in SQM to choose the so-called Wess-Zumino gauge in such a way to gauge away the auxiliary component fields in the vector multiplet, while it is shown that the time development of the auxiliary component fields is determined by the Langevin equations for the physical component fields of the vector multiplet in an ''almost Wess-Zumino gauge''. The physical component expressions of the superfield Langevin equation are naturally extended to the 10 dimensional case, where the spinor field is Majorana-Weyl. By taking a naive zero volume limit of the SYM 10 , the IIB matrix model is studied in this context. (author)
Perturbations of the Yang-Mills field in the universe
International Nuclear Information System (INIS)
Zhao Wen
2009-01-01
It has been suggested that the Yang-Mills (YM) field can be a kind of candidate for the inflationary field at high energy scales or dark energy at very low energy scales, which can naturally give the equation of state -1 -2 , from which it follows that the equation of state of the YM field always goes to -1, independent of the initial conditions. By solving the first order Einstein equations and the YM field equations, we find that in the YM field inflationary models, the scale-invariant primordial perturbation power spectrum cannot be generated. Therefore, only using this kind of YM field is not enough to account for inflationary sources. However, as a kind of candidate for dark energy, the YM field has the 'sound speed' cs 2 S = -1/3 < 0, which makes the perturbation oe have a damping behavior at large scales. This provides a way to distinguish the YM field dark energy models from other kinds of models. (research papers)
Supersymmetric Yang-Mills and supergravity amplitudes at one loop
International Nuclear Information System (INIS)
Hall, Anthony
2009-01-01
By applying the known expressions for super Yang-Mills (SYM) and supergravity (SUGRA) tree amplitudes, we write generating functions for the next-to-next-to-maximally helicity violating (NNMHV) box coefficients of SYM as well as the maximally helicity violating, next-to-maximally helicity violating, and NNMHV box coefficients for SUGRA. The all-multiplicity generating functions utilize covariant, on-shell superspace whereby the contribution from arbitrary external states in the supermultiplet can be extracted by Grassmann operators. In support of the relation between dual-Wilson loops and SYM scattering amplitudes at weak coupling, the SYM amplitudes are presented in a manifestly dual superconformal form. We introduce ordered box coefficients for calculating SUGRA quadruple cuts and prove that ordered coefficients generate physical cut amplitudes after summing over permutations of the external legs. The ordered box coefficients are produced by sewing ordered subamplitudes, previously used in applying on-shell recursion relations at tree level. We describe our verification of the results against the literature, and a formula for extracting the contributions from external gluons or gravitons to NNMHV superamplitudes is presented.
String tensions in deformed Yang-Mills theory
Poppitz, Erich; Shalchian T., M. Erfan
2018-01-01
We study k-strings in deformed Yang-Mills (dYM) with SU(N) gauge group in the semiclassically calculable regime on R^3× S^1 . Their tensions Tk are computed in two ways: numerically, for 2 ≤ N ≤ 10, and via an analytic approach using a re-summed perturbative expansion. The latter serves both as a consistency check on the numerical results and as a tool to analytically study the large-N limit. We find that dYM k-string ratios Tk/T1 do not obey the well-known sine- or Casimir-scaling laws. Instead, we show that the ratios Tk/T1 are bound above by a square root of Casimir scaling, previously found to hold for stringlike solutions of the MIT Bag Model. The reason behind this similarity is that dYM dynamically realizes, in a theoretically controlled setting, the main model assumptions of the Bag Model. We also compare confining strings in dYM and in other four-dimensional theories with abelian confinement, notably Seiberg-Witten theory, and show that the unbroken Z_N center symmetry in dYM leads to different properties of k-strings in the two theories; for example, a "baryon vertex" exists in dYM but not in softly-broken Seiberg-Witten theory. Our results also indicate that, at large values of N, k-strings in dYM do not become free.
A Yang-Mills structure for string field theory
International Nuclear Information System (INIS)
Tsousheung Tsun
1990-01-01
String theorists believe that one way to achieve a fully quantized theory of string is through string field theory. The other way is to study conformal field theory on Riemann surfaces of different genera, which is the subject of many of the talks at this Conference. In a way, string field theory is the more conservative approach, since it aims just to replace the spacetime points of conventional quantum field theory by string, which are extended objects. However, from this point of view string theory has one rather unsatisfactory aspect, in the sense that although it has been very well developed and minutely studied, we are still rather unclear about its basic structure. We can contrast this to both general relativity, which is based on the geometry of spacetime, and to gauge theory, which is about the structure of various natural bundles over spacetime. And yet string theory is supposed to embody both these two essentially geometric theories. To paraphrase Witten, in string theory we seem to have to work backwards to get at the still unknown basic structure. Some joint work with Chan Hong-Mo is reported in an attempt to gain some understanding in that general direction. It seems that one could in some sense consider string field theory as a generalized Yang-Mills theory. This idea is explored. (author)
One-dimensional structures behind twisted and untwisted superYang-Mills theory
Baulieu, Laurent
2011-01-01
We give a one-dimensional interpretation of the four-dimensional twisted N=1 superYang-Mills theory on a Kaehler manifold by performing an appropriate dimensional reduction. We prove the existence of a 6-generator superalgebra, which does not possess any invariant Lagrangian but contains two different subalgebras that determine the twisted and untwisted formulations of the N=1 superYang-Mills theory.
The limit of the Yang-Mills-Higgs flow on Higgs bundles
Li, Jiayu; Zhang, Xi
2014-01-01
In this paper, we consider the gradient flow of the Yang-Mills-Higgs functional for Higgs pairs on a Hermitian vector bundle $(E, H_{0})$ over a compact K\\"ahler manifold $(M, \\omega )$. We study the asymptotic behavior of the Yang-Mills-Higgs flow for Higgs pairs at infinity, and show that the limiting Higgs sheaf is isomorphic to the double dual of the graded Higgs sheaves associated to the Harder-Narasimhan-Seshadri filtration of the initial Higgs bundle.
A Unified Field Theory of Gravity, Electromagnetism, and the Yang-Mills Gauge Field
Directory of Open Access Journals (Sweden)
Suhendro I.
2008-01-01
Full Text Available In this work, we attempt at constructing a comprehensive four-dimensional unified field theory of gravity, electromagnetism, and the non-Abelian Yang-Mills gauge field in which the gravitational, electromagnetic, and material spin fields are unified as intrinsic geometric objects of the space-time manifold S4 via the connection, with the general- ized non-Abelian Yang-Mills gauge field appearing in particular as a sub-field of the geometrized electromagnetic interaction.
One-dimensional structures behind twisted and untwisted super Yang-Mills theory
Energy Technology Data Exchange (ETDEWEB)
Baulieu, Laurent [CERN, Geneve (Switzerland). Theoretical Div.; Toppan, Francesco, E-mail: baulieu@lpthe.jussieu.f, E-mail: toppan@cbpf.b [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)
2010-07-01
We give a one-dimensional interpretation of the four-dimensional twisted N = 1 super Yang-Mills theory on a Kaehler manifold by performing an appropriate dimensional reduction. We prove the existence of a 6-generator superalgebra, which does not possess any invariant Lagrangian but contains two different subalgebras that determine the twisted and untwisted formulations of the N = 1 super Yang-Mills theory. (author)
Observables in topological Yang-Mills theories with extended shift supersymmetry
Energy Technology Data Exchange (ETDEWEB)
Constantinidis, Clisthenis P; Piguet, Olivier [Universidade Federal do Espirito Santo (UFES), Vitoria, ES (Brazil); Spalenza, Wesley [Scuola Internazionale Superiore di Studi Avanzati (SISSA), Trieste (Italy); Centro Brasileiro de Pesquisas Fsicas (CBPF), Rio de Janeiro (Brazil)
2006-01-01
We present a complete classification, at the classical level, of the observables of topological Yang-Mills theories with an extended shift supersymmetry of N generators, in any space-time dimension. The observables are defined as the Yang-Mills BRST cohomology classes of shift supersymmetry invariants. These cohomology classes turn out to be solutions of an N-extension of Witten's equivariant cohomology. This work generalizes results known in the case of shift supersymmetry with a single generator. (orig.)
One-dimensional structures behind twisted and untwisted super Yang-Mills theory
International Nuclear Information System (INIS)
Baulieu, Laurent
2010-01-01
We give a one-dimensional interpretation of the four-dimensional twisted N = 1 super Yang-Mills theory on a Kaehler manifold by performing an appropriate dimensional reduction. We prove the existence of a 6-generator superalgebra, which does not possess any invariant Lagrangian but contains two different subalgebras that determine the twisted and untwisted formulations of the N = 1 super Yang-Mills theory. (author)
Masslessness of ghosts in equivariantly gauge-fixed Yang-Mills theories
International Nuclear Information System (INIS)
Golterman, Maarten; Zimmerman, Leah
2005-01-01
We show that the one-loop ghost self-energy in an equivariantly gauge-fixed Yang-Mills theory vanishes at zero momentum. A ghost mass is forbidden by equivariant BRST symmetry, and our calculation confirms this explicitly. The four-ghost self interaction which appears in the equivariantly gauge-fixed Yang-Mills theory is needed in order to obtain this result
Stiefel-Skyrem-Higgs models, their classical static solutions and Yang-Mills-Higgs monopoles
International Nuclear Information System (INIS)
Dobrev, V.K.
1981-07-01
A new series of models is introduced by adding Higgs fields to the earlier proposed euclidean four-dimensional Skyrme-like models with Yang-Mills composite fields constructed from Stiefel manifold-valued fields. The classical static versions of these models are discussed. The connection with the monopole solutions of the Yang-Mills-Higgs models in the Prasad-Sommerfield limit is pointed out and the BPS monopole is reobtained as an example. (author)
Numerical solution to the hermitian Yang-Mills equation on the Fermat quintic
International Nuclear Information System (INIS)
Douglas, Michael R.; Karp, Robert L.; Lukic, Sergio; Reinbacher, Rene
2007-01-01
We develop an iterative method for finding solutions to the hermitian Yang-Mills equation on stable holomorphic vector bundles, following ideas recently developed by Donaldson. As illustrations, we construct numerically the hermitian Einstein metrics on the tangent bundle and a rank three vector bundle on P 2 . In addition, we find a hermitian Yang-Mills connection on a stable rank three vector bundle on the Fermat quintic
Non-commutative arithmetic circuits with division
Czech Academy of Sciences Publication Activity Database
Hrubeš, Pavel; Wigderson, A.
2015-01-01
Roč. 11, Article 14 (2015), s. 357-393 ISSN 1557-2862 EU Projects: European Commission(XE) 339691 - FEALORA Institutional support: RVO:67985840 Keywords : arithmetic circuits * non-commutative rational function * skew field Subject RIV: BA - General Mathematics http://theoryofcomputing.org/articles/v011a014/
Representation dependence of k -strings in pure Yang-Mills theory via supersymmetry
Anber, Mohamed M.; Pellizzani, Vito
2017-12-01
We exploit a conjectured continuity between super Yang-Mills on R3×S1 and pure Yang-Mills to study k -strings in the latter theory. As expected, we find that Wilson-loop correlation functions depend on the N-ality of a representation R to the leading order. However, the next-to-leading order correction is not universal and is given by the group characters, in the representation R , of the permutation group. We also study W-bosons in super Yang-Mills. We show that they are deconfined on the string world sheet, and therefore, they can change neither the string N-ality nor its tension. This phenomenon mirrors the fact that soft gluons do not screen probe charges with nonzero N-ality in pure Yang-Mills. Finally, we comment on the scaling law of k -strings in super Yang-Mills and compare our findings with strings in Seiberg-Witten theory, deformed Yang-Mills theory, and holographic studies that were performed in the 't Hooft large-N limit.
Two-dimensional black holes and non-commutative spaces
International Nuclear Information System (INIS)
Sadeghi, J.
2008-01-01
We study the effects of non-commutative spaces on two-dimensional black hole. The event horizon of two-dimensional black hole is obtained in non-commutative space up to second order of perturbative calculations. A lower limit for the non-commutativity parameter is also obtained. The observer in that limit in contrast to commutative case see two horizon
Finite field equation of Yang--Mills theory
International Nuclear Information System (INIS)
Brandt, R.A.; Wing-Chiu, N.; Yeung, W.
1980-01-01
We consider the finite local field equation -][1+1/α (1+f 4 )]g/sup munu/D'Alembertian-partial/sup μ/partial/sup ν/]A/sup nua/ =-(1+f 3 ) g 2 N[A/sup c/νA/sup a/μA/sub ν//sup c/] +xxx+(1-s) 2 M 2 A/sup a/μ, introduced by Lowenstein to rigorously describe SU(2) Yang--Mills theory, which is written in terms of normal products. We also consider the operator product expansion A/sup c/ν(x+xi) A/sup a/μ(x) A/sup b/lambda(x-xi) approx.ΣM/sup c/abνμlambda/sub c/'a'b'ν'μ'lambda' (xi) N[A/sup nuprimec/'A/sup muprimea/'A/sup lambdaprimeb/'](x), and using asymptotic freedom, we compute the leading behavior of the Wilson coefficients M/sup ...//sub .../(xi) with the help of a computer, and express the normal products in the field equation in terms of products of the c-number Wilson coefficients and of operator products like A/sup c/ν(x+xi) A/sup a/μ(x) A/sup b/lambda(x-xi) at separated points. Our result is -][1+(1/α)(1+f 4 )]g/sup munu/D'Alembertian-partial/sup μ/partial/sup ν/]A/sup nua/ =-(1+f 3 ) g 2 lim/sub xiarrow-right0/] (lnxi)/sup -0.28/2b/[A/sup c/ν (x+xi) A/sup a/μ(x) A/sub ν//sup c/(x-xi) +epsilon/sup a/bcA/sup muc/(x+xi) partial/sup ν/A/sup b//sub ν/(x)+xxx] +xxx]+(1-s) 2 M 2 A/sup a/μ, where β (g) =-bg 3 , and so (lnxi)/sup -0.28/2b/ is the leading behavior of the c-number coefficient multiplying the operator products in the field equation
Gluon scattering in N=4 super Yang-Mills at finite temperature
International Nuclear Information System (INIS)
Ito, Katsushi; Iwasaki, Koh; Nastase, Horatiu
2008-01-01
We extend the AdS/CFT prescription of Alday and Maldacena to finite temperature T, defining an amplitude for gluon scattering in N=4 Super Yang-Mills at strong coupling from string theory. It is defined by a lightlike 'Wilson loop' living at the horizon of the T-dual to the black hole in AdS space. Unlike the zero temperature case, this is different from the Wilson loop contour defined at the boundary of the AdS black hole metric. Thus at nonzero T there is no relation between gluon scattering amplitudes and the Wilson loop. We calculate a gauge theory observable that can be interpreted as the amplitude at strong coupling for forward scattering of a low energy gluon (E >T) in both cutoff and generalized dimensional regularization. The generalized dimensional regularization is defined in string theory as an IR modified dimensional reduction. For this calculation, the corresponding usual Wilson loop of the same boundary shape was argued to be related to the jet quenching parameter of the finite temperature N=4 SYM plasma, while the gluon scattering amplitude is related to the viscosity coefficient. (author)
Singular Minkowski and Euclidean solutions for SU(2) Yang-Mills theory
International Nuclear Information System (INIS)
Singleton, D.
1996-01-01
In this paper it is examined a solution to the SU(2) Yang-Mills-Higgs system, which is a trivial mathematical extension of recently discovered Schwarzschild- like solutions (Singleton D., Phys. Rev. D, 51 (1955) 5911). Physically, however, this new solution has drastically different properties from the Schwarzschild-like solutions. It is also studied a new classical solution for Euclidean SU(2) Yang-Mills theory. Again this new solution is a mathematically trivial extension of the Belavin-Polyakov-Schwartz-Tyupkin (BPST) (Belavin A. A. et al., Phys. Lett. B, 59 (1975) 85) instanton, but is physically very different. Unlike the usual instanton solution, the present solution is singular on a sphere of arbitrary radius in Euclidean space. Both of these solutions are infinite-energy solutions, so their practical value is somewhat unclear. However, they may be useful in exploring some of the mathematical aspects of classical Yang-Mills theory
Super Yang-Mills theory with impurity walls and instanton moduli spaces
Cherkis, Sergey A.; O'Hara, Clare; Sämann, Christian
2011-06-01
We explore maximally supersymmetric Yang-Mills theory with walls of impurities respecting half of the supersymmetries. The walls carry fundamental or bifundamental matter multiplets. We employ three-dimensional N=2 superspace language to identify the Higgs branch of this theory. We find that the vacuum conditions determining the Higgs branch are exactly the bow equations yielding Yang-Mills instantons on a multi-Taub-NUT space. Under electric-magnetic duality, the super Yang-Mills theory describing the bulk is mapped to itself, while the fundamental- and bifundamental-carrying impurity walls are interchanged. We perform a one-loop computation on the Coulomb branch of the dual theory to find the asymptotic metric on the original Higgs branch.
Maximally Generalized Yang-Mills Model and Dynamical Breaking of Gauge Symmetry
International Nuclear Information System (INIS)
Wang Dianfu; Song Heshan
2006-01-01
A maximally generalized Yang-Mills model, which contains, besides the vector part V μ , also an axial-vector part A μ , a scalar part S, a pseudoscalar part P, and a tensor part T μν , is constructed and the dynamical breaking of gauge symmetry in the model is also discussed. It is shown, in terms of the Nambu-Jona-Lasinio mechanism, that the gauge symmetry breaking can be realized dynamically in the maximally generalized Yang-Mills model. The combination of the maximally generalized Yang-Mills model and the NJL mechanism provides a way to overcome the difficulties related to the Higgs field and the Higgs mechanism in the usual spontaneous symmetry breaking theory.
Radiating black holes in Einstein-Yang-Mills theory and cosmic censorship
International Nuclear Information System (INIS)
Ghosh, Sushant G.; Dadhich, Naresh
2010-01-01
Exact nonstatic spherically symmetric black-hole solutions of the higher dimensional Einstein-Yang-Mills equations for a null dust with Yang-Mills gauge charge are obtained by employing Wu-Yang ansatz, namely, HD-EYM Vaidya solution. It is interesting to note that gravitational contribution of Yang-Mills (YM) gauge charge for this ansatz is indeed opposite (attractive rather than repulsive) that of Maxwell charge. It turns out that the gravitational collapse of null dust with YM gauge charge admits strong curvature shell focusing naked singularities violating cosmic censorship. However, there is significant shrinkage of the initial data space for a naked singularity of the HD-Vaidya collapse due to presence of YM gauge charge. The effect of YM gauge charge on structure and location of the apparent and event horizons is also discussed.
Spin foam models of Yang-Mills theory coupled to gravity
International Nuclear Information System (INIS)
Mikovic, A
2003-01-01
We construct a spin foam model of Yang-Mills theory coupled to gravity by using a discretized path integral of the BF theory with polynomial interactions and the Barrett-Crane ansatz. In the Euclidean gravity case, we obtain a vertex amplitude which is determined by a vertex operator acting on a simple spin network function. The Euclidean gravity results can be straightforwardly extended to the Lorentzian case, so that we propose a Lorentzian spin foam model of Yang-Mills theory coupled to gravity
Unconstrained SU(2) and SU(3) Yang-Mills clasical mechanics
International Nuclear Information System (INIS)
Dahmen, B.; Raabe, B.
1992-01-01
A systematic study of constraints in SU(2) and SU(3) Yang-Mills classical mechanics is performed. Expect for the SU(2) case with vanishing spatial angular momenta they turn out to be non-holonomic. Using Dirac's constraint formalism we achieve a complete elimination of the unphysical gauge and rotational degrees of freedom. This leads to an effective unconstrained formulation both for the full SU(2) Yang-Mills classical mechanics and for the SU(3) case in the subspace of vanishing spatial angular momenta. We believe that our results are well suited for further explicit dynamical investigations. (orig.)
Self-dual Yang-Mills equation and deformation of surfaces
International Nuclear Information System (INIS)
Serikbaev, N.S.; Myrzakul, K.; Sajymbetova, S.K.; Koshkinbaev, A.D.; Myrzakulov, R.
2003-01-01
We show that many integrable systems and integrable spin systems in 2+1 dimensions can be obtained from the (2+1)- dimensional Gauss-Mainardi-Codazzi and Gauss-Weingarten equations, respectively. We also show that the (2+1)-dimensional Gauss-Mainardi-Codazzi equation which describes the deformation (motion) of surfaces is the exact reduction of the Yang-Mills-Higgs-Bogomolny and self-dual Yang-Mills equations. On the basis of this observation, we suggest that the (2+1)-dimensional Gauss-Mainardi-Codazzi equation is a candidate to be integrable, and the associated linear problem (Lax representation) with the spectral parameter is presented. (author)
Color Memory: A Yang-Mills Analog of Gravitational Wave Memory
Pate, Monica; Raclariu, Ana-Maria; Strominger, Andrew
2017-12-01
A transient color flux across null infinity in classical Yang-Mills theory is considered. It is shown that a pair of test "quarks" initially in a color singlet generically acquire net color as a result of the flux. A nonlinear formula is derived for the relative color rotation of the quarks. For a weak color flux, the formula linearizes to the Fourier transform of the soft gluon theorem. This color memory effect is the Yang-Mills analog of the gravitational memory effect.
Unconstrained SU(2) and SU(3) Yang-Mills classical mechanics
International Nuclear Information System (INIS)
Dahmen, B.; Raabe, B.
1992-01-01
A systematic study of contraints in SU(2) and SU(3) Yang-Mills classical mechanics is performed. Expect for the SU(2) case with spatial angular momenta they turn out to be nonholonomic. The complete elimination of the unphysical gauge and rotatinal degrees of freedom is achieved using Dirac's constraint formalism. We present an effective unconstrained formulation of the general SU(2) Yang-Mills classical mechanics as well as for SU(3) in the subspace of vanishing spatial angular momenta that is well suited for further explicit dynamical investigations. (orig.)
Yang-Mills-Higgs solitons dynamics in (2+1)-dimensions
International Nuclear Information System (INIS)
Getmanov, B.S.; Sutcliffe, P.M.
1998-01-01
Dimensional reduction of the self-dual Yang-Mills (sd YM) equation in (2+2) dimensions produces an integrable Yang-Mills-Higgs-Bogomolny equation in (2+1) dimensions. For an SU(1,1) gauge group a t'Hooft-like ansatz is used to construct a monopole-like solution and an N-soliton-type solution, which describes static deformed monopoles together with exotic monopole dynamics, including transmutation. Finally, we show how our monopole solution has a surprisingly simple form in terms of the twistor construction, and make some remarks regarding multimonopole solutions
Reduction of 4-dim self dual super Yang-Mills onto super Riemann surfaces
International Nuclear Information System (INIS)
Mendoza, A.; Restuccia, A.; Martin, I.
1990-05-01
Recently self dual super Yang-Mills over a super Riemann surface was obtained as the zero set of a moment map on the space of superconnections to the dual of the super Lie algebra of gauge transformations. We present a new formulation of 4-dim Euclidean self dual super Yang-Mills in terms of constraints on the supercurvature. By dimensional reduction we obtain the same set of superconformal field equations which define self dual connections on a super Riemann surface. (author). 10 refs
Non-commutative tools for topological insulators
International Nuclear Information System (INIS)
Prodan, Emil
2010-01-01
This paper reviews several analytic tools for the field of topological insulators, developed with the aid of non-commutative calculus and geometry. The set of tools includes bulk topological invariants defined directly in the thermodynamic limit and in the presence of disorder, whose robustness is shown to have nontrivial physical consequences for the bulk states. The set of tools also includes a general relation between the current of an observable and its edge index, a relation that can be used to investigate the robustness of the edge states against disorder. The paper focuses on the motivations behind creating such tools and on how to use them.
Freedom and confinement in lattice Yang-Mills theories: a case for divorce
International Nuclear Information System (INIS)
Colangelo, P.; Cosmai, L.; Pellicoro, M.; Preparata, G.
1986-01-01
It is presented evidence that nonperturbative effects in lattice gauge theories do not obey at small coupling constant (large β) asymptotic scaling, but they rather behave as suggested by a recent result in continuum Yang-Mills theories. It is also discussed the possible impact of these results on our understanding of QCD
Scattering amplitudes in N=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity
Chiodaroli, Marco; Johansson, Henrik; Roiban, Radu
2015-01-01
We expose a double-copy structure in the scattering amplitudes of the generic Jordan family of N=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity theories in four and five dimensions. The Maxwell-Einstein supergravity amplitudes are obtained through the color/kinematics duality as a product of two gauge-theory factors; one originating from pure N=2 super-Yang-Mills theory and the other from the dimensional reduction of a bosonic higher-dimensional pure Yang-Mills theory. We identify a specific symplectic frame in four dimensions for which the on-shell fields and amplitudes from the double-copy construction can be identified with the ones obtained from the supergravity Lagrangian and Feynman-rule computations. The Yang-Mills/Einstein supergravity theories are obtained by gauging a compact subgroup of the isometry group of their Maxwell-Einstein counterparts. For the generic Jordan family this process is identified with the introduction of cubic scalar couplings on the bosonic gauge-theory side, which th...
Some preliminary results on the dynamics of Einstein-Yang-Mills-Higgs systems
Energy Technology Data Exchange (ETDEWEB)
Csizmadia, Peter; Racz, Istvan [RMKI, Budapest, Konkoly Thege Miklos ut 29-33, H-1121 (Hungary); Kovacs, Gergely, E-mail: gkovacs@rmki.kfki.h, E-mail: iracz@rmki.kfki.h [Eoetvoes University, Department of Astronomy, Budapest, POB. 32, H-1518 (Hungary)
2010-03-01
A mathematical and numerical framework for the study of dynamical properties of spherically symmetric Einstein-Yang-Mills-Higgs systems is introduced. The quantitative investigations of the time evolution of some simple magnetic monopole type configurations are presented. Long living breather type states are found to develop.
Perturbative Yang-Mills theory without Faddeev-Popov ghost fields
Huffel, Helmuth; Markovic, Danijel
2018-05-01
A modified Faddeev-Popov path integral density for the quantization of Yang-Mills theory in the Feynman gauge is discussed, where contributions of the Faddeev-Popov ghost fields are replaced by multi-point gauge field interactions. An explicit calculation to O (g2) shows the equivalence of the usual Faddeev-Popov scheme and its modified version.
Infrared stability of the Yang-Mills theory in the zero-instanton sector
International Nuclear Information System (INIS)
Olesen, P.
1976-12-01
Abstracting the decoupling theorem of Appelquist and Carazzone from perturbation theory it is shown that the Yang-Mills theory is infrared stable in the zero-instanton sector. It is pointed out that the argument is not valid when instantons are present. (Auth.)
Ito calculus for σ-models and Yang-Mills theories
International Nuclear Information System (INIS)
Patrascioiu, A.; Richard, J.L.
1984-07-01
It is pointed out that the effective continuum action for σ-models and Yang-Mills theories may differ from the naive continuum action by terms of order g 2 or higher, which are non-symmetric. The modifications are produced by a generalization of the Ito calculus to dimensions higher than one
SO(4)-symmetric solutions of Minkowskian Yang-Mills field equations
International Nuclear Information System (INIS)
Luescher, M.
1977-06-01
We construct all solutions to the SU(2) Yang-Mills field equations in Minkowski space that are invariant under an SO(4) subgroup of the conformal group. They are real, regular and have finite energy and action. A connection with the instanton solution is pointed out. (orig.) [de
Two-dimensional Yang-Mills theory in the leading 1/N expansion
International Nuclear Information System (INIS)
Wu, T.T.
1977-01-01
Recent controversies about the gauge invariance of the two-dimensional SU(N) Yang-Mills theory in the 't Hooft limit of large N are resolved. The fermion (quark) propagator is found explicitly, and is qualitatively different from those in the previous literature. (Auth.)
Supersymmetric renormalization prescription in N=4 super-Yang-Mills theory
International Nuclear Information System (INIS)
Baulieu, Laurent; Bossard, Guillaume
2006-01-01
Using the shadow dependent decoupled Slavnov-Taylor identities associated to gauge invariance and supersymmetry, we discuss the renormalization of the N=4 super-Yang-Mills theory and of its coupling to gauge-invariant operators. We specify the method for the determination of non-supersymmetric counterterms that are needed to maintain supersymmetry
Asymptotic properties of spherically symmetric, regular and static solutions to Yang-Mills equations
International Nuclear Information System (INIS)
Cronstrom, C.
1987-01-01
In this paper the author discusses the asymptotic properties of solutions to Yang-Mills equations with the gauge group SU(2), for spherically symmetric, regular and static potentials. It is known, that the pure Yang-Mills equations cannot have nontrivial regular solutions which vanish rapidly at space infinity (socalled finite energy solutions). So, if regular solutions exist, they must have non-trivial asymptotic properties. However, if the asymptotic behaviour of the solutions is non-trivial, then the fact must be explicitly taken into account in constructing the proper action (and energy) for the theory. The elucidation of the appropriate surface correction to the Yang-Mills action (and hence the energy-momentum tensor density) is one of the main motivations behind the present study. In this paper the author restricts to the asymptotic behaviour of the static solutions. It is shown that this asymptotic behaviour is such that surface corrections (at space-infinity) are needed in order to obtain a well-defined (classical) theory. This is of relevance in formulating a quantum Yang-Mills theory
Massive and mass-less Yang-Mills and gravitational fields
Veltman, M.J.G.; Dam, H. van
1970-01-01
Massive and mass-less Yang-Mills and gravitational fields are considered. It is found that there is a discrete difference between the zero-mass theories and the very small, but non-zero mass theories. In the case of gravitation, comparison of massive and mass-less theories with experiment, in
Classical and semi-classical solutions of the Yang--Mills theory
International Nuclear Information System (INIS)
Jackiw, R.; Nohl, C.; Rebbi, C.
1977-12-01
This review summarizes what is known at present about classical solutions to Yang-Mills theory both in Euclidean and Minkowski space. The quantal meaning of these solutions is also discussed. Solutions in Euclidean space expose multiple vacua and tunnelling of the quantum theory. Those in Minkowski space-time provide a semi-classical spectrum for a conformal generator
Center-stabilized Yang-Mills Theory:Confinement and Large N Volume Independence
International Nuclear Information System (INIS)
Unsal, Mithat; Yaffe, Laurence G.
2008-01-01
We examine a double trace deformation of SU(N) Yang-Mills theory which, for large N and large volume, is equivalent to unmodified Yang-Mills theory up to O(1/N 2 ) corrections. In contrast to the unmodified theory, large N volume independence is valid in the deformed theory down to arbitrarily small volumes. The double trace deformation prevents the spontaneous breaking of center symmetry which would otherwise disrupt large N volume independence in small volumes. For small values of N, if the theory is formulated on R 3 x S 1 with a sufficiently small compactification size L, then an analytic treatment of the non-perturbative dynamics of the deformed theory is possible. In this regime, we show that the deformed Yang-Mills theory has a mass gap and exhibits linear confinement. Increasing the circumference L or number of colors N decreases the separation of scales on which the analytic treatment relies. However, there are no order parameters which distinguish the small and large radius regimes. Consequently, for small N the deformed theory provides a novel example of a locally four-dimensional pure gauge theory in which one has analytic control over confinement, while for large N it provides a simple fully reduced model for Yang-Mills theory. The construction is easily generalized to QCD and other QCD-like theories
Center-stabilized Yang-Mills theory: Confinement and large N volume independence
International Nuclear Information System (INIS)
Uensal, Mithat; Yaffe, Laurence G.
2008-01-01
We examine a double trace deformation of SU(N) Yang-Mills theory which, for large N and large volume, is equivalent to unmodified Yang-Mills theory up to O(1/N 2 ) corrections. In contrast to the unmodified theory, large N volume independence is valid in the deformed theory down to arbitrarily small volumes. The double trace deformation prevents the spontaneous breaking of center symmetry which would otherwise disrupt large N volume independence in small volumes. For small values of N, if the theory is formulated on R 3 xS 1 with a sufficiently small compactification size L, then an analytic treatment of the nonperturbative dynamics of the deformed theory is possible. In this regime, we show that the deformed Yang-Mills theory has a mass gap and exhibits linear confinement. Increasing the circumference L or number of colors N decreases the separation of scales on which the analytic treatment relies. However, there are no order parameters which distinguish the small and large radius regimes. Consequently, for small N the deformed theory provides a novel example of a locally four-dimensional pure-gauge theory in which one has analytic control over confinement, while for large N it provides a simple fully reduced model for Yang-Mills theory. The construction is easily generalized to QCD and other QCD-like theories.
Scattering amplitudes on the Coulomb branch of N=4 super Yang-Mills
International Nuclear Information System (INIS)
Henn, J.M.
2010-01-01
We discuss planar scattering amplitudes on the Coulomb branch of N=4 super Yang-Mills. The vacuum expectation values on the Coulomb branch can be used to regulate infrared divergences. We argue that this has a number of conceptual as well as practical advantages over dimensional regularisation.
On the quantization and asymptotic freedom of Yang-Mills theory in the temporal gauge
International Nuclear Information System (INIS)
Frenkel, J.
1979-01-01
The relevance of the longitudinal gluons in the derivation of the Feynman rules in the temporal gauge is studied, via the canonical approach. It is then shown that these gluons are also fundamental for the asymptotic freedom of the Yang-Mills theory [pt
Unconstrained N=2 matter, Yang-Mills and supergravity theories in harmonic superspace
International Nuclear Information System (INIS)
Galperin, A.; Kalitzin, S.; Sokatchev, E.
1984-04-01
A new approach to N=2 supersymmetry based on the concept of harmonic superspace is proposed and is used to give an unconstrained superfield geometric description of N=2 super Yang-Mills and supergravity theories as well as of matter N=2 hypermultiplets. The harmonic N=2 superspace has as independent coordinates, in addition to the usual ones, the isospinor harmonics Usub(i)sup(+-) on the sphere SU(2)/U(1). The role of Usub(i)sup(+-) is to relate the SU(2) group realized on the component fields to a U(1) group acting on the relevant superfields. Their introduction makes it possible to SU(2)-covariantize the notion of Grassmann analyticity. Crucial for our construction is the existence of an analytic subspace of the general harmonic N=2 superspace. The hypermultiplet superfields and the true prepotentials (pre-prepotentials) of N=2 super Yang-Mills and supergravity are unconstrained superfunctions over this analytic subspace. The pre-prepotentials have a clear geometric interpretation as gauge connections with respect to the internal SU(2)/U(1)-directions. A radically new feature arises: the number of gauge and auxiliary degrees of freedom becomes infinite while the number of physical degrees of freedom remains finite. Other new results are the massive N=2 Yang-Mills theory and various off-shell self-interactions of hypermultiplets. The propagators for matter and Yang-Mills superfields are given. (author)
Trapped surfaces in monopole-like Cauchy data of Einstein-Yang-Mills-Higgs equations
International Nuclear Information System (INIS)
Malec, E.; Koc, P.
1989-08-01
We choose the nonabelian monopole solution of Bogomolny, Prasad and Sommerfield as a part of Cauchy data for the evolution of Einstein-Yang-Mills-Higgs equations. Momentarily static spherically symmetric data for gravitational fields are obtained numerically via the Lichnerowicz equation. In the case of generic scaling of fields we have found initial data with trapped surfaces. (author). 13 refs
Non-integrability of time-dependent spherically symmetric Yang-Mills equations
International Nuclear Information System (INIS)
Matinyan, S.G.; Prokhorenko, E.V.; Savvidy, G.K.
1986-01-01
The integrability of time-dependent spherically symmetric Yang-Mills equations is studied using the Fermi-Pasta-Ulam method. The phase space of this system is shown to have no quasi-periodic motion specific for integrable systems. In particular, the well-known Wu-Yang static solution is unstable, so its vicinity in phase is the stochasticity region
Scattering amplitudes in N=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity
International Nuclear Information System (INIS)
Chiodaroli, Marco; Günaydin, Murat; Johansson, Henrik; Roiban, Radu
2015-01-01
We expose a double-copy structure in the scattering amplitudes of the generic Jordan family of N=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity theories in four and five dimensions. The Maxwell-Einstein supergravity amplitudes are obtained through the color/kinematics duality as a product of two gauge-theory factors; one originating from pure N=2 super-Yang-Mills theory and the other from the dimensional reduction of a bosonic higher-dimensional pure Yang-Mills theory. We identify a specific symplectic frame in four dimensions for which the on-shell fields and amplitudes from the double-copy construction can be identified with the ones obtained from the supergravity Lagrangian and Feynman-rule computations. The Yang-Mills/Einstein supergravity theories are obtained by gauging a compact subgroup of the isometry group of their Maxwell-Einstein counterparts. For the generic Jordan family this process is identified with the introduction of cubic scalar couplings on the bosonic gauge-theory side, which through the double copy are responsible for the non-abelian vector interactions in the supergravity theory. As a demonstration of the power of this structure, we present explicit computations at tree-level and one loop. The double-copy construction allows us to obtain compact expressions for the supergravity superamplitudes, which are naturally organized as polynomials in the gauge coupling constant.
q-trace for quantum groups and q-deformed Yang-Mills theory
International Nuclear Information System (INIS)
Isaev, A.P.; Popowicz, Z.
1992-01-01
The definitions of orbits and q-trace for the quantum groups are introduced. Then the q-trace is used to construct the invariants for the quantum group orbits and to formulate the q-deformed Yang-Mills theory. The amusing formal relation of the Weinberg type mixing angle with the quantum group deformation parameter is discussed. (orig.)
Spontaneous compactification of space in an Einstein-Yang-Mills-Higgs model
International Nuclear Information System (INIS)
Cremmer, E.; Scherk, J.
1976-01-01
It is shown that classical solutions of an Einstein-Yang-Mills-Higgs system exist such that space-time is the direct product of the Minkowski space by a compact internal space of constant curvature. The symmetry group of the internal space determines the masses in such a way that singlets have the lowest energy, non-singlet states having huge masses. (Auth.)
N = 1 quasi self-duality in the N = 2 Yang-Mills theory
International Nuclear Information System (INIS)
Pavlik, O.V.; Yatsun, V.A.
1998-01-01
The system of first-order equations-quasi self-duality equations-for component fields of the N = 2 SUSY Yang-Mills theory is suggested, which leads to equations of motion and reduces to self-duality equations if scalar fields vanish. The symmetries of quasi self-duality equations are studied
Proof of ultraviolet finiteness for a planar non-supersymmetric Yang-Mills theory
International Nuclear Information System (INIS)
Ananth, Sudarshan; Kovacs, Stefano; Shimada, Hidehiko
2007-01-01
This paper focuses on a three-parameter deformation of N=4 Yang-Mills that breaks all the supersymmetry in the theory. We show that the resulting non-supersymmetric gauge theory is scale invariant, in the planar approximation, by proving that its Green functions are ultraviolet finite to all orders in light-cone perturbation theory
On a relation between massive Yang-Mills theories and dual string models
International Nuclear Information System (INIS)
Mickelsson, J.
1983-01-01
The relations between mass terms in Yang-Mills theories, projective representations of the group of gauge transformations, boundary conditions on vector potentials and Schwinger terms in local charge algebra commutation relations are discussed. The commutation relations (with Schwinger terms) are similar to the current algebra commutation relations of the SU(N) extended dual string model. (orig.)
Non-integrability of time-dependent spherically symmetric Yang-Mills equations
Energy Technology Data Exchange (ETDEWEB)
Matinyan, S G; Prokhorenko, E B; Savvidy, G K
1988-03-07
The integrability of time-dependent spherically symmetric Yang-Mills equations is studied using the Fermi-Pasta-Ulam method. It is shown that the motion of this system is ergodic, while the system itself is non-integrable, i.e. manifests dynamical chaos.
International Nuclear Information System (INIS)
Wang Dianfu
2008-01-01
In terms of the Nambu-Jona-Lasinio mechanism, dynamical breaking of gauge symmetry for the maximally generalized Yang-Mills model is investigated. The gauge symmetry behavior at finite temperature is also investigated and it is shown that the gauge symmetry broken dynamically at zero temperature can be restored at finite temperatures
Equations of motion for the new D=10 N=1 supergravity-Yang-Mills theory
International Nuclear Information System (INIS)
Vashakidze, Sh.I.
1988-01-01
An on-shell superfield formulation of the dual (type IB) ten-dimensional N=1 supergravity coupled to Yang-Mills theory is presented. The coupling is completely specified in superspace by A-tensor supercurrent which, at the same time, takes into account all superstring corrections in the slope parameter expansion. The complete set of equations of motion is derived
Spontaneous transition to a stochastic state in a four-dimensional Yang-Mills quantum theory
International Nuclear Information System (INIS)
Semikhatov, A.M.
1983-01-01
The quantum expectation values in a four-dimensional Yang-Mills theory are represented in each topological sector as expectation values over the diffusion which develops in the ''fourth'' Euclidean time. The Langevin equations of this diffusion are stochastic duality equations in the A 4 = 0 gauge
A generalized Yang-Mills Theory I: general aspects of the classical theory
International Nuclear Information System (INIS)
Galvao, C.A.P.
1987-01-01
A generalized Yang-Mills theory which is the non-Abelian version of the generalized eletrodinamics proposed by Podolsky is analysed both in the Lagrangian an Hamiltonian formulation. A simple class of solutions to the Euler-Lagrange equations is presented and the structure of the Hamiltonian constraints is studied in details. (Author) [pt
Lectures on strings in flat space and plane waves from N = 4 super Yang Mills
International Nuclear Information System (INIS)
Maldacena, J.
2003-01-01
In these lecture notes we explain how the string spectrum in flat space and plane waves arises from the large N limit of U(N) N = 4 super Yang Mills. We reproduce the spectrum by summing a subset of the planar Feynman diagrams. We also describe some other aspects of string propagation on plane wave backgrounds. (author)
Classical mechanics in non-commutative phase space
International Nuclear Information System (INIS)
Wei Gaofeng; Long Chaoyun; Long Zhengwen; Qin Shuijie
2008-01-01
In this paper the laws of motion of classical particles have been investigated in a non-commutative phase space. The corresponding non-commutative relations contain not only spatial non-commutativity but also momentum non-commutativity. First, new Poisson brackets have been defined in non-commutative phase space. They contain corrections due to the non-commutativity of coordinates and momenta. On the basis of this new Poisson brackets, a new modified second law of Newton has been obtained. For two cases, the free particle and the harmonic oscillator, the equations of motion are derived on basis of the modified second law of Newton and the linear transformation (Phys. Rev. D, 2005, 72: 025010). The consistency between both methods is demonstrated. It is shown that a free particle in commutative space is not a free particle with zero-acceleration in the non-commutative phase space, but it remains a free particle with zero-acceleration in non-commutative space if only the coordinates are non-commutative. (authors)
On tea, donuts and non-commutative geometry
Directory of Open Access Journals (Sweden)
Igor V. Nikolaev
2018-03-01
Full Text Available As many will agree, it feels good to complement a cup of tea by a donut or two. This sweet relationship is also a guiding principle of non-commutative geometry known as Serre Theorem. We explain the algebra behind this theorem and prove that elliptic curves are complementary to the so-called non-commutative tori.
Linearization of non-commuting operators in the partition function
International Nuclear Information System (INIS)
Ahmed, M.
1983-06-01
A generalization of the Stratonovich-Hubbard scheme for evaluating the grand canonical partition function is given. The scheme involves linearization of products of non-commuting operators using the functional integral method. The non-commutivity of the operators leads to an additional term which can be absorbed in the single-particle Hamiltonian. (author)
International Nuclear Information System (INIS)
Chau, L.L.
1983-01-01
Integrable properties, i.e., existence of linear systems, infinite number of conservation laws, Reimann-Hilbert transforms, affine Lie algebra of Kac-Moody, and Bianchi-Baecklund transformation, are discussed for the constraint equations of the supersymmetric Yang-Mills fields. For N greater than or equal to 3 these constraint equations give equations of motion of the fields. These equations of motion reduce to the ordinary Yang-Mills equations as the spinor and scalar fields are eliminated. These understandings provide a possible method to solve the full Yang-Mills equations. Connections with other non-linear systems are also discussed. 53 references
Extended Soliton Solutions in an Effective Action for SU(2 Yang-Mills Theory
Directory of Open Access Journals (Sweden)
Nobuyuki Sawado
2006-01-01
Full Text Available The Skyrme-Faddeev-Niemi (SFN model which is an O(3 σ model in three dimensional space up to fourth-order in the first derivative is regarded as a low-energy effective theory of SU(2 Yang-Mills theory. One can show from the Wilsonian renormalization group argument that the effective action of Yang-Mills theory recovers the SFN in the infrared region. However, the theory contains an additional fourth-order term which destabilizes the soliton solution. We apply the perturbative treatment to the second derivative term in order to exclude (or reduce the ill behavior of the original action and show that the SFN model with the second derivative term possesses soliton solutions.
BRST cohomology of N = 2 super-Yang-Mills theory in four dimensions
International Nuclear Information System (INIS)
Tanzini, A.; Ventura, O.S.; Vilar, L.C.Q.; Sorella, S.P.
2000-01-01
The BRST cohomology of the N = 2 supersymmetric Yang-Mills theory in four dimensions is discussed by making use of the twisted version of the N = 2 algebra. By the introduction of a set of suitable constant ghosts associated with the generators of N = 2, the quantization of the model can be done by taking into account both gauge invariance and supersymmetry. In particular, we show how the twisted N = 2 algebra can be used to obtain in a straightforward way the relevant cohomology classes. Moreover, we shall be able to establish a very useful relationship between the local gauge-invariant polynomial tr φ 2 and the complete N = 2 Yang-Mills action. This important relation can be considered as the first step towards a fully algebraic proof of the one-loop exactness of the N = 2 β-function.
Duality transformations in supersymmetric Yang-Mills theories coupled to supergravity
Ceresole, Anna T; Ferrara, Sergio; Van Proeyen, A; Ceresole, A; D'Auria, R; Ferrara, S; Van Proeyen, A
1995-01-01
We consider duality transformations in N=2, d=4 Yang-Mills theory coupled to N=2 supergravity. A symplectic and coordinate covariant framework is established, which allows one to discuss stringy `classical and quantum duality symmetries' (monodromies), incorporating T and S dualities. In particular, we shall be able to study theories (like N=2 heterotic strings) which are formulated in symplectic basis where a `holomorphic prepotential' F does not exist, and yet give general expressions for all relevant physical quantities. Duality transformations and symmetries for the N=1 matter coupled Yang--Mills supergravity system are also exhibited. The implications of duality symmetry on all N>2 extended supergravities are briefly mentioned. We finally give the general form of the central charge and the N=2 semiclassical spectrum of the dyonic BPS saturated states (as it comes by truncation of the N=4 spectrum).
An off-shell superspace reformulation of D = 4, N = 4 super-Yang-Mills theory
Energy Technology Data Exchange (ETDEWEB)
Cederwall, Martin [Division for Theoretical Physics, Department of Physics, Chalmers University of Technology, Gothenburg (Sweden)
2018-01-15
D = 4, N = 4 super-Yang-Mills theory has an off-shell superspace formulation in terms of pure spinor superfields, which is directly inherited from the D = 10 theory. That superspace, in particular the choice of pure spinor variables, is less suitable for dealing with fields that are inherently 4-dimensional, such as the superfields based on the scalars, which are gauge-covariant, and traces of powers of scalars, which are gauge-invariant. We give a reformulation of D = 4, N = 4 super-Yang-Mills theory in N = 4 superspace, using inherently 4-dimensional pure spinors. All local degrees of freedom reside in a superfield based on the physical scalars. The formalism should be suited for calculations of correlators of traces of scalar superfields. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
A model of unified quantum chromodynamics and Yang-Mills gravity
Institute of Scientific and Technical Information of China (English)
HSU Jong-Ping
2012-01-01
Based on a generalized Yang-Mills framework,gravitational and strong interactions can be unified in analogy with the unification in the clectroweak theory.By gauging T(4) × [SU(3)]color in fiat space-time,we have a unified model of chromo-gravity with a new tensor gauge field,which couples universally to all gluons,quarks and anti-quarks.The space-time translational gauge symmetry assures that all wave equations of quarks and gluons reduce to a Hamilton-Jacobi equation with the same ‘effective Riemann metric tensors' in the geometric-optics (or classical) limit.The emergence of effective metric tensors in the classical limit is essential for the unified model to agree with experiments.The unified model suggests that all gravitational,strong and electroweak interactions appear to be dictated by gauge symmetries in the generalized Yang-Mills framework.
BRST quantization of Yang-Mills theory: A purely Hamiltonian approach on Fock space
Öttinger, Hans Christian
2018-04-01
We develop the basic ideas and equations for the BRST quantization of Yang-Mills theories in an explicit Hamiltonian approach, without any reference to the Lagrangian approach at any stage of the development. We present a new representation of ghost fields that combines desirable self-adjointness properties with canonical anticommutation relations for ghost creation and annihilation operators, thus enabling us to characterize the physical states on a well-defined Fock space. The Hamiltonian is constructed by piecing together simple BRST invariant operators to obtain a minimal invariant extension of the free theory. It is verified that the evolution equations implied by the resulting minimal Hamiltonian provide a quantum version of the classical Yang-Mills equations. The modifications and requirements for the inclusion of matter are discussed in detail.
Bäcklund Transformations in 10D SUSY Yang-Mills Theories
Gervais, Jean-Loup
A Bäcklund transformation is derived for the Yang's type (super) equations previously derived (hep-th/9811108) by M. Saveliev and the author, from the ten-dimensional super-Yang-Mills field equations in an on-shell light cone gauge. It is shown to be based upon a particular gauge transformation satisfying nonlinear conditions which ensure that the equations retain the same form. These Yang's type field equations are shown to be precisely such that they automatically provide a solution of these conditions. This Bäcklund transformation is similar to the one proposed by A. Leznov for self-dual Yang-Mills in four dimensions. In the introduction a personal recollection on the birth of supersymmetry is given.
Nonperturbative construction of massive Yang-Mills fields without the Higgs field
Kondo, Kei-Ichi
2013-01-01
In order to understand the so-called decoupling solution for gluon and ghost propagators in QCD, we give a nonperturbative construction of a massive vector field describing a non-Abelian massive spin-one particle, which has the correct physical degrees of freedom and is invariant under a modified Becchi-Rouet-Stora-Tyutin transformation, in a massive Yang-Mills model without the Higgs field, i.e., the Curci-Ferrari model. The resulting non-Abelian massive vector boson field is written by using a nonlinear but local transformation from the original fields in the Curci-Ferrari model. As an application, we write down a local mass term for the Yang-Mills field and a dimension-two condensate, which are exactly invariant under the modified Becchi-Rouet-Stora-Tyutin transformation, Lorentz transformation, and color rotation.
A Note on Supergravity Duals of Noncommutative Yang-Mills Theory
International Nuclear Information System (INIS)
Das, Sumit R.; Ghosh, Banhiman
2000-01-01
A class of supergravity backgrounds have been proposed as dual descriptions of strong coupling large-N noncommutative Yang-Mills (NCYM) theories in 3+1 dimensions. However calculations of correlation functions in supergravity from an evaluation of relevant classical actions appear ambiguous. We propose a resolution of this ambiguity. Assuming that holographic description exists - regardless of whether it is the NCYM theory - we argue that there should be operators in the holographic boundary theory which create normalized states of definite energy and momenta. An operator version of the dual correspondence then provides a calculation of correlators of these operators in terms of bulk Green's functions. We show that in the low energy limit the correlators reproduce expected answers of the ordinary Yang-Mills theory. (author)
Non-linear Yang-Mills instantons from strings are π-stable D-branes
International Nuclear Information System (INIS)
Enger, H.; Luetken, C.A.
2004-01-01
We show that B-type Π-stable D-branes do not in general reduce to the (Gieseker-) stable holomorphic vector bundles used in mathematics to construct moduli spaces. We show that solutions of the almost Hermitian Yang-Mills equations for the non-linear deformations of Yang-Mills instantons that appear in the low-energy geometric limit of strings exist iff they are π-stable, a geometric large volume version of Π-stability. This shows that π-stability is the correct physical stability concept. We speculate that this string-canonical choice of stable objects, which is encoded in and derived from the central charge of the string-algebra, should find applications to algebraic geometry where there is no canonical choice of stable geometrical objects
Amplitude relations in heterotic string theory and Einstein-Yang-Mills
Energy Technology Data Exchange (ETDEWEB)
Schlotterer, Oliver [Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut, Am Mühlenberg 1, D-14476 Potsdam (Germany)
2016-11-11
We present all-multiplicity evidence that the tree-level S-matrix of gluons and gravitons in heterotic string theory can be reduced to color-ordered single-trace amplitudes of the gauge multiplet. Explicit amplitude relations are derived for up to three gravitons, up to two color traces and an arbitrary number of gluons in each case. The results are valid to all orders in the inverse string tension α{sup ′} and generalize to the ten-dimensional superamplitudes which preserve 16 supercharges. Their field-theory limit results in an alternative proof of the recently discovered relations between Einstein-Yang-Mills amplitudes and those of pure Yang-Mills theory. Similarities and differences between the integrands of the Cachazo-He-Yuan formulae and the heterotic string are investigated.
Covariant field equations, gauge fields and conservation laws from Yang-Mills matrix models
International Nuclear Information System (INIS)
Steinacker, Harold
2009-01-01
The effective geometry and the gravitational coupling of nonabelian gauge and scalar fields on generic NC branes in Yang-Mills matrix models is determined. Covariant field equations are derived from the basic matrix equations of motions, known as Yang-Mills algebra. Remarkably, the equations of motion for the Poisson structure and for the nonabelian gauge fields follow from a matrix Noether theorem, and are therefore protected from quantum corrections. This provides a transparent derivation and generalization of the effective action governing the SU(n) gauge fields obtained in [1], including the would-be topological term. In particular, the IKKT matrix model is capable of describing 4-dimensional NC space-times with a general effective metric. Metric deformations of flat Moyal-Weyl space are briefly discussed.
Four-dimensional Yang-Mills theory, gauge invariant mass and fluctuating three-branes
International Nuclear Information System (INIS)
Niemi, Antti J; Slizovskiy, Sergey
2010-01-01
We are interested in a gauge invariant coupling between four-dimensional Yang-Mills field and a three-brane that can fluctuate into higher dimensions. For this we interpret the Yang-Mills theory as a higher dimensional bulk gravity theory with dynamics that is governed by the Einstein action, and with a metric tensor constructed from the gauge field in a manner that displays the original gauge symmetry as an isometry. The brane moves in this higher dimensional spacetime under the influence of its bulk gravity, with dynamics determined by the Nambu action. This introduces the desired interaction between the brane and the gauge field in a way that preserves the original gauge invariance as an isometry of the induced metric. After a prudent change of variables the result can be interpreted as a gauge invariant and massive vector field that propagates in the original spacetime R 4 . The presence of the brane becomes entirely invisible, expect for the mass.
The three-loop form factor in N=4 super Yang-Mills theory
Energy Technology Data Exchange (ETDEWEB)
Gehrmann, Thomas [Universitaet Zuerich (Switzerland); Henn, Johannes [IAS Princeton (United States); Huber, Tobias [Universitaet Siegen (Germany)
2012-07-01
We present the calculation of the Sudakov form factor in N=4 super Yang-Mills theory to the three-loop order. At leading colour, the latter is expressed in terms of planar and non-planar loop integrals. We show that it is possible to choose a representation in which each loop integral has uniform transcendentality in the Riemann {zeta}-function. We comment on the expected exponentiation of the infrared divergences and the values of the three-loop cusp and collinear anomalous dimensions in dimensional regularisation. We also compare the form factor in N=4 super Yang-Mills to the leading transcendentality pieces of the quark and gluon form factor in QCD. Finally, we investigate the ultraviolet properties of the form factor in D>4 dimensions.
Non-Abelian sigma models from Yang-Mills theory compactified on a circle
Ivanova, Tatiana A.; Lechtenfeld, Olaf; Popov, Alexander D.
2018-06-01
We consider SU(N) Yang-Mills theory on R 2 , 1 ×S1, where S1 is a spatial circle. In the infrared limit of a small-circle radius the Yang-Mills action reduces to the action of a sigma model on R 2 , 1 whose target space is a 2 (N - 1)-dimensional torus modulo the Weyl-group action. We argue that there is freedom in the choice of the framing of the gauge bundles, which leads to more general options. In particular, we show that this low-energy limit can give rise to a target space SU (N) ×SU (N) /ZN. The latter is the direct product of SU(N) and its Langlands dual SU (N) /ZN, and it contains the above-mentioned torus as its maximal Abelian subgroup. An analogous result is obtained for any non-Abelian gauge group.
Multiple direct exchange in a Yang-Mills theory at high energy
International Nuclear Information System (INIS)
McCoy, B.M.; Wu, T.T.
1976-01-01
For eighth and higher orders, we obtain the leading high-energy behavior of the sum of all one-layer Feynman diagrams in Yang-Mills theory. These are the contributions from Feynman diagrams where the two incident fast particles exchange directly Yang-Mills bosons that are much less energetic. The incident particles may be either bosons or fermions of arbitrary isospin, and the result is also generalized to include the case of the Higgs scalar. The scattering amplitudes in all these cases are closely related, and all behave as s ln/sub n/ -1 s in the 2n + 2 order. Furthermore, in this leading order for n > or = 2, the exchanged isospins are always 0 and 2, no matter how high the isospins of the incident particles are
Finiteness preserving mass terms in N=4 super Yang-Mills theory
International Nuclear Information System (INIS)
Rajpoot, S.; Taylor, J.G.; Zaimi, M.
1983-01-01
It is shown using light cone gauge techniques that N = 4 super Yang-Mills theory is ultraviolet finite in the presence of a wide range of explicit symmetry breaking mass terms for (a) scalars and fermions (b) scalars alone. These mass terms satisfy sum rules that are part of the more general sum rule: μsub(s=0,) sub(1/2) (-1)sup(2S+1)(2s + 1)msub(S) 2 = 0, in which the mass of vector bosons is set to zero for reasons of gauge invariance. The resulting lagrangians offer the exciting possibility of realising explicit hierarchical descent of N = 4 super Yang-Mills through N = 2 and N = 1 supersymmetries. Tree level spontaneous symmetry breaking from the resulting scalar potentials are briefly discussed. (orig.)
Interacting fields of arbitrary spin and N > 4 supersymmetric self-dual Yang-Mills equations
International Nuclear Information System (INIS)
Devchand, Ch.; Ogievetsky, V.
1996-06-01
We show that the self-dual Yang-Mills equations afford supersymmetrization to systems of equations invariant under global N-extended super-Poincare transformations for arbitrary values of N, without the limitation (N ≤ 4) applicable to standard non-self-dual Yang-Mills theories. These systems of equations provide novel classically consistent interactions for vector supermultiplets containing fields of spin up to N-2/2. The equations of motion of the component fields of spin greater than 1/2 are interacting variants of the first-order Dirac-Fierz equations for zero rest-mass fields of arbitrary spin. The interactions are governed by conserved currents which are constructed by an iterative procedure. In (arbitrarily extended) chiral superspace, the equations of motion for the (arbitrarily large) self-dual supermultiplet are shown to be completely equivalent to the set of algebraic supercurvature defining the self-dual superconnection. (author). 25 refs
Chiral expansion and Macdonald deformation of two-dimensional Yang-Mills theory
Kökényesi, Zoltán; Sinkovics, Annamaria; Szabo, Richard J.
2016-11-01
We derive the analog of the large $N$ Gross-Taylor holomorphic string expansion for the refinement of $q$-deformed $U(N)$ Yang-Mills theory on a compact oriented Riemann surface. The derivation combines Schur-Weyl duality for quantum groups with the Etingof-Kirillov theory of generalized quantum characters which are related to Macdonald polynomials. In the unrefined limit we reproduce the chiral expansion of $q$-deformed Yang-Mills theory derived by de Haro, Ramgoolam and Torrielli. In the classical limit $q=1$, the expansion defines a new $\\beta$-deformation of Hurwitz theory wherein the refined partition function is a generating function for certain parameterized Euler characters, which reduce in the unrefined limit $\\beta=1$ to the orbifold Euler characteristics of Hurwitz spaces of holomorphic maps. We discuss the geometrical meaning of our expansions in relation to quantum spectral curves and $\\beta$-ensembles of matrix models arising in refined topological string theory.
A model of unified quantum chromodynamics and Yang-Mills gravity
International Nuclear Information System (INIS)
HSU Jongping
2012-01-01
Based on a generalized Yang-Mills framework, gravitational and strong interactions can be unified in analogy with the unification in the electroweak theory. By gauging T(4) × [SU(3)] color in flat space-time, we have a unified model of chromo-gravity with a new tensor gauge field, which couples universally to all gluons, quarks and anti-quarks. The space-time translational gauge symmetry assures that all wave equations of quarks and gluons reduce to a Hamilton-Jacobi equation with the same 'effective Riemann metric tensors’ in the geometric-optics (or classical) limit. The emergence of effective metric tensors in the classical limit is essential for the unified model to agree with experiments. The unified model suggests that all gravitational, strong and electroweak interactions appear to be dictated by gauge symmetries in the generalized Yang-Mills framework. (author)
Some Comments on the String Singularity of the Yang-Mills-Higgs Theory
International Nuclear Information System (INIS)
Lim, Kok-Geng; Teh, Rosy
2010-01-01
We are going to make use of the regulated polar angle which had been introduced by Boulware et al.. to show that in the SU(2) Yang-Mills-Higgs theory when the magnetic monopole is carried by the gauge field, the Higgs field does not carry the monopole and vice versa. In the Yang-Mills-Higgs theory, our solution shows that when the parameter ε ≠ 0, the monopole is carried by the gauge field and there is a string singularity in the gauge field. When the parameter ε → 0, the monopole is transferred from the gauge field to the Higgs field and the string singularity disappeared. The solution is only singular at the origin, that is at r = 0 as it becomes the Wu-Yang monopole.
The thermodynamics of quantum Yang-Mills theory theory and applications
Hofmann, Ralf
2016-01-01
This latest edition enhances the material of the first edition with a derivation of the value of the action for each of the Harrington-Shepard calorons/anticalorons that are relevant for the emergence of the thermal ground state. Also included are discussions of the caloron center versus its periphery, the role of the thermal ground state in U(1) wave propagation, photonic particle-wave duality, and calculational intricacies and book-keeping related to one-loop scattering of massless modes in the deconfining phase of an SU(2) Yang-Mills theory. Moreover, a derivation of the temperature-redshift relation of the CMB in deconfining SU(2) Yang-Mills thermodynamics and its application to explaining an apparent early re-ionization of the Universe are given. Finally, a mechanism of mass generation for cosmic neutrinos is proposed.
Towards N = 2 SUSY homogeneous quantum cosmology; Einstein-Yang-Mills systems
International Nuclear Information System (INIS)
Donets, E.E.; Tentyukov, M.N.; Tsulaya, M.M.
1998-01-01
The application of N = 2 supersymmetric Quantum Mechanics for the quantization of homogeneous systems coupled with gravity is discussed. Starting with the superfield formulation of N = 2 SUSY sigma-model, Hermitian self-adjoint expressions for quantum Hamiltonians and Lagrangians for any signature of a sigma-model metric are obtained. This approach is then applied to coupled SU (2) Einstein-Yang-Mills (EYM) systems in axially-symmetric Bianchi - I,II,VIII, IX, Kantowski-Sachs and closed Friedmann-Robertson-Walker cosmological models. It is shown that all these models admit the embedding into N = 2 SUSY sigma-model with the explicit expressions for superpotentials, being direct sums of gravitational and Yang-Mills (YM) parts. In addition, YM parts of superpotentials exactly coincide with the corresponding Chern-Simons terms. The spontaneous SUSY breaking, caused by YM instantons in EYM systems is discussed in a number of examples
Green functions in a super self-dual Yang-Mills background
International Nuclear Information System (INIS)
McArthur, I.N.
1984-01-01
In euclidean supersymmetric theories of chiral superfields and vector superfields coupled to a super-self-dual Yang-Mills background, we define Green functions for the Laplace-type differential operators which are obtained from the quadratic parot the action. These Green functions are expressed in terms of the Green function on the space of right chiral superfields, and an explicit expression for the right chiral Green function in the fundamental representation of an SU(n) gauge group is presented using the supersymmetric version of the ADHM formalism. The superfield kernels associated with the Laplace-type operators are used to obtain the one-loop quantum corrections to the super-self-dual Yang-Mills action, and also to provide a superfield version of the super-index theorems for the components of chiral superfields in a self-dual background. (orig.)
International Nuclear Information System (INIS)
Daniel, M.
1980-01-01
We give explicit expressions for the Seeley coefficients of the fluctuation operator and the operator that appears in the Faddeev-Popov determinant, which arise in the calculation of quantum fluctuations around Yang-Mills multi-instantons. (orig.)
On electromagnetic duality in locally supersymmetric N = 2 Yang-Mills theory
Ceresole, Anna; Ferrara, S.; Van Proeyen, Antoine; Ceresole, A; D'Auria, R; Ferrara, S; Van Proeyen, A
1995-01-01
We consider duality transformations in N=2 Yang--Mills theory coupled to N=2 supergravity, in a manifestly symplectic and coordinate covariant setting. We give the essential of the geometrical framework which allows one to discuss stringy classical and quantum monodromies, the form of the spectrum of BPS saturated states and the Picard--Fuchs identities encoded in the special geometry of N=2 supergravity theories.
Some New Integrable Equations from the Self-Dual Yang-Mills Equations
International Nuclear Information System (INIS)
Ivanova, T.A.; Popov, A.D.
1994-01-01
Using the symmetry reductions of the self-dual Yang-Mills (SDYM) equations in (2+2) dimensions, we introduce new integrable equations which are 'deformations' of the chiral model in (2+1) dimensions, generalized nonlinear Schroedinger, Korteweg-de Vries, Toda lattice, Garnier, Euler-Arnold, generalized Calogero-Moser and Euler-Calogero-Moser equations. The Lax pairs for all of these equations are derived by the symmetry reductions of the Lax pair for the SDYM equations. 34 refs
On generating functional of vertex functions in the Yang-Mills theories
International Nuclear Information System (INIS)
Lavrov, P.M.; Tyutin, I.V.
1981-01-01
It is shown that the generating functional GITA(kappa, PHI) in the Yang-Mills gauge theories for linear gauge conditions may be written as GITA(kappa, PHI)=GITA tilde(phi(kappa, PHI))-1/2t 2 , where t is a gauge function and GITA tilde(PHI) is a universal functional independent of kappa, parameters of the gauge condition [ru
The quantum dual string wave functional in Yang-Mills theories
International Nuclear Information System (INIS)
Gervais, J.-L.; Neveu, A.
1979-01-01
From any solution of the classical Yang-Mills equations, a string wave functional based on the Wilson loop integral is defined. Its precise definition is given by replacing the string by a finite set of N points, and taking the limit N → infinity. It is shown that this functional satisfies the Schroedinger equation of the relativistic dual string to leading order in N. The relevance of this object to the quantum problem is speculated. (Auth.)
5D maximally supersymmetric Yang-Mills in 4D superspace. Applications
International Nuclear Information System (INIS)
McGarrie, Moritz
2013-03-01
We reformulate 5D maximally supersymmetric Yang-Mills in 4D Superspace, for a manifold with boundaries. We emphasise certain features and conventions necessary to allow for supersymmetric model building applications. Finally we apply the holographic interpretation of a slice of AdS and show how to generate Dirac soft masses between external source fields, as well as kinetic mixing, as a boundary effective action.
A novel supersymmetry in 2-dimensional Yang-Mills theory on Riemann surfaces
International Nuclear Information System (INIS)
Soda, Jiro
1991-02-01
We find a novel supersymmetry in 2-dimensional Maxwell and Yang-Mills theories. Using this supersymmetry, it is shown that the 2-dimensional Euclidean pure gauge theory on a closed Riemann surface Σ can be reduced to a topological field theory which is the 3-dimensional Chern-Simons gauge theory in the special space-time topology Σ x R. Related problems are also discussed. (author)
Integrality of the monopole number in SU(2) Yang-Mills-Higgs theory on R3
International Nuclear Information System (INIS)
Groisser, D.
1984-01-01
We prove that in classical SU(2) Yang-Mills-Higgs theories on R 3 with a Higgs field in the adjoint representation, an integer-valued monopole number (magnetic charge) is canonically defined for any finite-action L 2 sub(1,loc) configuration. In particular the result is true for smooth configurations. The monopole number is shown to decompose the configuration space into path components. (orig.)
Wess-Zumino and super Yang-Mills theories in D=4 integral superspace
Castellani, L.; Catenacci, R.; Grassi, P. A.
2018-05-01
We reconstruct the action of N = 1 , D = 4 Wess-Zumino and N = 1 , 2 , D = 4 super-Yang-Mills theories, using integral top forms on the supermanifold M^{(.4|4)} . Choosing different Picture Changing Operators, we show the equivalence of their rheonomic and superspace actions. The corresponding supergeometry and integration theory are discussed in detail. This formalism is an efficient tool for building supersymmetric models in a geometrical framework.
Higher conservation laws for ten-dimensional supersymmetric Yang-Mills theories
International Nuclear Information System (INIS)
Abdalla, E.; Forger, M.; Freiburg Univ.; Jacques, M.
1988-01-01
It is shown that ten-dimensional supersymmetric Yang-Mills theories are integrable systems, in the (weak) sense of admitting a (superspace) Lax representation for their equations of motion. This is achieved by means of an explicit proof that the equations of motion are not only a consequence of but in fact fully equivalent to the superspace constraint F αβ =0. Moreover, a procedure for deriving infinite series of non-local conservation laws is outlined. (orig.)
Low energy dynamics of monopoles in supersymmetric Yang-Mills theories with hypermultiplets
International Nuclear Information System (INIS)
Kim, Chanju
2006-01-01
We derive the low energy dynamics of monopoles and dyons in N = 2 supersymmetric Yang-Mills theories with hypermultiplets in arbitrary representations by utilizing a collective coordinate expansion. We consider the most general case that Higgs fields both in the vector multiplet and in the hypermultiplets have nonzero vacuum expectation values. The resulting theory is a supersymmetric quantum mechanics which has been obtained by a nontrivial dimensional reduction of two-dimensional (4,0) supersymmetric sigma models with potentials
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.)
Simulations of N = 2 super Yang-Mills theory in two dimensions
International Nuclear Information System (INIS)
Catterall, Simon
2006-01-01
We present results from lattice simulations of N = 2 super Yang-Mills theory in two dimensions. The lattice formulation we use was developed and retains both gauge invariance and an exact (twisted) supersymmetry for any lattice spacing. Results for both U(2) and SU(2) gauge groups are given. We focus on supersymmetric Ward identities, the phase of the Pfaffian resulting from integration over the Grassmann fields and the nature of the quantum moduli space
Diffeomorphism-type symmetries of the self-dual Yang-Mills equations
International Nuclear Information System (INIS)
Ivanova, T.A.
1998-01-01
The infinite-dimensional algebra of diffeomorphism-type symmetries of the self-dual Yang-Mills equations is described as the algebra of 0-cochains with values in a sheaf of germs of holomorphic sections of the (1,0) tangent bundle over the twistor space. It is shown that the extended conformal symmetries are obtained as particular cases of the aforementioned algebra
5D maximally supersymmetric Yang-Mills in 4D superspace. Applications
Energy Technology Data Exchange (ETDEWEB)
McGarrie, Moritz
2013-03-15
We reformulate 5D maximally supersymmetric Yang-Mills in 4D Superspace, for a manifold with boundaries. We emphasise certain features and conventions necessary to allow for supersymmetric model building applications. Finally we apply the holographic interpretation of a slice of AdS and show how to generate Dirac soft masses between external source fields, as well as kinetic mixing, as a boundary effective action.
Analytic supersymmetric regularization for the pure N=1 super-Yang-Mills model
International Nuclear Information System (INIS)
Abdalla, E.; Jasinschi, R.S.
1987-01-01
We calculate for the pure N=1 super-Yang-Mills model the quantum correction to the background field strength up to two loops. In using background field method, analytic regularization and Seeley coefficient expansion we show how these corrections arise. Our method differs from the dimensional regularization via dimensional reduction scheme in various respects, in particular to the origin of the background field strength as appearing in the divergent expressions. (orig.)
Onset of chaos in the classical SU(2) Yang-Mills theory
Energy Technology Data Exchange (ETDEWEB)
Furusawa, Toyoaki
1988-12-28
Chaotic behaviors of color electric and magnetic fields are numerically demonstrated in the classical SU(2) Yang-Mills system in the case that the field configuration depends only on one spatial coordinate and time. We show that the homogeneous color fields evolve into the disordered one as time passes. Power spectra of the color fields are investigated and the maximum Lyapunov exponent is evaluated.
The quantum cosmology of Einstein-Yang-Mills theory in Eight-dimensions
International Nuclear Information System (INIS)
Su Bing; Li Xinzhou
1991-01-01
The quantum cosmology of Einstein-Yang-Mills has been studied. The Hartle-Hawking's proposal for the boundary conditions of the universe is extended to Eight-dimensional Einstein-Yong-Mills theory. A miniuperspace wave function is calculated in the classical limit corresponding to a superposition of classical solutions in which four of the dimensions remain small while the other four behave like an inflationary universe
Monopole dynamics of yang-mills theory without gauge-fixing
International Nuclear Information System (INIS)
Jia Duojie; Li Xiguo
2003-01-01
A new off-shell decomposition of SU(2) gauge field without any gauge fixing is proposed. This decomposition yields, for an appropriate gauge-fixing, a Skyme-Faddeev-like Wilsonian action and confirms the presence of high-order derivatives of a color-unit-vector at the classical level. The 't Hooft's conjecture that 'monopole' dynamics of infrared Yang-Mills theory is projection independent is also independently demonstrated
Black Hole Solution of Einstein-Born-Infeld-Yang-Mills Theory
Directory of Open Access Journals (Sweden)
Kun Meng
2017-01-01
Full Text Available A new four-dimensional black hole solution of Einstein-Born-Infeld-Yang-Mills theory is constructed; several degenerated forms of the black hole solution are presented. The related thermodynamical quantities are calculated, with which the first law of thermodynamics is checked to be satisfied. Identifying the cosmological constant as pressure of the system, the phase transition behaviors of the black hole in the extended phase space are studied.
Correlation functions in topological Yang-Mills theory with two fermionic charges
International Nuclear Information System (INIS)
Marculescu, S.
1997-01-01
The solution of the Donaldson cohomology problem for the topological Yang-Mills theory with two fermionic symmetries needs besides the gauge field and its descendants additional fields, hereafter called ascendants of the gauge field. It is shown that the dependence of the ascendants disappears in the all the correlation functions. This property allows one for the usual interpretation of the Donaldson invariants as cocycles of the instanton moduli space. (orig.)
N=4 SUSY Yang-Mills: Three loops made simple(r)
Energy Technology Data Exchange (ETDEWEB)
Dokshitzer, Yu.L. [LPTHE, Universities of Paris-VI and VII and CNRS, Paris (France); Marchesini, G. [University of Milano-Bicocca and INFN Sezione di Milano-Bicocca, Milan (Italy)]. E-mail: marchesini@mib.infn.it
2007-03-15
We construct universal parton evolution equation that produces space- and time-like anomalous dimensions for the maximally super-symmetric N=4 Yang-Mills field theory model, and find that its kernel satisfies the Gribov-Lipatov reciprocity relation in three loops. Given a simple structure of the evolution kernel, this should help to generate the major part of multi-loop contributions to QCD anomalous dimensions, due to classical soft gluon radiation effects.
On possibility of the conformal infrared asymptotics in nonabelian Yang-Mills theories
International Nuclear Information System (INIS)
Vasil'ev, A.N.; Perekalin, M.M.; Pis'mak, Yu.M.
1983-01-01
A possibility of the conformal-invariant infrared asymptotics in nonabelian Yang-Mills theories is discussed. In the framework of the conformal bootstrap method it is shown that the hypothesis about the exact conformal invariance contradicts the transversality of the polarization operator i.e. the Ward identities. However, it is still possible to use the conformal theory as an approximate solution to the bootstrap equations
Algebraic renormalization of Yang-Mills theory with background field method
International Nuclear Information System (INIS)
Grassi, P.A.
1996-01-01
In this paper the renormalizability of Yang-Mills theory in the background gauge fixing is studied. By means of Ward identities of background gauge invariance and Slavnov-Taylor identities, in a regularization-independent way, the stability of the model under radiative corrections is proved and its renormalizability is verified. In particular, it is shown that the splitting between background and quantum field is stable under radiative corrections and this splitting does not introduce any new anomalies. (orig.)
Non-Douglas-Kazakov phase transition of two-dimensional generalized Yang-Mills theories
International Nuclear Information System (INIS)
Khorrami, M.; Alimohammadi, M.
2007-01-01
In two-dimensional Yang-Mills and generalized Yang-Mills theories for large gauge groups, there is a dominant representation determining the thermodynamic limit of the system. This representation is characterized by a density, the value of which should everywhere be between zero and one. This density itself is determined by means of a saddle-point analysis. For some values of the parameter space, this density exceeds one in some places. So one should modify it to obtain an acceptable density. This leads to the well-known Douglas-Kazakov phase transition. In generalized Yang-Mills theories, there are also regions in the parameter space where somewhere this density becomes negative. Here too, one should modify the density so that it remains nonnegative. This leads to another phase transition, different from the Douglas-Kazakov one. Here the general structure of this phase transition is studied, and it is shown that the order of this transition is typically three. Using carefully-chosen parameters, however, it is possible to construct models with the order of the phase transition not equal to three. A class of these non-typical models is also studied. (orig.)
Sigma-model formulation of the Yang-Mills theory on four-dimensional hypersphere
International Nuclear Information System (INIS)
Ivanov, E.A.; Krivonos, S.O.
1983-01-01
The bilocal sigma-model representation is constructed for Yang-Mills theory in the simplest conformally flat hyperspherical spases SO(1, 4)/SO(1, 3), SO(2, 3)/SO(1, 3) and SO(5)/SO(4) (for the Euclidean Yang-Mills). Like in the case of Minkowski and Euclidean spaces, Yang-Mills potential is defined as bsub(μ)(x)=dsub(μ)sup(y)b(x, y)sub(y=0), b(x, y) being a bilocal Goldstone field which takes values in the gauge group algebra and is subjected to certain covariant constraints. The minimal version of these constraints results in the ''string'' representation for b(x, y) through the P exponential of bsub(μ)(x) along the fixed paths coinciding with geodesics. Due to the presence of closed geodesics, the contour functional naturally appear in the theory, with contours being the circles with the hypersphere radius. The sigma-model representation is shown to be Weyl-covariant: its formulations in different conformally flat spaces are related by transformations of ysup(rho). The geometric meaning ysup(rho) and minimal constraints is explained, and the conformal group transofrmation of ysup(rho) is found
Non-Abelian Yang-Mills analogue of classical electromagnetic duality
International Nuclear Information System (INIS)
Chan, Hong-Mo; Faridani, J.; Tsun, T.S.
1995-01-01
The classic question of non-Abelian Yang-Mills analogue to electromagnetic duality is examined here in a minimalist fashion at the strictly four-dimensional, classical field, and point charge level. A generalization of the Abelian Hodge star duality is found which, though not yet known to give dual symmetry, reproduces analogues to many dual properties of the Abelian theory. For example, there is a dual potential, but it is a two-indexed tensor T μν of the Freedman-Townsend-type. Though not itself functioning as such, T μν gives rise to a dual parallel transport A μ for the phase of the wave function of the color magnetic charge, this last being a monopole of the Yang-Mills field but a source of the dual field. The standard color (electric) charge itself is found to be a monpole of A μ . At the same time, the gauge symmetry is found doubled from say SU(N) to SU(N)xSU(N). A novel feature is that all equations of motion, including the standard Yang-Mills and Wong equations, are here derived from a ''universal'' principle, namely, the Wu-Yang criterion for monpoles, where interactions arise purely as a consequence of the topological definition of the monopole charge. The technique used is the loop space formulation of Polyakov
1992 Trieste lectures on topological gauge theory and Yang-Mills theory
International Nuclear Information System (INIS)
Thompson, G.
1993-05-01
In these lecture notes we explain a connection between Yang-Mills theory on arbitrary Riemann surfaces and two types of topological field theory, the so called BF and cohomological theories. The quantum Yang-Mills theory is solved exactly using path integral techniques. Explicit expressions, in terms of group representation theory, are obtained for the partition function and various correlation functions. In a particular limit the Yang-Mills theory devolves to the topological models and the previously determined correlation functions give topological information about the moduli spaces of flat connections. In particular, the partition function yields the volume of the moduli space for which an explicit expression is derived. These notes are self contained, with a basic introduction to the various ideas underlying the topological field theories. This includes some relatively new work on handling problems that arise in the presence of reducible connections, which in turn, forms the bridge between the various models under consideration. These notes are identical to those made available to participants of the 1992 summer school in Trieste, except for one or two additions added circa January 1993. (author). 52 refs, 6 figs
Supercurrent and the Adler-Bardeen theorem in coupled supersymmetric Yang-Mills theories
International Nuclear Information System (INIS)
Ensign, P.W.
1987-01-01
By the Adler-Bardeen theorem, only one-loop Feynman diagrams contribute to the anomalous divergences of quantum axial currents. The anomalous nature of scale transformations is manifested by an anomalous trace of the energy-momentum tensor, T/sup μ//sub μ/. Renormalization group arguments show that the quantum T/sup μ//sub μ/ must be proportional to the β-function. Since the β-function receives contributions at all loop levels, the Adler-Bardeen theorem appears to conflict with supersymmetry. Recently Grisaru, Milewski and Zanon constructed a supersymmetric axial current for pure supersymmetric Yang-Mills theory which satisfies the Adler-Bardeen theorem to two-loops. They used supersymmetric background field theory and regularization by dimensional reduction to maintain manifest supersymmetry and gauge invariance. In this thesis, their construction is extended to supersymmetric Yang-Mills theory coupled to chiral matter fields. The Adler-Bardeen theorem is then proven to all orders in perturbation theory for both the pure and coupled theories. The extension to coupled supersymmetric Yang-Mills supports the general validity of these techniques, and adds considerable insight into the structure of the anomalies. The all orders proof demonstrates that there is no conflict between supersymmetry and the Adler-Bardeen theorem
Ward identities and mass spectrum of N=1 Super Yang-Mills theory on the lattice
International Nuclear Information System (INIS)
Kirchner, R.
2000-11-01
We study the lattice regularization of N=1 Super Yang-Mills theory. Projecting operators for the low-lying spectrum are discussed. We also consider a ''baryonic'' state consisting of three gluinos, and develop a numerical strategy to determine its mass in a Monte Carlo simulation. We present numerical results on the low-lying spectrum of SU(2) N=1 Super Yang-Mills theory with light dynamical gluinos. The lattice regularization of N=1 Super Yang-Mills theory breaks supersymmetry at any finite lattice spacing. We derive the form of the corresponding SUSY Ward identity and carry out renormalization. The ratios of the renormalization coefficients Z T /Z S and M R /Z S are determined non-perturbatively in a numerical simulation. The form of the renormalized SUSY Ward identity is confirmed numerically. We discuss how the SUSY Ward identity can be used to define a supersymmetric continuum limit, and how its approach can be monitored in numerical simulations. (orig.)
Chern-Simons matrix models, two-dimensional Yang-Mills theory and the Sutherland model
International Nuclear Information System (INIS)
Szabo, Richard J; Tierz, Miguel
2010-01-01
We derive some new relationships between matrix models of Chern-Simons gauge theory and of two-dimensional Yang-Mills theory. We show that q-integration of the Stieltjes-Wigert matrix model is the discrete matrix model that describes q-deformed Yang-Mills theory on S 2 . We demonstrate that the semiclassical limit of the Chern-Simons matrix model is equivalent to the Gross-Witten model in the weak-coupling phase. We study the strong-coupling limit of the unitary Chern-Simons matrix model and show that it too induces the Gross-Witten model, but as a first-order deformation of Dyson's circular ensemble. We show that the Sutherland model is intimately related to Chern-Simons gauge theory on S 3 , and hence to q-deformed Yang-Mills theory on S 2 . In particular, the ground-state wavefunction of the Sutherland model in its classical equilibrium configuration describes the Chern-Simons free energy. The correspondence is extended to Wilson line observables and to arbitrary simply laced gauge groups.
Quantum metamorphosis of conformal symmetry in N=4 super Yang-Mills theory
International Nuclear Information System (INIS)
Kuzenko, S.M.; McArthur, I.N.
2002-01-01
In gauge theories, not all rigid symmetries of the classical action can be maintained manifestly in the quantization procedure, even in the absence of anomalies. If this occurs for an anomaly-free symmetry, the effective action is invariant under a transformation that differs from its classical counterpart by quantum corrections. As shown by Fradkin and Palchik years ago, such a phenomenon occurs for conformal symmetry in quantum Yang-Mills theories with vanishing beta function, such as the N=4 super Yang-Mills theory. More recently, Jevicki et al. demonstrated that the quantum metamorphosis of conformal symmetry sheds light on the nature of the AdS/CFT correspondence. In this paper, we derive the conformal Ward identity for the bosonic sector of the N=4 super Yang-Mills theory using the background field method. We then compute the leading quantum modification of the conformal transformation for a specific Abelian background which is of interest in the context of the AdS/CFT correspondence. In the case of scalar fields, our final result agrees with that of Jevicki et al. The resulting vector and scalar transformations coincide with those which are characteristic of a D3-brane embedded in AdS 5 xS 5 . (author)
International Nuclear Information System (INIS)
Wang, L.C.
1980-01-01
Baecklund Transformations (BT) and the derivation of local conservation laws are first reviewed in the classic case of the Sine-Gordon equation. The BT, conservation laws (local and nonlocal), and the inverse-scattering formulation are discussed for the chiral and the self-dual Yang-Mills fields. Their possible applications to the loop formulation for the Yang-Mills fields are mentioned. 55 references, 1 figure
Continuum strong-coupling expansion of Yang-Mills theory: quark confinement and infra-red slavery
International Nuclear Information System (INIS)
Mansfield, P.
1994-01-01
We solve Schroedinger's equation for the ground-state of four-dimensional Yang-Mills theory as an expansion in inverse powers of the coupling. Expectation values computed with the leading-order approximation are reduced to a calculation in two-dimensional Yang-Mills theory which is known to confine. Consequently the Wilson loop in the four-dimensional theory obeys an area law to leading order and the coupling becomes infinite as the mass scale goes to zero. (orig.)
Geometry of time-spaces non-commutative algebraic geometry, applied to quantum theory
Landau, Olav Arnfinn
2011-01-01
This is a monograph about non-commutative algebraic geometry, and its application to physics. The main mathematical inputs are the non-commutative deformation theory, moduli theory of representations of associative algebras, a new non-commutative theory o
On the development of non-commutative translation-invariant quantum gauge field models
International Nuclear Information System (INIS)
Sedmik, R.I.P.
2009-01-01
models Attaching at these considerations, the present work aims to investigate and enhance a rather new ansatz, originally proposed by Gurau et. al.. This model combines all positive features of recent approaches, as it is translation invariant and renormalizable. Starting at a simple scalar implementation the core achievement, being a damping mechanism which implements the demanded symmetry of scales, and thereby restricts the occurrence of uV/IR mixing, is analyzed. In a further step the theory is generalized to gauge models of the Yang-Mills type, where new problems appear, from which the need for additional modifications arises. A detailed investigation of the obstacles hindering a fully viable proof of renormalization is presented, and possible ways to overcome the current problems are identified. In a final step the insights, which have been gained, are utilized to construct a promising new gauge model - the BRSW model. Renormalizability is demonstrated by explicit computations at the one loop level. A general proof, however, will require a substantial effort in order to establish the required mathematical methods in the non-commutative regime prior to their application - a topic which unfortunately cannot be addressed within the framework of this thesis. (author) [de
Non-Commutative Mechanics in Mathematical & in Condensed Matter Physics
Directory of Open Access Journals (Sweden)
Peter A. Horváthy
2006-12-01
Full Text Available Non-commutative structures were introduced, independently and around the same time, in mathematical and in condensed matter physics (see Table 1. Souriau's construction applied to the two-parameter central extension of the planar Galilei group leads to the ''exotic'' particle, which has non-commuting position coordinates. A Berry-phase argument applied to the Bloch electron yields in turn a semiclassical model that has been used to explain the anomalous/spin/optical Hall effects. The non-commutative parameter is momentum-dependent in this case, and can take the form of a monopole in momentum space.
Computational commutative and non-commutative algebraic geometry
Cojocaru, S; Ufnarovski, V
2005-01-01
This publication gives a good insight in the interplay between commutative and non-commutative algebraic geometry. The theoretical and computational aspects are the central theme in this study. The topic is looked at from different perspectives in over 20 lecture reports. It emphasizes the current trends in commutative and non-commutative algebraic geometry and algebra. The contributors to this publication present the most recent and state-of-the-art progresses which reflect the topic discussed in this publication. Both researchers and graduate students will find this book a good source of information on commutative and non-commutative algebraic geometry.
Minimal length uncertainty and generalized non-commutative geometry
International Nuclear Information System (INIS)
Farmany, A.; Abbasi, S.; Darvishi, M.T.; Khani, F.; Naghipour, A.
2009-01-01
A generalized formulation of non-commutative geometry for the Bargmann-Fock space of quantum field theory is presented. The analysis is related to the symmetry of the simplistic space and a minimal length uncertainty.
Vectors and covectors in non-commutative setting
Parfionov, G. N.; Romashev, Yu. A.; Zapatrine, R. R.
1995-01-01
Following the guidelines of classical differential geometry the `building material' for the tensor calculus in non-commutative geometry is suggested. The algebraic account of moduli of vectors and covectors is carried out.
Non-commutative geometry on quantum phase-space
International Nuclear Information System (INIS)
Reuter, M.
1995-06-01
A non-commutative analogue of the classical differential forms is constructed on the phase-space of an arbitrary quantum system. The non-commutative forms are universal and are related to the quantum mechanical dynamics in the same way as the classical forms are related to classical dynamics. They are constructed by applying the Weyl-Wigner symbol map to the differential envelope of the linear operators on the quantum mechanical Hilbert space. This leads to a representation of the non-commutative forms considered by A. Connes in terms of multiscalar functions on the classical phase-space. In an appropriate coincidence limit they define a quantum deformation of the classical tensor fields and both commutative and non-commutative forms can be studied in a unified framework. We interprete the quantum differential forms in physical terms and comment on possible applications. (orig.)
Differential Galois obstructions for non-commutative integrability
Energy Technology Data Exchange (ETDEWEB)
Maciejewski, Andrzej J. [Institute of Astronomy, University of Zielona Gora, Podgorna 50, PL-65-246 Zielona Gora (Poland)], E-mail: maciejka@astro.ia.uz.zgora.pl; Przybylska, Maria [Torun Centre for Astronomy, N. Copernicus University, Gagarina 11, PL-87-100 Torun (Poland)], E-mail: mprzyb@astri.uni.torun.pl
2008-08-11
We show that if a holomorphic Hamiltonian system is holomorphically integrable in the non-commutative sense in a neighbourhood of a non-equilibrium phase curve which is located at a regular level of the first integrals, then the identity component of the differential Galois group of the variational equations along the phase curve is Abelian. Thus necessary conditions for the commutative and non-commutative integrability given by the differential Galois approach are the same.
Trace Dynamics and a non-commutative special relativity
International Nuclear Information System (INIS)
Lochan, Kinjalk; Singh, T.P.
2011-01-01
Trace Dynamics is a classical dynamical theory of non-commuting matrices in which cyclic permutation inside a trace is used to define the derivative with respect to an operator. We use the methods of Trace Dynamics to construct a non-commutative special relativity. We define a line-element using the Trace over space-time coordinates which are assumed to be operators. The line-element is shown to be invariant under standard Lorentz transformations, and is used to construct a non-commutative relativistic dynamics. The eventual motivation for constructing such a non-commutative relativity is to relate the statistical thermodynamics of this classical theory to quantum mechanics. -- Highlights: → Classical time is external to quantum mechanics. → This implies need for a formulation of quantum theory without classical time. → A starting point could be a non-commutative special relativity. → Such a relativity is developed here using the theory of Trace Dynamics. → A line-element is defined using the Trace over non-commuting space-time operators.
Non-commutative representation for quantum systems on Lie groups
Energy Technology Data Exchange (ETDEWEB)
Raasakka, Matti Tapio
2014-01-27
The topic of this thesis is a new representation for quantum systems on weakly exponential Lie groups in terms of a non-commutative algebra of functions, the associated non-commutative harmonic analysis, and some of its applications to specific physical systems. In the first part of the thesis, after a review of the necessary mathematical background, we introduce a {sup *}-algebra that is interpreted as the quantization of the canonical Poisson structure of the cotangent bundle over a Lie group. From the physics point of view, this represents the algebra of quantum observables of a physical system, whose configuration space is a Lie group. We then show that this quantum algebra can be represented either as operators acting on functions on the group, the usual group representation, or (under suitable conditions) as elements of a completion of the universal enveloping algebra of the Lie group, the algebra representation. We further apply the methods of deformation quantization to obtain a representation of the same algebra in terms of a non-commutative algebra of functions on a Euclidean space, which we call the non-commutative representation of the original quantum algebra. The non-commutative space that arises from the construction may be interpreted as the quantum momentum space of the physical system. We derive the transform between the group representation and the non-commutative representation that generalizes in a natural way the usual Fourier transform, and discuss key properties of this new non-commutative harmonic analysis. Finally, we exhibit the explicit forms of the non-commutative Fourier transform for three elementary Lie groups: R{sup d}, U(1) and SU(2). In the second part of the thesis, we consider application of the non-commutative representation and harmonic analysis to physics. First, we apply the formalism to quantum mechanics of a point particle on a Lie group. We define the dual non-commutative momentum representation, and derive the phase
Non-commutative representation for quantum systems on Lie groups
International Nuclear Information System (INIS)
Raasakka, Matti Tapio
2014-01-01
The topic of this thesis is a new representation for quantum systems on weakly exponential Lie groups in terms of a non-commutative algebra of functions, the associated non-commutative harmonic analysis, and some of its applications to specific physical systems. In the first part of the thesis, after a review of the necessary mathematical background, we introduce a * -algebra that is interpreted as the quantization of the canonical Poisson structure of the cotangent bundle over a Lie group. From the physics point of view, this represents the algebra of quantum observables of a physical system, whose configuration space is a Lie group. We then show that this quantum algebra can be represented either as operators acting on functions on the group, the usual group representation, or (under suitable conditions) as elements of a completion of the universal enveloping algebra of the Lie group, the algebra representation. We further apply the methods of deformation quantization to obtain a representation of the same algebra in terms of a non-commutative algebra of functions on a Euclidean space, which we call the non-commutative representation of the original quantum algebra. The non-commutative space that arises from the construction may be interpreted as the quantum momentum space of the physical system. We derive the transform between the group representation and the non-commutative representation that generalizes in a natural way the usual Fourier transform, and discuss key properties of this new non-commutative harmonic analysis. Finally, we exhibit the explicit forms of the non-commutative Fourier transform for three elementary Lie groups: R d , U(1) and SU(2). In the second part of the thesis, we consider application of the non-commutative representation and harmonic analysis to physics. First, we apply the formalism to quantum mechanics of a point particle on a Lie group. We define the dual non-commutative momentum representation, and derive the phase space path
Reformulations of the Yang-Mills theory toward quark confinement and mass gap
Energy Technology Data Exchange (ETDEWEB)
Kondo, Kei-Ichi; Shinohara, Toru [Department of Physics, Graduate School of Science, Chiba University, Chiba 263-8522 (Japan); Kato, Seikou [Fukui National College of Technology, Sabae 916-8507 (Japan); Shibata, Akihiro [Computing Research Center, High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801 (Japan)
2016-01-22
We propose the reformulations of the SU (N) Yang-Mills theory toward quark confinement and mass gap. In fact, we have given a new framework for reformulating the SU (N) Yang-Mills theory using new field variables. This includes the preceding works given by Cho, Faddeev and Niemi, as a special case called the maximal option in our reformulations. The advantage of our reformulations is that the original non-Abelian gauge field variables can be changed into the new field variables such that one of them called the restricted field gives the dominant contribution to quark confinement in the gauge-independent way. Our reformulations can be combined with the SU (N) extension of the Diakonov-Petrov version of the non-Abelian Stokes theorem for the Wilson loop operator to give a gauge-invariant definition for the magnetic monopole in the SU (N) Yang-Mills theory without the scalar field. In the so-called minimal option, especially, the restricted field is non-Abelian and involves the non-Abelian magnetic monopole with the stability group U (N− 1). This suggests the non-Abelian dual superconductivity picture for quark confinement. This should be compared with the maximal option: the restricted field is Abelian and involves only the Abelian magnetic monopoles with the stability group U(1){sup N−1}, just like the Abelian projection. We give some applications of this reformulation, e.g., the stability for the homogeneous chromomagnetic condensation of the Savvidy type, the large N treatment for deriving the dimensional transmutation and understanding the mass gap, and also the numerical simulations on a lattice which are given by Dr. Shibata in a subsequent talk.
Reformulations of the Yang-Mills theory toward quark confinement and mass gap
Kondo, Kei-Ichi; Kato, Seikou; Shibata, Akihiro; Shinohara, Toru
2016-01-01
We propose the reformulations of the SU (N) Yang-Mills theory toward quark confinement and mass gap. In fact, we have given a new framework for reformulating the SU (N) Yang-Mills theory using new field variables. This includes the preceding works given by Cho, Faddeev and Niemi, as a special case called the maximal option in our reformulations. The advantage of our reformulations is that the original non-Abelian gauge field variables can be changed into the new field variables such that one of them called the restricted field gives the dominant contribution to quark confinement in the gauge-independent way. Our reformulations can be combined with the SU (N) extension of the Diakonov-Petrov version of the non-Abelian Stokes theorem for the Wilson loop operator to give a gauge-invariant definition for the magnetic monopole in the SU (N) Yang-Mills theory without the scalar field. In the so-called minimal option, especially, the restricted field is non-Abelian and involves the non-Abelian magnetic monopole with the stability group U (N- 1). This suggests the non-Abelian dual superconductivity picture for quark confinement. This should be compared with the maximal option: the restricted field is Abelian and involves only the Abelian magnetic monopoles with the stability group U(1)N-1, just like the Abelian projection. We give some applications of this reformulation, e.g., the stability for the homogeneous chromomagnetic condensation of the Savvidy type, the large N treatment for deriving the dimensional transmutation and understanding the mass gap, and also the numerical simulations on a lattice which are given by Dr. Shibata in a subsequent talk.
Connection between Einstein equations, nonlinear sigma models, and self-dual Yang-Mills theory
International Nuclear Information System (INIS)
Sanchez, N.; Whiting, B.
1986-01-01
The authors analyze the connection between nonlinear sigma models self-dual Yang-Mills theory, and general relativity (self-dual and non-self-dual, with and without killing vectors), both at the level of the equations and at the level of the different type of solutions (solitons and calorons) of these theories. They give a manifestly gauge invariant formulation of the self-dual gravitational field analogous to that given by Yang for the self-dual Yang-Mills field. This formulation connects in a direct and explicit way the self-dual Yang-Mills and the general relativity equations. They give the ''R gauge'' parametrization of the self-dual gravitational field (which corresponds to modified Yang's-type and Ernst equations) and analyze the correspondence between their different types of solutions. No assumption about the existence of symmetries in the space-time is needed. For the general case (non-self-dual), they show that the Einstein equations contain an O nonlinear sigma model. This connection with the sigma model holds irrespective of the presence of symmetries in the space-time. They found a new class of solutions of Einstein equations depending on holomorphic and antiholomorphic functions and we relate some subclasses of these solutions to solutions of simpler nonlinear field equations that are well known in other branches of physics, like sigma models, SineGordon, and Liouville equations. They include gravitational plane wave solutions. They analyze the response of different accelerated quantum detector models, compare them to the case when the detectors are linterial in an ordinary Planckian gas at a given temperature, and discuss the anisotropy of the detected response for Rindler observers
Local integrands for two-loop all-plus Yang-Mills amplitudes
International Nuclear Information System (INIS)
Badger, Simon; Mogull, Gustav; Peraro, Tiziano
2016-01-01
We express the planar five- and six-gluon two-loop Yang-Mills amplitudes with all positive helicities in compact analytic form using D-dimensional local integrands that are free of spurious singularities. The integrand is fixed from on-shell tree amplitudes in six dimensions using D-dimensional generalised unitarity cuts. The resulting expressions are shown to have manifest infrared behaviour at the integrand level. We also find simple representations of the rational terms obtained after integration in 4−2ϵ dimensions.
Spinors in self-dual Yang-Mills fields in minkowski space
International Nuclear Information System (INIS)
Pervushin, V.N.
1981-01-01
Yang-Mills theory with infrared divergences removed by spontaneous vacuum symmetry breaking is considered. The corresponding vacuum fields are self-dual and are defined in the Minkowski space. The complete set of solutions of Dirac equations with self-dual fields, depending on certain arbitrary function, is found. Physical observables (charge, energy, spin) for the spinor fields within the self-dual vacuum are calculated and a Hermitean Hamiltonian is obtained. The physical picture corresponds to a relativistic generalization of the hadron bag model [ru
FIFTY YEARS OF YANG-MILLS THEORIES: A Phenomenological Point of View
de Rújula, Alvaro
On the occasion of the celebration of the first half-century of Yang-Mills theories, I am contributing a personal recollection of how the subject, in its early times, confronted physical reality, that is, its "phenomenology". There is nothing original in this work, except, perhaps, my own points of view. But I hope that the older practitioners of the field will find here grounds form nostalgia, or good reasons to disagree with me. Younger addicts may learn that history does not resemble at all what is reflected in current textbooks: it was orders of magnitude more fascinating.
Post-Newtonian approximation of the maximum four-dimensional Yang-Mills gauge theory
International Nuclear Information System (INIS)
Smalley, L.L.
1982-01-01
We have calculated the post-Newtonian approximation of the maximum four-dimensional Yang-Mills theory proposed by Hsu. The theory contains torsion; however, torsion is not active at the level of the post-Newtonian approximation of the metric. Depending on the nature of the approximation, we obtain the general-relativistic values for the classical Robertson parameters (γ = β = 1), but deviations for the Nordtvedt effect and violations of post-Newtonian conservation laws. We conclude that in its present form the theory is not a viable theory of gravitation
Verifying the Kugo-Ojima Confinement Criterion in Landau Gauge Yang-Mills Theory
International Nuclear Information System (INIS)
Watson, Peter; Alkofer, Reinhard
2001-01-01
Expanding the Landau gauge gluon and ghost two-point functions in a power series we investigate their infrared behavior. The corresponding powers are constrained through the ghost Dyson-Schwinger equation by exploiting multiplicative renormalizability. Without recourse to any specific truncation we demonstrate that the infrared powers of the gluon and ghost propagators are uniquely related to each other. Constraints for these powers are derived, and the resulting infrared enhancement of the ghost propagator signals that the Kugo-Ojima confinement criterion is fulfilled in Landau gauge Yang-Mills theory
Canonical formulations of a classical particle in a Yang-Mills field and Wong's equations
International Nuclear Information System (INIS)
Montgomery, R.
1984-01-01
Wong (1970) introduced equations of motion for a spin 0 particle in a Yang-Mills field which was widely accepted among physicists. It is shown that these are equivalent to the various mathematical formulations for the motion of such particles as given by the Kaluza-Klein formulation of Kerner, and those of Sternberg, and Weinstein. In doing this, we show that Sternberg's space is, in a natural way, a symplectic leaf of a reduced Poisson manifold and relations to a construction of Kummer's for dynamics on the cotangent bundle of a principle bundle are clarified. (orig.)
Lorentz-violating Yang-Mills theory. Discussing the Chern-Simons-like term generation
Energy Technology Data Exchange (ETDEWEB)
Santos, Tiago R.S.; Sobreiro, Rodrigo F. [UFF-Universidade Federal Fluminense, Instituto de Fisica, Niteroi, RJ (Brazil)
2017-12-15
We analyze the Chern-Simons-like term generation in the CPT-odd Lorentz-violating Yang-Mills theory interacting with fermions. Moreover, we study the anomalies of this model as well as its quantum stability. The whole analysis is performed within the algebraic renormalization theory, which is independent of the renormalization scheme. In addition, all results are valid to all orders in perturbation theory. We find that the Chern-Simons-like term is not generated by radiative corrections, just like its Abelian version. Additionally, the model is also free of gauge anomalies and quantum stable. (orig.)
From decay to complete breaking: pulling the strings in SU(2) Yang-Mills theory.
Pepe, M; Wiese, U-J
2009-05-15
We study {2Q+1} strings connecting two static charges Q in (2+1)D SU(2) Yang-Mills theory. While the fundamental {2} string between two charges Q=1/2 is unbreakable, the adjoint {3} string connecting two charges Q=1 can break. When a {4} string is stretched beyond a critical length, it decays into a {2} string by gluon pair creation. When a {5} string is stretched, it first decays into a {3} string, which eventually breaks completely. The energy of the screened charges at the ends of a string is well described by a phenomenological constituent gluon model.
Unified theory of gravitation, electromagnetism, and the Yang-Mills field
International Nuclear Information System (INIS)
Borchsenius, K.
1976-01-01
The recent modification and extension of Einstein's nonsymmetric unified field theory for gravitation and electromagnetism is generalized to include the Yang-Mills field theory. The generalization consists in assuming that the components of the linear connection and of the fundamental tensor are not ordinary c numbers but are matrices related to some unitary symmetry. As an example we consider the SU(2) case. The theory is applied to the gauge-covariant formulation of electrically and isotopically charged spin-1/2 field theories
Note on dual superconformal symmetry of the N=4 super Yang-Mills S matrix
International Nuclear Information System (INIS)
Brandhuber, Andreas; Heslop, Paul; Travaglini, Gabriele
2008-01-01
We present a supersymmetric recursion relation for tree-level scattering amplitudes in N=4 super Yang-Mills. Using this recursion relation, we prove that the tree-level S matrix of the maximally supersymmetric theory is covariant under dual superconformal transformations. We further analyze the consequences that the transformation properties of the trees under this symmetry have on those of the loops. In particular, we show that the coefficients of the expansion of generic one-loop amplitudes in a basis of pseudoconformally invariant scalar box functions transform covariantly under dual superconformal symmetry, and in exactly the same way as the corresponding tree-level amplitudes.
Integrable model of Yang-Mills theory with scalar field and quasi-instantons
International Nuclear Information System (INIS)
Yatsun, V.A.
1988-01-01
In the framework of Euclidean conformally invariant Yang-Mills theory with a scalar field a study is made of a Hamiltonian system with two degrees of freedom that is integrable for a definite relationship between the coupling constants. A particular solution of the Hamilton-Jacobi equation leads to first-order equations that ensure a nonself-dual solution of instanton type of the considered model. As generalization of the first-order equations a quasiself-dual equation that can be integrated by means of the 't Hooft ansatz and leads to quasiself-dual instantons - quasi-instantons - is proposed
Integrable model of Yang-Mills theory and quasi-instantons
International Nuclear Information System (INIS)
Yatsun, V.A.
1986-01-01
Within the framework of Euclidean conformal invariant Yang-Mills theory with a scalar field, a two-dimensional Hamiltonian system integrable for a definite relation between the coupling constants is considered. A particular solution of the Hamilton-Jacobi equation leads to a system of first-order equations providing a nonself-dual instanton-like solution of the model concerned. As a generalizationof the system, a quasi-self-duality equation is suggested which is integrated by means of the 't Hooft ansatz and results in quasi-self-dual instantons (quasi-instantons). (orig.)
Towards a precise determination of the topological susceptibility in the SU(3) Yang-Mills theory
Giusti, Leonardo; Petrarca, Silvano
2009-01-01
An ongoing effort to compute the topological susceptibility for the SU(3) Yang-Mills theory in the continuum limit with a precison of about 2% is reported. The susceptibility is computed by using the definition of the charge suggested by Neuberger fermions for two values of the negative mass parameter s. Finite volume and discretization effects are estimated to meet this level of precision. The large statistics required has been obtained by using PCs of the INFN-GRID. Simulations with larger lattice volumes are necessary in order to better understanding the continuum limit at small lattice spacing values.
Local integrands for two-loop all-plus Yang-Mills amplitudes
Energy Technology Data Exchange (ETDEWEB)
Badger, Simon; Mogull, Gustav; Peraro, Tiziano [Higgs Centre for Theoretical Physics, School of Physics and Astronomy,The University of Edinburgh, James Clerk Maxwell Building,Peter Guthrie Tait Road, Edinburgh EH9 3FD (United Kingdom)
2016-08-09
We express the planar five- and six-gluon two-loop Yang-Mills amplitudes with all positive helicities in compact analytic form using D-dimensional local integrands that are free of spurious singularities. The integrand is fixed from on-shell tree amplitudes in six dimensions using D-dimensional generalised unitarity cuts. The resulting expressions are shown to have manifest infrared behaviour at the integrand level. We also find simple representations of the rational terms obtained after integration in 4−2ϵ dimensions.
Supersymmetric Yang-Mills theory on conformal supergravity backgrounds in ten dimensions
Energy Technology Data Exchange (ETDEWEB)
Medeiros, Paul de; Figueroa-O’Farrill, José [Maxwell Institute and School of Mathematics, The University of Edinburgh,James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh EH9 3FD (United Kingdom)
2016-03-14
We consider bosonic supersymmetric backgrounds of ten-dimensional conformal supergravity. Up to local conformal isometry, we classify the maximally supersymmetric backgrounds, determine their conformal symmetry superalgebras and show how they arise as near-horizon geometries of certain half-BPS backgrounds or as a plane-wave limit thereof. We then show how to define Yang-Mills theory with rigid supersymmetry on any supersymmetric conformal supergravity background and, in particular, on the maximally supersymmetric backgrounds. We conclude by commenting on a striking resemblance between the supersymmetric backgrounds of ten-dimensional conformal supergravity and those of eleven-dimensional Poincaré supergravity.
Canonical formulation of the self-dual Yang-Mills system: Algebras and hierarchies
International Nuclear Information System (INIS)
Chau, L.; Yamanaka, I.
1992-01-01
We construct a canonical formulation of the self-dual Yang-Mills system formulated in the gauge-invariant group-valued J fields and derive their Hamiltonian and the quadratic algebras of the fundamental Dirac brackets. We also show that the quadratic algebras satisfy Jacobi identities and their structure matrices satisfy modified Yang-Baxter equations. From these quadratic algebras, we construct Kac-Moody-like and Virasoro-like algebras. We also discuss their related symmetries, involutive conserved quantities, and hierarchies of nonlinear and linear equations
Exact Gell-Mann-Low function of supersymmetric Yang-Mills theories from instanton calculus
International Nuclear Information System (INIS)
Novikov, V.A.; Shifman, M.A.; Vainshtein, A.I.; Zakharov, V.I.
1983-01-01
The instanton contribution to the vacuum energy is supersymmetric Yang-Mills theories is considered. Using renormalizability of the theory the exact beta function for n-extended supersymmetry (n=1, 2, 4) is found. The coefficients of the beta function have a geometrical meaning - they are associated with the number of boson and fermion zero modes in the instanton field. If extra matter superfields are added the method allows one to fix the first two coefficients. A non-renormalization theorem which extends cancellation of vacuum loops to the case of the external instanton field is proved
Cut-and-join operators and N=4 super Yang-Mills
International Nuclear Information System (INIS)
Brown, T.W.
2010-02-01
We show which multi-trace structures are compatible with the symmetrisation of local operators in N=4 super Yang-Mills when they are organised into representations of the global symmetry group. Cut-and-join operators give the non-planar expansion of correlation functions of these operators in the free theory. Using these techniques we find the 1/N corrections to the quarter-BPS operators which remain protected at weak coupling. We also present a new way of counting these chiral ring operators using the Weyl group S N . (orig.)
The asymptotic spectrum of the N = 4 super-Yang-Mills spin chain
International Nuclear Information System (INIS)
Chen, H.-Y.; Dorey, Nick; Okamura, Keisuke
2007-01-01
In this paper we discuss the asymptotic spectrum of the spin chain description of planar N = 4 SUSY Yang-Mills. The states appearing in the spectrum belong to irreducible representations of the unbroken supersymmetry SU(2 vertical bar 2) x SU(2 vertical bar 2) with non-trivial extra central extensions. The elementary magnon corresponds to the bifundamental representation while boundstates of Q magnons form a certain short representation of dimension 16Q 2 . Generalising the Beisert's analysis of the Q = 1 case, we derive the exact dispersion relation for these states by purely group theoretic means
Variational study of mass generation and deconfinement in Yang-Mills theory
Comitini, Giorgio; Siringo, Fabio
2018-03-01
A very simple variational approach to pure SU (N ) Yang-Mills theory is proposed, based on the Gaussian effective potential in a linear covariant gauge. The method provides an analytical variational argument for mass generation. The method can be improved order by order by a perturbative massive expansion around the optimal trial vacuum. At finite temperature, a weak first-order transition is found (at Tc≈250 MeV for N =3 ) where the mass scale drops discontinuously. Above the transition the optimal mass increases linearly as expected for deconfined bosons. The equation of state is found in good agreement with the lattice data.
The state equation of Yang-Mills field dark energy models
International Nuclear Information System (INIS)
Zhao Wen; Zhang Yang
2006-01-01
In this paper, we study the possibility of building Yang-Mills (YM) field dark energy models with equation of state (EoS) crossing -1, and find that it cannot be realized by the single YM field models, no matter what kind of Lagrangian or initial condition. But the states of -1 -1 to <-1, and it will go to the critical state of ω = -1 with the expansion of the universe, which character is the same as the single YM field models, and the big rip is naturally avoided
A complete two-loop, five-gluon helicity amplitude in Yang-Mills theory
International Nuclear Information System (INIS)
Badger, Simon; Mogull, Gustav; Ochirov, Alexander; O’Connell, Donal
2015-01-01
We compute the integrand of the full-colour, two-loop, five-gluon scattering amplitude in pure Yang-Mills theory with all helicities positive, using generalized unitarity cuts. Tree-level BCJ relations, satisfied by amplitudes appearing in the cuts, allow us to deduce all the necessary non-planar information for the full-colour amplitude from known planar data. We present our result in terms of irreducible numerators, with colour factors derived from the multi-peripheral colour decomposition. Finally, the leading soft divergences are checked to reproduce the expected infrared behaviour.
Cut-and-join operators and N=4 super Yang-Mills
Energy Technology Data Exchange (ETDEWEB)
Brown, T W [DESY, Hamburg (Germany). Theory Group
2010-02-15
We show which multi-trace structures are compatible with the symmetrisation of local operators in N=4 super Yang-Mills when they are organised into representations of the global symmetry group. Cut-and-join operators give the non-planar expansion of correlation functions of these operators in the free theory. Using these techniques we find the 1/N corrections to the quarter-BPS operators which remain protected at weak coupling. We also present a new way of counting these chiral ring operators using the Weyl group S{sub N}. (orig.)
Supergravity and Yang-Mills theories as generalized topological fields with constraints
International Nuclear Information System (INIS)
Ling Yi; Tung Rohsuan; Guo Hanying
2004-01-01
We present a general approach to construct a class of generalized topological field theories with constraints by means of generalized differential calculus and its application to connection theory. It turns out that not only the ordinary BF formulations of general relativity and Yang-Mills theories, but also the N=1,2 chiral supergravities can be reformulated as these constrained generalized topological field theories once the free parameters in the Lagrangian are specially chosen. We also show that the Chern-Simons action on the boundary may naturally be induced from the generalized topological action in the bulk, rather than introduced by hand
Fifty years of Yang-Mills Theories: a phenomenological point of view
De Rújula, Alvaro
2005-01-01
On the occasion of the celebration of the first half-century of Yang--Mills theories, I am contributing a personal recollection of how the subject, in its early times, confronted physical reality, that is, its "phenomenology". There is nothing original in this work, except, perhaps, my own points of view. But I hope that the older practitioners of the field will find here grounds for nostalgia, or good reasons to disagree with me. Younger addicts may learn that history does not resemble at all what is reflected in current textbooks: it was orders of magnitude more fascinating.
Exact Gell-Mann-Low function of supersymmetric Yang-Mills theories from instanton calculus
International Nuclear Information System (INIS)
Novikov, V.A.; Shifman, M.A.; Vainshtein, A.I.; Zakharov, V.I.
1983-01-01
The instanton contribution to the vacuum energy in supersymmetric Yang-Mills theories is considered. Using the renormalizability of the theory we find the exact beta function for n-extended supersymmetry (n=1, 2, 4). The coefficients of the beta function have a geometrical meaning: they are associated with the number of boson and fermion zero modes in the instanton field. If extra matter superfields are added our method allows one to fix the first two coefficients. We prove a non-renormalization theorem which extends the cancellation of vacuum loops to the case of the external instanton field. (orig.)
A new quantum representation for canonical gravity and SU(2) Yang-Mills theory
International Nuclear Information System (INIS)
Loll, R.
1990-04-01
Starting from Rovelli-Smolin's infinite-dimensional graded Poisson-bracket algebra of loop variables, we propose a new way of constructing a corresponding quantum representation. After eliminating certain quadratic constraints, we 'integrate' an infinite-dimensional subalgebra of loop variables, using a formal group law expansion. With the help of techniques from the representation theory of semidirect-product groups, we find an exact quantum representation of the full classical Poisson-bracket algebra of loop variables, without any higher-order correction terms. This opens new ways of tackling the quantum dynamics for both canonical gravity and Yang-Mills theory. (orig.)
A new quantum representation for canonical gravity and SU(2) Yang-Mills theory
International Nuclear Information System (INIS)
Loll, R.
1991-01-01
Starting from Rovelli-Smolin's infinite-dimensional graded Poisson-bracket algebra of loop variables, we propose a new way of constructing a corresponding quantum representation. After eliminating certain quadratic constraints, we 'integrate' an infinite-dimensional subalgebra of loop variables, using a formal group law expansion. With the help of techniques from the representation theory of semidirect-product groups, we find an exact quantum representation of the full classical Poisson-bracket algebra of loop variables, without any higher-order correction terms. This opens new ways of tackling the quantum dynamics for both canonical gravity and Yang-Mills theory. (orig.)
Pure spinors as auxiliary fields in the ten-dimensional supersymmetric Yang-Mills theory
International Nuclear Information System (INIS)
Nilsson, B.E.W.
1986-01-01
A new way of introducing auxiliary fields into the ten-dimensional supersymmetric Yang-Mills theory is proposed. The auxiliary fields are commuting 'pure spinors' and constitute a non-linear realisation of the Lorentz group. This invalidates previous no-go theorems concerning the possibility of going off-shell in this theory. There seems to be a close relation between pure spinors and the concepts usually used in twistor theory. The non-Abelian theory can be constructed for all groups having pseudo-real representations. (author)
Supersymmetric Adler-Bardeen anomaly in N=1 super-Yang-Mills theories
International Nuclear Information System (INIS)
Baulieu, Laurent; Martin, Alexis
2008-01-01
We provide a study of the supersymmetric Adler-Bardeen anomaly in the N=1, d=4,6,10 super-Yang-Mills theories. We work in the component formalism that includes shadow fields, for which Slavnov-Taylor identities can be independently set for both gauge invariance and supersymmetry. We find a method with improved descent equations for getting the solutions of the consistency conditions of both Slavnov-Taylor identities and finding the local field polynomials for the standard Adler-Bardeen anomaly and its supersymmetric counterpart. We give the explicit solution for the ten-dimensional case
Exact and microscopic one-instanton calculations in N=2 supersymmetric Yang-Mills theories
International Nuclear Information System (INIS)
Ito, K.; Sasakura, N.
1997-01-01
We study the low-energy effective theory in N=2 super Yang-Mills theories by microscopic and exact approaches. We calculate the one-instanton correction to the prepotential for any simple Lie group from the microscopic approach. We also study the Picard-Fuchs equations and their solutions in the semi-classical regime for classical gauge groups with rank r≤3. We find that for gauge groups G=A r , B r , C r (r≤3) the microscopic results agree with those from the exact solutions. (orig.)
Higher order BLG supersymmetry transformations from 10-dimensional super Yang Mills
Energy Technology Data Exchange (ETDEWEB)
Hall, John [Alumnus of Physics Department, Imperial College,South Kensington, London, SW7 2AZ (United Kingdom); Low, Andrew [Physics Department, Wimbledon High School,Mansel Road, London, SW19 4AB (United Kingdom)
2014-06-26
We study a Simple Route for constructing the higher order Bagger-Lambert-Gustavsson theory - both supersymmetry transformations and Lagrangian - starting from knowledge of only the 10-dimensional Super Yang Mills Fermion Supersymmetry transformation. We are able to uniquely determine the four-derivative order corrected supersymmetry transformations, to lowest non-trivial order in Fermions, for the most general three-algebra theory. For the special case of Euclidean three-algbera, we reproduce the result presented in arXiv:1207.1208, with significantly less labour. In addition, we apply our method to calculate the quadratic fermion terms in the higher order BLG fermion supersymmetry transformation.
Chern-Simons theory, 2d Yang-Mills, and Lie algebra wanderers
International Nuclear Information System (INIS)
Haro, Sebastian de
2005-01-01
We work out the relation between Chern-Simons, 2d Yang-Mills on the cylinder, and Brownian motion. We show that for the unitary, orthogonal and symplectic groups, various observables in Chern-Simons theory on S 3 and lens spaces are exactly given by counting the number of paths of a Brownian particle wandering in the fundamental Weyl chamber of the corresponding Lie algebra. We construct a fermionic formulation of Chern-Simons on S 3 which allows us to identify the Brownian particles as B-model branes moving on a noncommutative two-sphere, and construct 1- and 2-matrix models to compute Brownian motion ensemble averages
(2,0)-Super-Yang-Mills coupled to non-linear {sigma}-model
Energy Technology Data Exchange (ETDEWEB)
Goes-Negrao, M.S.; Penna-Firme, A.B. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil); Negrao, M.R. [Universidade Federal, Rio de Janeiro, RJ (Brazil). Inst. de Fisica
1999-07-01
Considering a class of (2,0)-super yang-Mills multiplets that accommodate a pair of independent gauge potentials in connection with a single symmetry group, we present here their coupling to ordinary matter to non-linear {sigma}-models in (2,0)-superspace. The dynamics and the coupling of the gauge potentials are discussed and the interesting feature that comes out is a sort of chirality for one of the gauge potentials are discussed and the interesting feature that comes out is a sort of chirality for one of the gauge potentials once light-cone coordinates are chosen. (author)
(2,0)-Super-Yang-Mills coupled to non-linear σ-model
International Nuclear Information System (INIS)
Goes-Negrao, M.S.; Penna-Firme, A.B.; Negrao, M.R.
1999-07-01
Considering a class of (2,0)-super yang-Mills multiplets that accommodate a pair of independent gauge potentials in connection with a single symmetry group, we present here their coupling to ordinary matter to non-linear σ-models in (2,0)-superspace. The dynamics and the coupling of the gauge potentials are discussed and the interesting feature that comes out is a sort of chirality for one of the gauge potentials are discussed and the interesting feature that comes out is a sort of chirality for one of the gauge potentials once light-cone coordinates are chosen. (author)
A complete two-loop, five-gluon helicity amplitude in Yang-Mills theory
Energy Technology Data Exchange (ETDEWEB)
Badger, Simon; Mogull, Gustav; Ochirov, Alexander [Higgs Centre for Theoretical Physics, School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3JZ, Scotland (United Kingdom); O’Connell, Donal [Higgs Centre for Theoretical Physics, School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3JZ, Scotland (United Kingdom); Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106-4030 (United States)
2015-10-09
We compute the integrand of the full-colour, two-loop, five-gluon scattering amplitude in pure Yang-Mills theory with all helicities positive, using generalized unitarity cuts. Tree-level BCJ relations, satisfied by amplitudes appearing in the cuts, allow us to deduce all the necessary non-planar information for the full-colour amplitude from known planar data. We present our result in terms of irreducible numerators, with colour factors derived from the multi-peripheral colour decomposition. Finally, the leading soft divergences are checked to reproduce the expected infrared behaviour.
The (confinement) structure of Yang-Mills-theories within a Bose-BCS-theory
International Nuclear Information System (INIS)
Schuette, D.
1984-01-01
It is the purpose of this talk to report on a first attempt to apply (non-perturbative) techniques of many-body theory to a field-theory of the Yang-Mills-type. The procedure is in principle analogous to lattice calculations: In order to make the field-theoretical hamiltonian a well-behaved operator in the Fock-space, a phasespace-cutoff is assumed for the definition of the field operators. The coupling constant g then becomes a function of this cutoff which is fixed by some physical property like a glue-ball mass. (orig./HSI)
Four-loop collinear anomalous dimension in N=4 Yang-Mills theory
International Nuclear Information System (INIS)
Cachazo, Freddy; Spradlin, Marcus; Volovich, Anastasia
2007-01-01
We report a calculation in N=4 Yang-Mills of the four-loop term g (4) in the collinear anomalous dimension g(λ) which governs the universal subleading infrared structure of gluon scattering amplitudes. Using the method of obstructions to extract this quantity from the 1/ε singularity in the four-gluon iterative relation at four loops, we find g (4) =-1240.9 with an estimated numerical uncertainty of 0.02%. We also analyze the implication of our result for the strong coupling behavior of g(λ), finding support for the string theory prediction computed recently by Alday and Maldacena using AdS/CFT
Gravitational matter-antimatter asymmetry and four-dimensional Yang-Mills gauge symmetry
Hsu, J. P.
1981-01-01
A formulation of gravity based on the maximum four-dimensional Yang-Mills gauge symmetry is studied. The theory predicts that the gravitational force inside matter (fermions) is different from that inside antimatter. This difference could lead to the cosmic separation of matter and antimatter in the evolution of the universe. Moreover, a new gravitational long-range spin-force between two fermions is predicted, in addition to the usual Newtonian force. The geometrical foundation of such a gravitational theory is the Riemann-Cartan geometry, in which there is a torsion. The results of the theory for weak fields are consistent with previous experiments.
International Nuclear Information System (INIS)
Engelhardt, M.
2006-01-01
A random vortex world-surface model for the infrared sector of SU(4) Yang-Mills theory is constructed, focusing on the confinement properties and the behavior at the deconfinement phase transition. Although the corresponding data from lattice Yang-Mills theory can be reproduced, the model requires a more complex action and considerably more tuning than the SU(2) and SU(3) cases studied previously. Its predictive capabilities are accordingly reduced. This behavior has a definite physical origin, which is elucidated in detail in the present work. As the number of colors is raised in Yang-Mills theory, the corresponding infrared effective vortex description cannot indefinitely continue to rely on dynamics determined purely by vortex world-surface characteristics; additional color structures present on the vortices begin to play a role. As evidenced by the modeling effort reported here, definite signatures of this behavior appear in the case of four colors
Hendi, Seyed Hossein; Momennia, Mehrab
2018-02-01
Motivated by the interesting non-abelian gauge field, in this paper, we look for the analytical solutions of Yang-Mills theory in the context of gravity's rainbow. Regarding the trace of quantum gravity in black hole thermodynamics, we examine the first law of thermodynamics and also thermal stability in the canonical ensemble. We show that although the rainbow functions and Yang-Mills charge modify the solutions, the first law of thermodynamics is still valid. Based on the phenomenological similarities between the adS black holes and van der Waals liquid/gas systems, we study the critical behavior of the Yang-Mills black holes in the extended phase space thermodynamics. We also investigate the effects of various parameters on thermal instability as well as critical properties by using appropriate figures.
Sigma-model formulation of the Yang-Mills theory on four-dimensional hypersphere
International Nuclear Information System (INIS)
Ivanov, E.A.; Krivonos, S.O.
1981-01-01
The bilocal sigma-model representation is constructed for the Yang-Mills theory in the simplest conformally flat hyperspherical spaces So(1,4)/SO(1,3), SO(2,3)/SO(1,3) and SO(5)/SO(4). Like in the case of Minkowski and Euclidean spaces, Yang-Mills potential is defined as bsub(μ)(x)=dsub(μ)sup(y)b(x,y)|y=0 , b(x,y) being a bilocal Goldstone field which takes values in the gauge group algebra and is subjected to certain covariant constraints. The minimal version of these constraints results in the ''string'' representation for b(x,y) through the P-exponential of bsub(μ)(x) along the fixed paths coinciding with geodesics. Due to the presence of closed geodesics, the contour fuctionals naturally appear in the theory, with contours being the circles with the hypersphere radius. The sigma-model representation is shown to be Weyl-covariant: its formulations indifferent conformally flat spaces are related by transformations of ysup(rho). The geometric meaning of ysup(rho) and minimal constraints is explained, and the conformal group gransformation for ysup(rho) is found [ru
Gravity duals for the Coulomb branch of marginally deformed N=4 Yang-Mills
Hernández, R; Zoakos, D; Hernandez, Rafael; Sfetsos, Konstadinos; Zoakos, Dimitrios
2006-01-01
Supergravity backgrounds dual to a class of exactly marginal deformations of N supersymmetric Yang-Mills can be constructed through an SL(2,R) sequence of T-dualities and coordinate shifts. We apply this transformation to multicenter solutions and derive supergravity backgrounds describing the Coulomb branch of N=1 theories at strong 't Hooft coupling as marginal deformations of N=4 Yang-Mills. For concreteness we concentrate to cases with an SO(4)xSO(2) symmetry preserved by continuous distributions of D3-branes on a disc and on a three-dimensional spherical shell. We compute the expectation value of the Wilson loop operator and confirm the Coulombic behaviour of the heavy quark-antiquark potential in the conformal case. When the vev is turned on we find situations where a complete screening of the potential arises, as well as a confining regime where a linear or a logarithmic potential prevails depending on the ratio of the quark-antiquark separation to the typical vev scale. The spectra of massless excitat...
International Nuclear Information System (INIS)
Bern, Zvi; Dixon, Lance J.; Smirnov, Vladimir A.
2005-01-01
We compute the leading-color (planar) three-loop four-point amplitude of N=4 supersymmetric Yang-Mills theory in 4-2ε dimensions, as a Laurent expansion about ε=0 including the finite terms. The amplitude was constructed previously via the unitarity method, in terms of two Feynman loop integrals, one of which has been evaluated already. Here we use the Mellin-Barnes integration technique to evaluate the Laurent expansion of the second integral. Strikingly, the amplitude is expressible, through the finite terms, in terms of the corresponding one- and two-loop amplitudes, which provides strong evidence for a previous conjecture that higher-loop planar N=4 amplitudes have an iterative structure. The infrared singularities of the amplitude agree with the predictions of Sterman and Tejeda-Yeomans based on resummation. Based on the four-point result and the exponentiation of infrared singularities, we give an exponentiated Ansatz for the maximally helicity-violating n-point amplitudes to all loop orders. The 1/ε 2 pole in the four-point amplitude determines the soft, or cusp, anomalous dimension at three loops in N=4 supersymmetric Yang-Mills theory. The result confirms a prediction by Kotikov, Lipatov, Onishchenko and Velizhanin, which utilizes the leading-twist anomalous dimensions in QCD computed by Moch, Vermaseren and Vogt. Following similar logic, we are able to predict a term in the three-loop quark and gluon form factors in QCD
Some Evolution Hierarchies Derived from Self-dual Yang-Mills Equations
International Nuclear Information System (INIS)
Zhang Yufeng; Hon, Y.C.
2011-01-01
We develop in this paper a new method to construct two explicit Lie algebras E and F. By using a loop algebra Ē of the Lie algebra E and the reduced self-dual Yang-Mills equations, we obtain an expanding integrable model of the Giachetti-Johnson (GJ) hierarchy whose Hamiltonian structure can also be derived by using the trace identity. This provides a much simpler construction method in comparing with the tedious variational identity approach. Furthermore, the nonlinear integrable coupling of the GJ hierarchy is readily obtained by introducing the Lie algebra g N . As an application, we apply the loop algebra E-tilde of the Lie algebra E to obtain a kind of expanding integrable model of the Kaup-Newell (KN) hierarchy which, consisting of two arbitrary parameters α and β, can be reduced to two nonlinear evolution equations. In addition, we use a loop algebra F of the Lie algebra F to obtain an expanding integrable model of the BT hierarchy whose Hamiltonian structure is the same as using the trace identity. Finally, we deduce five integrable systems in R 3 based on the self-dual Yang-Mills equations, which include Poisson structures, irregular lines, and the reduced equations. (general)
Spinor analysis of the Yang-Mills theory in the Minkowski space
International Nuclear Information System (INIS)
Pervushin, V.N.; Horejsi, J.
1982-01-01
Spinorial methods are applied to the solution of self-duality equations for Yang-Mills field and the Dirac equation with an external self-dual field in the Minkowski space. Gauge group SU(2) is considered. It is shown that in the spinorial formalism an analog of the Yang construction of self-dual fields emerges naturally. Solutions of the Dirac eqUation for massless fermion with an arbitrary isospin, interacting with an external self-dual or anti-self-dual field are obtained. The external field is chosen to be the Minkowskian analog of the EUclidean Hooft Ansatz. It is shown that for the isospin 1/2 and 1 the solutions of the Dirac equation may be expressed in terms of the solutions of d'Alembert equation. The solutions obtained may be employed in the approach to gauge theories proposed recently, which is based on an analogy with the superfluidity theory; in such an approach the self-dual solutions of the Yang-Mills equations represent the vacuum
Unified Maxwell-Einstein and Yang-Mills-Einstein supergravity theories in five dimensions
International Nuclear Information System (INIS)
Guenaydin, Murat; Zagermann, Marco
2003-01-01
Unified N = 2 Maxwell-Einstein supergravity theories (MESGTs) are supergravity theories in which all the vector fields, including the graviphoton, transform in an irreducible representation of a simple global symmetry group of the Lagrangian. As was established long time ago, in five dimensions there exist only four unified Maxwell-Einstein supergravity theories whose target manifolds are symmetric spaces. These theories are defined by the four simple euclidean Jordan algebras of degree three. In this paper, we show that, in addition to these four unified MESGTs with symmetric target spaces, there exist three infinite families of unified MESGTs as well as another exceptional one. These novel unified MESGTs are defined by non-compact (minkowskian) Jordan algebras, and their target spaces are in general neither symmetric nor homogeneous. The members of one of these three infinite families can be gauged in such a way as to obtain an infinite family of unified N = 2 Yang-Mills-Einstein supergravity theories, in which all vector fields transform in the adjoint representation of a simple gauge group of the type SU(N,1). The corresponding gaugings in the other two infinite families lead to Yang-Mills-Einstein supergravity theories coupled to tensor multiplets. (author)
Dual computations of non-Abelian Yang-Mills theories on the lattice
International Nuclear Information System (INIS)
Cherrington, J. Wade; Khavkine, Igor; Christensen, J. Daniel
2007-01-01
In the past several decades there have been a number of proposals for computing with dual forms of non-Abelian Yang-Mills theories on the lattice. Motivated by the gauge-invariant, geometric picture offered by dual models and successful applications of duality in the U(1) case, we revisit the question of whether it is practical to perform numerical computation using non-Abelian dual models. Specifically, we consider three-dimensional SU(2) pure Yang-Mills as an accessible yet nontrivial case in which the gauge group is non-Abelian. Using methods developed recently in the context of spin foam quantum gravity, we derive an algorithm for efficiently computing the dual amplitude and describe Metropolis moves for sampling the dual ensemble. We relate our algorithms to prior work in non-Abelian dual computations of Hari Dass and his collaborators, addressing several problems that have been left open. We report results of spin expectation value computations over a range of lattice sizes and couplings that are in agreement with our conventional lattice computations. We conclude with an outlook on further development of dual methods and their application to problems of current interest
International Nuclear Information System (INIS)
Kovtun, Pavel; Uensal, Mithat; Yaffe, Laurence G.
2005-01-01
In previous work, we found that necessary and sufficient conditions for large N c equivalence between parent and daughter theories, for a wide class of orbifold projections of U(N c ) gauge theories, are just the natural requirements that the discrete symmetry used to define the projection not be spontaneously broken in the parent theory, and the discrete symmetry permuting equivalent gauge group factors not be spontaneously broken in the daughter theory. In this paper, we discuss the application of this result to Z k projections of N=1 supersymmetric Yang-Mills theory in four dimensions, as well as various multiflavor generalizations. Z k projections with k>2 yielding chiral gauge theories violate the symmetry realization conditions needed for large N c equivalence, due to the spontaneous symmetry breaking of discrete chiral symmetry in the parent super-Yang-Mills theory. But for Z 2 projections, we show that previous assertions of large N c inequivalence, in infinite volume, between the parent and daughter theories were based on incorrect mappings of vacuum energies, theta angles, or connected correlators between the two theories. With the correct identifications, there is no sign of any inconsistency. A subtle but essential feature of the connection between parent and daughter theories involves multivaluedness in the mapping of theta parameters from parent to daughter
Constructing the tree-level Yang-Mills S-matrix using complex factorization
Schuster, Philip C.; Toro, Natalia
2009-06-01
A remarkable connection between BCFW recursion relations and constraints on the S-matrix was made by Benincasa and Cachazo in 0705.4305, who noted that mutual consistency of different BCFW constructions of four-particle amplitudes generates non-trivial (but familiar) constraints on three-particle coupling constants — these include gauge invariance, the equivalence principle, and the lack of non-trivial couplings for spins > 2. These constraints can also be derived with weaker assumptions, by demanding the existence of four-point amplitudes that factorize properly in all unitarity limits with complex momenta. From this starting point, we show that the BCFW prescription can be interpreted as an algorithm for fully constructing a tree-level S-matrix, and that complex factorization of general BCFW amplitudes follows from the factorization of four-particle amplitudes. The allowed set of BCFW deformations is identified, formulated entirely as a statement on the three-particle sector, and using only complex factorization as a guide. Consequently, our analysis based on the physical consistency of the S-matrix is entirely independent of field theory. We analyze the case of pure Yang-Mills, and outline a proof for gravity. For Yang-Mills, we also show that the well-known scaling behavior of BCFW-deformed amplitudes at large z is a simple consequence of factorization. For gravity, factorization in certain channels requires asymptotic behavior ~ 1/z2.
Constructing the tree-level Yang-Mills S-matrix using complex factorization
International Nuclear Information System (INIS)
Schuster, Philip C.; Toro, Natalia
2009-01-01
A remarkable connection between BCFW recursion relations and constraints on the S-matrix was made by Benincasa and Cachazo in 0705.4305, who noted that mutual consistency of different BCFW constructions of four-particle amplitudes generates non-trivial (but familiar) constraints on three-particle coupling constants - these include gauge invariance, the equivalence principle, and the lack of non-trivial couplings for spins > 2. These constraints can also be derived with weaker assumptions, by demanding the existence of four-point amplitudes that factorize properly in all unitarity limits with complex momenta. From this starting point, we show that the BCFW prescription can be interpreted as an algorithm for fully constructing a tree-level S-matrix, and that complex factorization of general BCFW amplitudes follows from the factorization of four-particle amplitudes. The allowed set of BCFW deformations is identified, formulated entirely as a statement on the three-particle sector, and using only complex factorization as a guide. Consequently, our analysis based on the physical consistency of the S-matrix is entirely independent of field theory. We analyze the case of pure Yang-Mills, and outline a proof for gravity. For Yang-Mills, we also show that the well-known scaling behavior of BCFW-deformed amplitudes at large z is a simple consequence of factorization. For gravity, factorization in certain channels requires asymptotic behavior ∼ 1/z 2 .
One-loop effect of null-like cosmology's holographic dual super-Yang-Mills
International Nuclear Information System (INIS)
Lin, F.-L.; Tomino, Dan
2007-01-01
We calculate the 1-loop effect in super-Yang-Mills which preserves 1/4-supersymmetries and is holographically dual to the null-like cosmology with a big-bang singularity. Though the bosonic and fermionic spectra do not agree precisely, we do obtain vanishing 1-loop vacuum energy for generic warped plane-wave type backgrounds with a big-bang singularity. Moreover, we find that the cosmological 'constant' contributed either by bosons or fermions is time-dependent. The issues about the particle production of some background and about the UV structure are also commented. We argue that the effective higher derivative interactions are suppressed as long as the Fourier transform of the time-dependent coupling is UV-finite. Our result holds for scalar configurations that are BPS but with arbitrary time-dependence. This suggests the existence of non-renormalization theorem for such a new class of time-dependent theories. Altogether, it implies that such a super-Yang-Mills is scale-invariant, and that its dual bulk quantum gravity might behave regularly near the big bang
Non-Gaussianities in the topological charge distribution of the SU(3) Yang-Mills theory
Cè, Marco; Consonni, Cristian; Engel, Georg P.; Giusti, Leonardo
2015-10-01
We study the topological charge distribution of the SU(3) Yang-Mills theory with high precision in order to be able to detect deviations from Gaussianity. The computation is carried out on the lattice with high statistics Monte Carlo simulations by implementing a naive discretization of the topological charge evolved with the Yang-Mills gradient flow. This definition is far less demanding than the one suggested from Neuberger's fermions and, as shown in this paper, in the continuum limit its cumulants coincide with those of the universal definition appearing in the chiral Ward identities. Thanks to the range of lattice volumes and spacings considered, we can extrapolate the results for the second and fourth cumulant of the topological charge distribution to the continuum limit with confidence by keeping finite volume effects negligible with respect to the statistical errors. Our best results for the topological susceptibility is t02χ =6.67 (7 )×1 0-4 , where t0 is a standard reference scale, while for the ratio of the fourth cumulant over the second, we obtain R =0.233 (45 ). The latter is compatible with the expectations from the large Nc expansion, while it rules out the θ behavior of the vacuum energy predicted by the dilute instanton model. Its large distance from 1 implies that, in the ensemble of gauge configurations that dominate the path integral, the fluctuations of the topological charge are of quantum nonperturbative nature.
Gauge theories of Yang-Mills vector fields coupled to antisymmetric tensor fields
International Nuclear Information System (INIS)
Anco, Stephen C.
2003-01-01
A non-Abelian class of massless/massive nonlinear gauge theories of Yang-Mills vector potentials coupled to Freedman-Townsend antisymmetric tensor potentials is constructed in four space-time dimensions. These theories involve an extended Freedman-Townsend-type coupling between the vector and tensor fields, and a Chern-Simons mass term with the addition of a Higgs-type coupling of the tensor fields to the vector fields in the massive case. Geometrical, field theoretic, and algebraic aspects of the theories are discussed in detail. In particular, the geometrical structure mixes and unifies features of Yang-Mills theory and Freedman-Townsend theory formulated in terms of Lie algebra valued curvatures and connections associated to the fields and nonlinear field strengths. The theories arise from a general determination of all possible geometrical nonlinear deformations of linear Abelian gauge theory for one-form fields and two-form fields with an Abelian Chern-Simons mass term in four dimensions. For this type of deformation (with typical assumptions on the allowed form considered for terms in the gauge symmetries and field equations), an explicit classification of deformation terms at first-order is obtained, and uniqueness of deformation terms at all higher orders is proven. This leads to a uniqueness result for the non-Abelian class of theories constructed here
Non-supersymmetric matrix strings from generalized Yang-Mills theory on arbitrary Riemann surfaces
International Nuclear Information System (INIS)
Billo, M.; D'Adda, A.; Provero, P.
2000-01-01
We quantize pure 2d Yang-Mills theory on an arbitrary Riemann surface in the gauge where the field strength is diagonal. Twisted sectors originate, as in Matrix string theory, from permutations of the eigenvalues around homotopically non-trivial loops. These sectors, that must be discarded in the usual quantization due to divergences occurring when two eigenvalues coincide, can be consistently kept if one modifies the action by introducing a coupling of the field strength to the space-time curvature. This leads to a generalized Yang-Mills theory whose action reduces to the usual one in the limit of zero curvature. After integrating over the non-diagonal components of the gauge fields, the theory becomes a free string theory (sum over unbranched coverings) with a U(1) gauge theory on the world-sheet. This is shown to be equivalent to a lattice theory with a gauge group which is the semi-direct product of S N and U(1) N . By using well known results on the statistics of coverings, the partition function on arbitrary Riemann surfaces and the kernel functions on surfaces with boundaries are calculated. Extensions to include branch points and non-abelian groups on the world-sheet are briefly commented upon
International Nuclear Information System (INIS)
Castro, Carlos
2006-01-01
We construct the Clifford-space tensorial-gauge fields generalizations of Yang-Mills theories and the Standard Model that allows to predict the existence of new particles (bosons, fermions) and tensor-gauge fields of higher-spins in the 10 Tev regime. We proceed with a detailed discussion of the unique D 4 - D 5 - E 6 - E 7 - E 8 model of Smith based on the underlying Clifford algebraic structures in D = 8, and which furnishes all the properties of the Standard Model and Gravity in four-dimensions, at low energies. A generalization and extension of Smith's model to the full Clifford-space is presented when we write explicitly all the terms of the extended Clifford-space Lagrangian. We conclude by explaining the relevance of multiple-foldings of D = 8 dimensions related to the modulo 8 periodicity of the real Cliford algebras and display the interplay among Clifford, Division, Jordan, and Exceptional algebras, within the context of D = 26, 27, 28 dimensions, corresponding to bosonic string, M and F theory, respectively, advanced earlier by Smith. To finalize we describe explicitly how the E 8 x E 8 Yang-Mills theory can be obtained from a Gauge Theory based on the Clifford (16) group
Canonical Yang-Mills field theory with invariant gauge-families
International Nuclear Information System (INIS)
Yokoyama, Kan-ichi
1978-01-01
A canonical Yang-Mills field theory with indefinite metric is presented on the basis of a covariant gauge formalism for quantum electrodynamics. As the first step of the formulation, a many-gauge-field problem, in which many massless Abelian-gauge fields coexist, is treated from a new standpoint. It is shown that only a single pair of a gaugeon field and its associated one can govern the gauge structure of the whole system. The result obtained is further extended to cases of non-Abelian gauge theories. Gauge parameters for respective components of the Yang-Mills fields are introduced as a group vector. There exists a q-number local gauge transformation which connects relevant fields belonging to the same invariant gauge family with one another in a manifestly covariant way. In canonical quantization, the Faddeev-Popov ghosts are introduced in order to guarantee the existence of a desirable physical subspace with positive semi-definite metric. As to treatment of the Faddeev-Popov ghosts, Kugo and Ojima's approach is adopted. Three supplementary conditions which are consistent with one another constrain the physical subspace. (author)
The standard model on non-commutative space-time
International Nuclear Information System (INIS)
Calmet, X.; Jurco, B.; Schupp, P.; Wohlgenannt, M.; Wess, J.
2002-01-01
We consider the standard model on a non-commutative space and expand the action in the non-commutativity parameter θ μν . No new particles are introduced; the structure group is SU(3) x SU(2) x U(1). We derive the leading order action. At zeroth order the action coincides with the ordinary standard model. At leading order in θ μν we find new vertices which are absent in the standard model on commutative space-time. The most striking features are couplings between quarks, gluons and electroweak bosons and many new vertices in the charged and neutral currents. We find that parity is violated in non-commutative QCD. The Higgs mechanism can be applied. QED is not deformed in the minimal version of the NCSM to the order considered. (orig.)
The standard model on non-commutative space-time
Energy Technology Data Exchange (ETDEWEB)
Calmet, X.; Jurco, B.; Schupp, P.; Wohlgenannt, M. [Sektion Physik, Universitaet Muenchen (Germany); Wess, J. [Sektion Physik, Universitaet Muenchen (Germany); Max-Planck-Institut fuer Physik, Muenchen (Germany)
2002-03-01
We consider the standard model on a non-commutative space and expand the action in the non-commutativity parameter {theta}{sup {mu}}{sup {nu}}. No new particles are introduced; the structure group is SU(3) x SU(2) x U(1). We derive the leading order action. At zeroth order the action coincides with the ordinary standard model. At leading order in {theta}{sup {mu}}{sup {nu}} we find new vertices which are absent in the standard model on commutative space-time. The most striking features are couplings between quarks, gluons and electroweak bosons and many new vertices in the charged and neutral currents. We find that parity is violated in non-commutative QCD. The Higgs mechanism can be applied. QED is not deformed in the minimal version of the NCSM to the order considered. (orig.)
Optimization of polynomials in non-commuting variables
Burgdorf, Sabine; Povh, Janez
2016-01-01
This book presents recent results on positivity and optimization of polynomials in non-commuting variables. Researchers in non-commutative algebraic geometry, control theory, system engineering, optimization, quantum physics and information science will find the unified notation and mixture of algebraic geometry and mathematical programming useful. Theoretical results are matched with algorithmic considerations; several examples and information on how to use NCSOStools open source package to obtain the results provided. Results are presented on detecting the eigenvalue and trace positivity of polynomials in non-commuting variables using Newton chip method and Newton cyclic chip method, relaxations for constrained and unconstrained optimization problems, semidefinite programming formulations of the relaxations and finite convergence of the hierarchies of these relaxations, and the practical efficiency of algorithms.
Non-commutative flux representation for loop quantum gravity
Baratin, A.; Dittrich, B.; Oriti, D.; Tambornino, J.
2011-09-01
The Hilbert space of loop quantum gravity is usually described in terms of cylindrical functionals of the gauge connection, the electric fluxes acting as non-commuting derivation operators. It has long been believed that this non-commutativity prevents a dual flux (or triad) representation of loop quantum gravity to exist. We show here, instead, that such a representation can be explicitly defined, by means of a non-commutative Fourier transform defined on the loop gravity state space. In this dual representation, flux operators act by sstarf-multiplication and holonomy operators act by translation. We describe the gauge invariant dual states and discuss their geometrical meaning. Finally, we apply the construction to the simpler case of a U(1) gauge group and compare the resulting flux representation with the triad representation used in loop quantum cosmology.
Continuum strong-coupling expansion of Yang-Mills theory: quark confinement and infra-red slavery
Energy Technology Data Exchange (ETDEWEB)
Mansfield, P. (Dept. of Mathematical Sciences, Univ. of Durham (United Kingdom))
1994-04-25
We solve Schroedinger's equation for the ground-state of four-dimensional Yang-Mills theory as an expansion in inverse powers of the coupling. Expectation values computed with the leading-order approximation are reduced to a calculation in two-dimensional Yang-Mills theory which is known to confine. Consequently the Wilson loop in the four-dimensional theory obeys an area law to leading order and the coupling becomes infinite as the mass scale goes to zero. (orig.)
High energy behavior of a six-point R-current correlator in N=4 supersymmetric Yang-Mills theory
International Nuclear Information System (INIS)
Bartels, Jochen; Hentschinski, Martin; Mischler, Anna-Maria
2009-12-01
We study the high energy limit of a six-point R-current correlator in N=4 supersymmetric Yang-Mills theory for finite N c . We make use of the framework of perturbative resummation of large logarithms of the energy. More specifically, we apply the (extended) generalized leading logarithmic approximation. We find that the same conformally invariant two-to-four gluon vertex occurs as in non-supersymmetric Yang-Mills theory. As a new feature we find a direct coupling of the four-gluon t-channel state to the R-current impact factor. (orig.)
Continuum strong-coupling expansion of Yang-Mills theory: quark confinement and infra-red slavery
Mansfield, Paul
1994-04-01
We solve Schrödinger's equation for the ground-state of four-dimensional Yang-Mills theory as an expansion in inverse powers of the coupling. Expectation values computed with the leading-order approximation are reduced to a calculation in two-dimensional Yang-Mills theory which is known to confine. Consequently the Wilson loop in the four-dimensional theory obeys an area law to leading order and the coupling becomes infinite as the mass scale goes to zero.
Pure classical SU(2) Yang-Mills theory with potentials invariant under a U(1) gauge subgroup
International Nuclear Information System (INIS)
Bacry, H.
1978-07-01
The present article is devoted to pure SU(2) classical Yang-Mills theories whose potentials are invariant under a U(1) gauge subgroup. Such potentials are shown to be associated with classical Maxwell-like fields with magnetic sources as 't Hooft's monopole is associated with the Dirac magnetic monopole. Conversely, the authors give Yang-Mills potentials corresponding to some Maxwell-like fields, in particular static magnetic fields with emphasis on those with cylindrical symmetry (including the dipole and other multipoles) and the ephemerons corresponding to an instantaneous magnetic multipole
Brandhuber, Andreas; Heslop, Paul; Travaglini, Gabriele; Young, Donovan
2015-10-02
It is known that the Yangian of PSU(2,2|4) is a symmetry of the tree-level S matrix of N=4 super Yang-Mills theory. On the other hand, the complete one-loop dilatation operator in the same theory commutes with the level-one Yangian generators only up to certain boundary terms found by Dolan, Nappi, and Witten. Using a result by Zwiebel, we show how the Yangian symmetry of the tree-level S matrix of N=4 super Yang-Mills theory implies precisely the Yangian invariance, up to boundary terms, of the one-loop dilatation operator.
International Nuclear Information System (INIS)
Arms, J.M.; Marsden, J.E.; Moncrief, V.
1982-01-01
The space of solutions of Einstein's vacuum equations is shown to have conical singularities at each spacetime possessing a compact Cauchy surface of constant mean curvature and a nontrivial set of Killing fields. Similar results are shown for the coupled Einstein-Yang-Mills system. Combined with an appropriate slice theorem, the results show that the space of geometrically equivalent solutions is a stratified manifold with each stratum being a symplectic manifold characterized by the symmetry type of its members. Contents: Introduction 1. The Kuranishi map and its properties. 2. The momentum constraints. 3. The Hamiltonian constraints. 4. The Einstein-Yang-Mills system. 5. Discussion and examples
U(1) decoupling, Kleiss-Kuijf and Bern-Carrasco-Johansson relations in N=4 super Yang-Mills
International Nuclear Information System (INIS)
Jia Yin; Huang Rijun; Liu Changyong
2010-01-01
By using the Britto-Cachazo-Feng-Witten recursion relation of N=4 super Yang-Mills theory, we proved the color reflection, U(1) decoupling, Kleiss-Kuijf and Bern-Carrasco-Johansson relations for color-ordered amplitudes of N=4 super Yang-Mills theory. This proof verified the conjectured Bern-Carrasco-Johansson relations of matter fields. The proof depended only on general properties of superamplitudes. We showed also that the color reflection relation and U(1)-decoupling relation are special cases of Kleiss-Kuijf relations.
Modular Theory, Non-Commutative Geometry and Quantum Gravity
Directory of Open Access Journals (Sweden)
Wicharn Lewkeeratiyutkul
2010-08-01
Full Text Available This paper contains the first written exposition of some ideas (announced in a previous survey on an approach to quantum gravity based on Tomita-Takesaki modular theory and A. Connes non-commutative geometry aiming at the reconstruction of spectral geometries from an operational formalism of states and categories of observables in a covariant theory. Care has been taken to provide a coverage of the relevant background on modular theory, its applications in non-commutative geometry and physics and to the detailed discussion of the main foundational issues raised by the proposal.
Non-commutative covering spaces and their symmetries
DEFF Research Database (Denmark)
Canlubo, Clarisson
dened and its corresponding Galois theory. Using this and basic concepts from algebraic geometryand spectral theory, we will give a full description of the general structure of non-centralcoverings. Examples of coverings of the rational and irrational non-commutative tori will alsobe studied. Using...... will explain this and relate it to bi-Galois theory.Using the OZ-transform, we will show that non-commutative covering spaces come in pairs.Several categories of covering spaces will be dened and studied. Appealing to Tannaka duality,we will explain how this lead to a notion of an etale fundamental group...
Thermodynamics of SU(2) quantum Yang-Mills theory and CMB anomalies
Hofmann, Ralf
2014-04-01
A brief review of effective SU(2) Yang-Mills thermodynamics in the deconfining phase is given, including the construction of the thermal ground-state estimate in terms of an inert, adjoint scalar field φ, based on non-propagating (anti)selfdual field configurations of topological charge unity. We also discuss kinematic constraints on interacting propagating gauge fields implied by the according spatial coarse-graining, and we explain why the screening physics of an SU(2) photon is subject to an electric-magnetically dual interpretation. This argument relies on the fact that only (anti)calorons of scale parameter ρ ˜ |φ|-1 contribute to the coarse-graining required for thermal-ground-state emergence at temperature T. Thus, use of the effective gauge coupling e in the (anti)caloron action is justified, yielding the value ħ for the latter at almost all temperatures. As a consequence, the indeterministic transition of initial to final plane waves caused by an effective, pointlike vertex is fundamentally mediated in Euclidean time by a single (anti)caloron being part of the thermal ground state. Next, we elucidate how a low-frequency excess of line temperature in the Cosmic Microwave Background (CMB) determines the value of the critical temperature of the deconfining-preconfining phase transition of an SU(2) Yang-Mills theory postulated to describe photon propagation, and we describe how, starting at a redshift of about unity, SU(2) photons collectively work 3D temperature depressions into the CMB. Upon projection along a line of sight, a given depression influences the present CMB sky in a cosmologically local way, possibly explaining the large-angle anomalies confirmed recently by the Planck collaboration. Finally, six relativistic polarisations residing in the SU(2) vector modes roughly match the number of degrees of freedom in cosmic neutrinos (Planck) which would disqualify the latter as radiation. Indeed, if interpreted as single center-vortex loops in
Thermodynamics of SU(2 quantum Yang-Mills theory and CMB anomalies
Directory of Open Access Journals (Sweden)
Hofmann Ralf
2014-04-01
Full Text Available A brief review of effective SU(2 Yang-Mills thermodynamics in the deconfining phase is given, including the construction of the thermal ground-state estimate in terms of an inert, adjoint scalar field φ, based on non-propagating (antiselfdual field configurations of topological charge unity. We also discuss kinematic constraints on interacting propagating gauge fields implied by the according spatial coarse-graining, and we explain why the screening physics of an SU(2 photon is subject to an electric-magnetically dual interpretation. This argument relies on the fact that only (anticalorons of scale parameter ρ ∼ |φ|−1 contribute to the coarse-graining required for thermal-ground-state emergence at temperature T. Thus, use of the effective gauge coupling e in the (anticaloron action is justified, yielding the value ħ for the latter at almost all temperatures. As a consequence, the indeterministic transition of initial to final plane waves caused by an effective, pointlike vertex is fundamentally mediated in Euclidean time by a single (anticaloron being part of the thermal ground state. Next, we elucidate how a low-frequency excess of line temperature in the Cosmic Microwave Background (CMB determines the value of the critical temperature of the deconfining-preconfining phase transition of an SU(2 Yang-Mills theory postulated to describe photon propagation, and we describe how, starting at a redshift of about unity, SU(2 photons collectively work 3D temperature depressions into the CMB. Upon projection along a line of sight, a given depression influences the present CMB sky in a cosmologically local way, possibly explaining the large-angle anomalies confirmed recently by the Planck collaboration. Finally, six relativistic polarisations residing in the SU(2 vector modes roughly match the number of degrees of freedom in cosmic neutrinos (Planck which would disqualify the latter as radiation. Indeed, if interpreted as single center
The M5-brane and non-commutative open strings
Bergshoeff, E.; Berman, D.S.; Schaar, J.P. van der; Sundell, P.
2001-01-01
The M-theory origin of non-commutative open-string theory is examined by investigating the M-theory 5-brane at near critical field strength. In particular, it is argued that the open-membrane metric provides the appropriate moduli when calculating the duality relations between M and II
On Subgroups of Non-Commutative General Rhotrix Group ...
African Journals Online (AJOL)
This paper considers the pair (GRn(F),o) consisting of the set of all invertible rhotrices of size n over an arbitrary field F; and together with the binary operation of row-column based method for rhotrix multiplication; 'o' , in order to introduce it as the concept of “non commutative general rhotrix group”. We identify a number of ...
Notes on algebraic invariants for non-commutative dynamical systems
Energy Technology Data Exchange (ETDEWEB)
Longo, R [Rome Univ. (Italy). Istituto di Matematica
1979-11-01
We consider an algebraic invariant for non-commutative dynamical systems naturally arising as the spectrum of the modular operator associated to an invariant state, provided certain conditions of mixing type are present. This invariant turns out to be exactly the annihilator of the invariant T of Connes. Further comments are included, in particular on the type of certain algebras of local observables
Newton's second law in a non-commutative space
International Nuclear Information System (INIS)
Romero, Juan M.; Santiago, J.A.; Vergara, J. David
2003-01-01
In this Letter we show that corrections to Newton's second law appear if we assume a symplectic structure consistent with the commutation rules of the non-commutative quantum mechanics. For central field we find that the correction term breaks the rotational symmetry. For the Kepler problem, this term is similar to a Coriolis force
Limit algebras of differential forms in non-commutative geometry
Indian Academy of Sciences (India)
The holomorphic functional calculus closure of Connes' non- commutative de Rham algebra. ∗. D. (p. 549 of [C]) leads to a couple of operator algebras which are briefly discussed in this section. In §5, which contains the main contributions of the paper, quantized integrals are constructed on ∞A by using Dixmier trace ...
quasi hyperrigidity and weak peak points for non-commutative ...
Indian Academy of Sciences (India)
7
Abstract. In this article, we introduce the notions of weak boundary repre- sentation, quasi hyperrigidity and weak peak points in the non-commutative setting for operator systems in C∗-algebras. An analogue of Saskin's theorem relating quasi hyperrigidity and weak Choquet boundary for particular classes of C∗-algebras is ...
A sketch to the geometrical N=2-d=5 Yang-Mills theory over a supersymmetric group-manifold - I
International Nuclear Information System (INIS)
Borges, M.; Turin Univ.; Pio, G.
1983-03-01
This work concerns the search and the construction of a geometrical structure for a supersymmetric N=2-d=5 Yang-Mills theory on the group manifold. From criteria established throughout this paper, we build up an ansatz for the curvatures of our theory and then solve the Bianchi identities, whose solution is fundamental for the construction of the geometrical action. (author)
Energy Technology Data Exchange (ETDEWEB)
Fargnoli, H.G.; Sampaio, Marcos; Nemes, M.C. [Federal University of Minas Gerais, ICEx, Physics Department, P.O. Box 702, Belo Horizonte, MG (Brazil); Hiller, B. [Coimbra University, Faculty of Science and Technology, Physics Department, Center of Computational Physics, Coimbra (Portugal); Baeta Scarpelli, A.P. [Setor Tecnico-Cientifico, Departamento de Policia Federal, Lapa, Sao Paulo (Brazil)
2011-05-15
We present both an ultraviolet and an infrared regularization independent analysis in a symmetry preserving framework for the N=1 Super Yang-Mills beta function to two loop order. We show explicitly that off-shell infrared divergences as well as the overall two loop ultraviolet divergence cancel out, whilst the beta function receives contributions of infrared modes. (orig.)
Krishnaswami, G.S.
2008-01-01
We consider large-N multi-matrix models whose action closely mimics that of Yang-Mills theory, including gauge-fixing and ghost terms. We show that the factorized Schwinger-Dyson loop equations, expressed in terms of the generating series of gluon and ghost correlations G( ), are quadratic equations
A Yang-Mills Type Gauge Theory of Gravity and the Dark Matter and Dark Energy Problems
Yang, Yi; Yeung, Wai Bong
2012-01-01
A Yang-Mills type gauge theory of gravity is shown to have a richer structure than the Einstein's General Theory of Relativity. This new structure can give an explanation of the form of the galactic rotation curves, of the amount of intergalactic gravitational lensing, and of the accelerating expansion of the Universe.
Zero value for the three-loop β function in N=4 supersymmetric Yang-Mills theory
International Nuclear Information System (INIS)
Grisaru, M.; Rocek, M.; Siegel, W.
1980-01-01
This Letter describes a calculation using superfield techniques, showing that the β function is zero to three loops in N=4 supersymmetric Yang-Mills theory. This result gives further indication that the theory is likely to be finite and conformally invariant order by order in perturbation theory
Periodic electromagnetic vacuum in the two-dimensional Yang-Mills theory with the Chern-Simons mass
International Nuclear Information System (INIS)
Skalozub, V.V.; Vilensky, S.A.; Zaslavsky, A.Yu.
1993-06-01
The periodic vacuum structure formed from magnetic and electric fields is derived in the two-dimensional Yang-Mills theory with the Chern-Simons term. It is shown that both the magnetic flux quantization in the fundamental sell and conductivity quantization inherent to the vacuum. Hence, the quantum Hall effect gets its natural explanation. (author). 10 refs
International Nuclear Information System (INIS)
Cazenave, T.; Shatah, J.; Tahvildar-Zadeh, A.S.
1998-01-01
In this article we explore some of the connections between the theories of Yang-Mills fields, wave maps, and harmonic maps. It has been shown that the search for similarity solutions of wave maps leads to harmonic maps of the hyperbolic space. On the other hand, Glassey and Strauss have shown that the equations for an SO(3)-equivariant Yang-Mills connection on the Minkowski space R 3,1 with gauge group SU(2) reduce to a certain nonlinear wave equation, which we can now identify as a wave map on R 1,1 . More generally, we will here show the reduction under equivariance of a Yang-Mills system on the Minkowski space R n,1 to a wave map system on R n-2,1 in the specific case of SO(n) bundles with SO(n) symmetry. We then prove for odd n the existence of equivariant harmonic maps from the hyperbolic space H n that are smooth at the ideal boundary of H n , thus establishing the existence of similarity solutions for equivariant wave maps and Yang-Mills fields. As a consequence we show that for n ≥ 7, it is possible to have a wave map into a negatively curved target manifold that develops from smooth initial data and blows up in finite time, in sharp contrast to the elliptic case of harmonic maps. Finally we show how these singular solutions can be lifted to one dimension higher to produce singular travelling waves. (orig.)
International Nuclear Information System (INIS)
Fargnoli, H.G.; Sampaio, Marcos; Nemes, M.C.; Hiller, B.; Baeta Scarpelli, A.P.
2011-01-01
We present both an ultraviolet and an infrared regularization independent analysis in a symmetry preserving framework for the N=1 Super Yang-Mills beta function to two loop order. We show explicitly that off-shell infrared divergences as well as the overall two loop ultraviolet divergence cancel out, whilst the beta function receives contributions of infrared modes. (orig.)
Total source charge and charge screening in Yang-Mills theories
International Nuclear Information System (INIS)
Campbell, W.B.; Norton, R.E.
1991-01-01
New gauge-invariant definitions for the total charge on a static Yang-Mills source are suggested which we argue are better suited for determining when true color screening has occurred. In particular, these new definitions imply that the Abelian Coulomb solution for a simple ''electric'' dipole source made up of two opposite point charges has zero total source charge and therefore no color screening. With the definition of total source charge previously suggested by other authors, such a source would have a total source charge of 2q and therefore a screening charge in the field of -2q, where q is the magnitude of the charge of either point charge. Our definitions for more general solutions are not unique because of the path dependence of the parallel transport of charges. Suggestions for removing this ambiguity are offered, but it is not known if a unique, physically meaningful definition of total source charge in fact exists
Counting domain walls in N=1 super Yang-Mills theory
International Nuclear Information System (INIS)
Ritz, Adam; Shifman, Mikhail; Vainshtein, Arkady
2002-01-01
We study the multiplicity of BPS domain walls in N=1 super Yang-Mills theory, by passing to a weakly coupled Higgs phase through the addition of fundamental matter. The number of domain walls connecting two specified vacuum states is then determined via the Witten index of the induced world volume theory, which is invariant under the deformation to the Higgs phase. The world volume theory is a sigma model with a Grassmanian target space which arises as the coset associated with the global symmetries broken by the wall solution. Imposing a suitable infrared regulator, the result is found to agree with recent work of Acharya and Vafa in which the walls were realized as wrapped D4-branes in type IIA string theory
SU(5)-invariant decomposition of ten-dimensional Yang-Mills supersymmetry
Baulieu, Laurent
2011-01-01
The N=1,d=10 superYang-Mills action is constructed in a twisted form, using SU(5)-invariant decomposition of spinors in 10 dimensions. The action and its off-shell closed twisted scalar supersymmetry operator Q derive from a Chern-Simons term. The action can be decomposed as the sum of a term in the cohomology of Q and of a term that is Q-exact. The first term is a fermionic Chern-Simons term for a twisted component of the Majorana-Weyl gluino and it is related to the second one by a twisted vector supersymmetry with 5 parameters. The cohomology of Q and some topological observables are defined from descent equations. In this SU(5)
BRST quantization of 2d-Yang Mills theory with anomalies
International Nuclear Information System (INIS)
Kalau, Wolfgang
1992-01-01
The BRST-quantization of anomalous 2d-Yang Mills (YM) theory is discussed. Since an oscillator basis for the YM-Fock-space is used the anomaly appears already for a pure YM-system and the constraints form a Kac-Moody algebra with negative central charge. The coupling of chiral fermions is also discussed and it is found that the BRST-cohomology for systems with chiral fermions in a sufficiently large representation of the gauge group is completely equivalent to the cohomology of the finite dimensional gauge group. For pure YM theory or YM theory coupled to chiral fermions in small representations there exists an infinite number of inequivalent cohomology classes. This is discussed in some detail for the example of SU(2). (author). 15 refs
Center-symmetric effective theory for high-temperature SU(2) Yang-Mills theory
International Nuclear Information System (INIS)
Forcrand, Ph. de; Kurkela, A.; Vuorinen, A.
2008-01-01
We construct and study a dimensionally reduced effective theory for high-temperature SU(2) Yang-Mills theory that respects all the symmetries of the underlying theory. Our main motivation is to study whether the correct treatment of the center symmetry can help extend the applicability of the dimensional reduction procedure towards the confinement transition. After performing perturbative matching to the full theory at asymptotically high temperatures, we map the phase diagram of the effective theory using nonperturbative lattice simulations. We find that at lower temperature the theory undergoes a second-order confining phase transition, in complete analogy with the full theory, which is a direct consequence of having incorporated the center symmetry
Off-diagonal mass generation for Yang-Mills theories in the maximal Abelian gauge
International Nuclear Information System (INIS)
Dudal, D.; Verschelde, H.; Sarandy, M.S.
2007-01-01
We investigate a dynamical mass generation mechanism for the off-diagonal gluons and ghosts in SU(N) Yang-Mills theories, quantized in the maximal Abelian gauge. Such a mass can be seen as evidence for the Abelian dominance in that gauge. It originates from the condensation of a mixed gluon-ghost operator of mass dimension two, which lowers the vacuum energy. We construct an effective potential for this operator by a combined use of the local composite operators technique with algebraic renormalization and we discuss the gauge parameter independence of the results. We also show that it is possible to connect the vacuum energy, due to the mass dimension two condensate discussed here, with the non-trivial vacuum energy originating from the condensate 2 μ >, which has attracted much attention in the Landau gauge. (author)
Yang-Mills instantons in Kähler spaces with one holomorphic isometry
Chimento, Samuele; Ortín, Tomás; Ruipérez, Alejandro
2018-03-01
We consider self-dual Yang-Mills instantons in 4-dimensional Kähler spaces with one holomorphic isometry and show that they satisfy a generalization of the Bogomol'nyi equation for magnetic monopoles on certain 3-dimensional metrics. We then search for solutions of this equation in 3-dimensional metrics foliated by 2-dimensional spheres, hyperboloids or planes in the case in which the gauge group coincides with the isometry group of the metric (SO(3), SO (1 , 2) and ISO(2), respectively). Using a generalized hedgehog ansatz the Bogomol'nyi equations reduce to a simple differential equation in the radial variable which admits a universal solution and, in some cases, a particular one, from which one finally recovers instanton solutions in the original Kähler space. We work out completely a few explicit examples for some Kähler spaces of interest.
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...
BFKL approach and six-particle MHV amplitude in N=4 super Yang-Mills
International Nuclear Information System (INIS)
Lipatov, L.N.; Prygarin, A.
2010-12-01
We consider the planar MHV amplitude in N=4 supersymmetric Yang-Mills theory for 2→4 particle scattering at two and three loops in the Regge kinematics. We perform an analytic continuation of two-loop result for the remainder function found by Goncharov, Spradlin, Vergu and Volovich to the physical region, where the remainder function does not vanish in the Regge limit. After the continuation both the leading and the subleading in the logarithm of the energy terms are extracted and analyzed. Using this result we calculate the next-to-leading corrections to the impact factors required in the BFKL approach. The BFKL technique was used to find the leading imaginary and real parts of the remainder function at three loops. (orig.)
On the renormalization of topological Yang-Mills field theory in N=1 superspace
Energy Technology Data Exchange (ETDEWEB)
Oliveira, M.W. de; Penna Firme, A.B.
1996-03-01
We discuss the renormalization aspects of topological super-Yang-Mills field theory in N=1 superspace. Our approach makes use of the regularization independent BRS algebraic technique adapted to the case of a N=1 supersymmetric model. We give the expression of the most general local counterterm to the classical action to all orders of the perturbative expansion. The counterterm is shown to be BRS-coboundary, implying that the co-homological properties of the super topological theory are not affected by quantum effects. We also demonstrate the vanishing of the Callan-Symanzik {beta}-function of the model by employing a recently discovered supersymmetric antighost Ward identity. (author). 30 refs.
BFKL approach and six-particle MHV amplitude in N=4 super Yang-Mills
Energy Technology Data Exchange (ETDEWEB)
Lipatov, L.N. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; St. Petersburg Inst. of Nuclear Physics, Gatchina (Russian Federation); Prygarin, A. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik
2010-12-15
We consider the planar MHV amplitude in N=4 supersymmetric Yang-Mills theory for 2{yields}4 particle scattering at two and three loops in the Regge kinematics. We perform an analytic continuation of two-loop result for the remainder function found by Goncharov, Spradlin, Vergu and Volovich to the physical region, where the remainder function does not vanish in the Regge limit. After the continuation both the leading and the subleading in the logarithm of the energy terms are extracted and analyzed. Using this result we calculate the next-to-leading corrections to the impact factors required in the BFKL approach. The BFKL technique was used to find the leading imaginary and real parts of the remainder function at three loops. (orig.)
Wilson loop, Regge trajectory and hadron masses in a Yang-Mills theory from semiclassical strings
International Nuclear Information System (INIS)
Bigazzi, F.; Cotrone, A.L.; Martucci, L.; Pando Zayas, L.A.
2004-07-01
We compute the one-loop string corrections to the Wilson loop, glueball Regge trajectory and stringy hadron masses in the Witten model of non supersymmetric, large-N Yang-Mills theory. The classical string configurations corresponding to the above field theory objects are respectively: open straight strings, folded closed spinning strings, and strings orbiting in the internal part of the supergravity background. For the rectangular Wilson loop we show that besides the standard Luscher term, string corrections provide a rescaling of the field theory string tension. The one-loop corrections to the linear glueball Regge trajectories render them nonlinear with a positive intercept, as in the experimental soft Pomeron trajectory. Strings orbiting in the internal space predict a spectrum of hadronic-like states charged under global flavor symmetries which falls in the same universality class of other confining models. (author)
On the renormalization of topological Yang-Mills field theory in N=1 superspace
International Nuclear Information System (INIS)
Oliveira, M.W. de; Penna Firme, A.B.
1996-03-01
We discuss the renormalization aspects of topological super-Yang-Mills field theory in N=1 superspace. Our approach makes use of the regularization independent BRS algebraic technique adapted to the case of a N=1 supersymmetric model. We give the expression of the most general local counterterm to the classical action to all orders of the perturbative expansion. The counterterm is shown to be BRS-coboundary, implying that the co-homological properties of the super topological theory are not affected by quantum effects. We also demonstrate the vanishing of the Callan-Symanzik β-function of the model by employing a recently discovered supersymmetric antighost Ward identity. (author). 30 refs
The anomalous dimension of the gluon-ghost mass operator in Yang-Mills theory
International Nuclear Information System (INIS)
Dudal, D.; Verschelde, H.; Lemes, V.E.R.; Sarandy, M.S.; Sobreiro, R.; Sorella, S.P.; Picariello, M.; Gracey, J.A.
2003-01-01
The local composite gluon-ghost operator (((1)/(2))A aμ A μ a +αc-bar a c a ) is analysed in the framework of the algebraic renormalization in SU(N) Yang-Mills theories in the Landau, Curci-Ferrari and maximal abelian gauges. We show, to all orders of perturbation theory, that this operator is multiplicatively renormalizable. Furthermore, its anomalous dimension is not an independent parameter of the theory, being given by a general expression valid in all these gauges. We also verify the relations we obtain for the operator anomalous dimensions by explicit 3-loop calculations in the MS-bar scheme for the Curci-Ferrari gauge
Non-perturbative BRST quantization of Euclidean Yang-Mills theories in Curci-Ferrari gauges
Pereira, A. D.; Sobreiro, R. F.; Sorella, S. P.
2016-10-01
In this paper we address the issue of the non-perturbative quantization of Euclidean Yang-Mills theories in the Curci-Ferrari gauge. In particular, we construct a refined Gribov-Zwanziger action for this gauge, which takes into account the presence of gauge copies as well as the dynamical formation of dimension-two condensates. This action enjoys a non-perturbative BRST symmetry recently proposed in Capri et al. (Phys. Rev. D 92(4), 045039. doi: 10.1103/PhysRevD.92.045039 arXiv:1506.06995 [hep-th], 2015). Finally, we pay attention to the gluon propagator in different space-time dimensions.
Non-perturbative BRST quantization of Euclidean Yang-Mills theories in Curci-Ferrari gauges
International Nuclear Information System (INIS)
Pereira, A.D.; Sobreiro, R.F.; Sorella, S.P.
2016-01-01
In this paper we address the issue of the non-perturbative quantization of Euclidean Yang-Mills theories in the Curci-Ferrari gauge. In particular, we construct a refined Gribov-Zwanziger action for this gauge, which takes into account the presence of gauge copies as well as the dynamical formation of dimension-two condensates. This action enjoys a non-perturbative BRST symmetry recently proposed in Capri et al. (Phys. Rev. D 92(4), 045039. doi:10.1103/PhysRevD.92.045039. arXiv:1506.06995 [hepth], 2015). Finally, we pay attention to the gluon propagator in different space-time dimensions. (orig.)
Singular pontentials and analytic regularization in classical Yang-Mills equations
International Nuclear Information System (INIS)
Bollini, C.G.; Giambiagi, J.J.; Tiomno, J.
1978-11-01
The class of instanton solutions with 'extension' parameter lambda 2 positive is extended to lambda 2 negative. The nature of the singular sphere of radius 'lambda' is analized in the light of the analytical regularization method. This leads to well defined solutions of the Yang-Mills equations. Some of them are sourceless ('+-io' and 'Vp'), others correspond to currents concentrated on the sphere of singularity ('+' and '-'). Although the equations are non-linear, the 'Vp' solution turns out to be real part of the '+-io' solutions. The anzats of t'Hooft for the superposition of instantons is used to sum the contributions corresponding to lambda 2 with positive and negative signs. A subsequent limiting process allows then the construction of solutions of the 'multipole' type. The general situation of potentials having a denominator D, with a corresponding surface of singularity at D=0, is also considered in the same light [pt
Singular potentials and analytic regularization in classical Yang-Mills equations
International Nuclear Information System (INIS)
Bollini, C.G.; Giambiagi, J.J.; Tiomno, J.
1978-10-01
The class of instanton solutions with 'extension' parameter Λ 2 positive is extended to Λ 2 negative. The nature of the singular sphere of radius |Λ| is analized in the light of the analytical regularization method. This leads to well defined solutions of the Yang - Mills equations. Some of them are sourceless ('+- i o' and 'Vp'), others correspond to currents concentrated on the sphere of singularity ('+' and '-'). Although the equations are non-linear, the 'Vp' solutions turns out to be the real part of the '+- i o' solutions. The anzats of t'Hooft for the superposition of instantons is used to sum the contributions corresponding to Λ 2 with positive and negative signs. A subsequent limiting process allows then the construction of solutions of the 'multipole' type. The general situation of potentials having a denominator D, with a corresponding surface of singularity at D=0, is also considered in the same light. (Author) [pt
Non-perturbative BRST quantization of Euclidean Yang-Mills theories in Curci-Ferrari gauges
Energy Technology Data Exchange (ETDEWEB)
Pereira, A.D. [UFF, Universidade Federal Fluminense, Instituto de Fisica, Campus da Praia Vermelha, Niteroi, RJ (Brazil); Max Planck Institute for Gravitational Physics, Albert Einstein Institute, Potsdam (Germany); UERJ, Universidade do Estado do Rio de Janeiro, Departamento de Fisica Teorica, Rio de Janeiro (Brazil); Sobreiro, R.F. [UFF, Universidade Federal Fluminense, Instituto de Fisica, Campus da Praia Vermelha, Niteroi, RJ (Brazil); Sorella, S.P. [UERJ, Universidade do Estado do Rio de Janeiro, Departamento de Fisica Teorica, Rio de Janeiro (Brazil)
2016-10-15
In this paper we address the issue of the non-perturbative quantization of Euclidean Yang-Mills theories in the Curci-Ferrari gauge. In particular, we construct a refined Gribov-Zwanziger action for this gauge, which takes into account the presence of gauge copies as well as the dynamical formation of dimension-two condensates. This action enjoys a non-perturbative BRST symmetry recently proposed in Capri et al. (Phys. Rev. D 92(4), 045039. doi:10.1103/PhysRevD.92.045039. arXiv:1506.06995 [hepth], 2015). Finally, we pay attention to the gluon propagator in different space-time dimensions. (orig.)
The large N limit of the topological susceptibility of Yang-Mills gauge theory
Energy Technology Data Exchange (ETDEWEB)
Ce, Marco [Scuola Normale Superiore, Pisa (Italy); INFN, Pisa (Italy); Garcia Vera, Miguel [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Humboldt Univ. Berlin (Germany). Inst. fuer Physik; Giusti, Leonardo [Milano Bicocca Univ., Milano (Italy); INFN, Milano Bicocca (Italy); Schaefer, Stefan [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC
2016-10-27
We present a precise computation of the topological susceptibility χ{sub YM} of SU(N) Yang-Mills theory in the large N limit. The computation is done on the lattice, using high-statistics Monte Carlo simulations with N=3,4,5,6 and three different lattice spacings. Two major improvements make it possible to go to finer lattice spacing and larger N compared to previous works. First, the topological charge is implemented through the gradient flow definition; and second, open boundary conditions in the time direction are employed in order to avoid the freezing of the topological charge. The results allow us to extrapolate the dimensionless quantity t{sub 0}{sup 2}χ{sub YM} to the continuum and large N limits with confidence. The accuracy of the final result represents a new quality in the verification of large N scaling.
Adventures of the coupled Yang-Mills oscillators: II. YM-Higgs quantum mechanics
International Nuclear Information System (INIS)
Matinyan, Sergei G; Mueller, Berndt
2006-01-01
We continue our study of the quantum mechanical motion in the x 2 y 2 potentials for n = 2, 3, which arise in the spatially homogeneous limit of the Yang-Mills (YM) equations. In the present paper, we develop a new approach to the calculation of the partition function Z(t) beyond the Thomas-Fermi (TF) approximation by adding a harmonic (Higgs) potential and taking the limit v → 0, where v is the vacuum expectation value of the Higgs field. Using the Wigner-Kirkwood method to calculate higher-order corrections in ℎ, we show that the limit v → 0 leads to power-like singularities of the type v -n , which reflect the possibility of escape of the particle along the channels in the classical limit. We show how these singularities can be eliminated by taking into account the quantum fluctuations dictated by the form of the potential
N=4 supersymmetric Yang Mills scattering amplitudes at high energies. The Regge cut contribution
International Nuclear Information System (INIS)
Bartels, J.; Sabio Vera, A.
2008-07-01
We further investigate, in N=4 supersymmetric Yang Mills theories, the high energy Regge behavior of six-point scattering amplitudes. In particular, for the new Regge cut contribution found in our previous paper, we compute in the leading logarithmic approximation (LLA) the energy spectrum of the BFKL equation in the color octet channel, and we calculate explicitly the two loop corrections to the discontinuities of the amplitudes for the transitions 2→4 and 3→3. We find an explicit solution of the BFKL equation for the octet channel for arbitrary momentum transfers and investigate the intercepts of the Regge singularities in this channel. As an important result we find that the universal collinear and infrared singularities of the BDS formula are not affected by this Regge-cut contribution. (orig.)
Unconstrained off-shell N=3 supersymmetric Yang-Mills theory
International Nuclear Information System (INIS)
Galperin, A.; Ivanov, E.; Kalitzin, S.; Ogievetsky, V.; Sokatchev, E.
1984-01-01
The harmonic superspace is used to build up an unconstrained off-shell formulation of N=3 supersymmetric Yang-Mills theory. The theory is defined in an analytic N=3 superspace having M 4 x(SU(3)/U(1)xU(1) as an even part. The basic objects are the analytic potentials which serve as gauge connections entering harmonic derivatives. The action is an integral over analytic superspace. The Lagrange density is surprisingly simple and it is gauge invariant up to total harmonic derivative. The equations of motion are integrability conditions on the internal space SU(3)/U(1)xU(1). The jumping over the ''N=3 barrier'' became possible due to the infinite number of auxiliary fields
On solutions of Einstein and Einstein-Yang-Mills equations with (maximal) conformal subsymmetries
International Nuclear Information System (INIS)
Sinzinkayo, S.; Demaret, J.
1985-01-01
The maximal subgroups of the conformal group (which have in common as a subgroup the group of pure spatial rotations) are considered as isometry groups of conformally flat space-times. The corresponding cosmological solutions of Einstein's field equations are identified. For each of them, the possibility is investigated that it could be generated by an SU(2) Yang-Mills field built, via the Corrigan-Fairlie-'t Hooft-Wilczek ansatz, from a scalar field identical with the square root of the conformal factor defining the space-time metric tensor. In particular, the Einstein cosmological model can be generated in this manner, but in the framework of strong gravity only, a micro-Einstein universe being then viewed as a possible model for a hadron. (author)
Screening masses in quenched (2+1)d Yang-Mills theory: Universality from dynamics?
International Nuclear Information System (INIS)
Frigori, Rafael B.
2010-01-01
We compute the spectrum of gluonic screening-masses in the 0 ++ channel of quenched 3d Yang-Mills theory near the phase-transition. Our finite-temperature lattice simulations are performed at scaling region, using state-of-art techniques for thermalization and spectroscopy, which allows for thorough data extrapolations to thermodynamic limit. Ratios among mass-excitations with the same quantum numbers on the gauge theory, 2d Ising and λφ 4 models are compared, resulting in a nice agreement with predictions from universality. In addition, a gauge-to-scalar mapping, previously employed to fit QCD Green's functions at deep IR, is verified to dynamically describe these universal spectroscopic patterns.
Compact invariant sets of the static spherically symmetric Einstein-Yang-Mills equations
International Nuclear Information System (INIS)
Starkov, Konstantin E.
2010-01-01
In this Letter we obtain results concerning compact invariant sets of the static spherically symmetric Einstein-Yang-Mills (EYM) equations with help of studies of its localization. Let a be a cosmological constant and s be another parameter entering into these equations which is used for considering the physical time as a temporal variable, with s=1, while s=-1 is used for considering the physical time as a spatial variable. We show that in case s=1; a 0 the set of all compact invariant sets consists of two equilibrium points only. Further, we state that in cases s=-1; a 0 there are only two equilibrium points and there are no periodic orbits. In addition, we prove that in the last two cases there are neither homoclinic orbits nor heteroclinic orbits as well.
The universe as a topological defect in a higher-dimensional Einstein-Yang-Mills theory
International Nuclear Information System (INIS)
Nakamura, A.; Shiraishi, K.
1989-04-01
An interpretation is suggested that a spontaneous compactification of space-time can be regarded as a topological defect in a higher-dimensional Einstein-Yang-Mills (EYM) theory. We start with D-dimensional EYM theory in our present analysis. A compactification leads to a D-2 dimensional effective action of Abelian gauge-Higgs theory. We find a 'vortex' solution in the effective theory. Our universe appears to be confined in a center of a 'vortex', which has D-4 large dimensions. In this paper we show an example with SU (2) symmetry in the original EYM theory, and the resulting solution is found to be equivalent to the 'instanton-induced compactification'. The cosmological implication is also mentioned. (author)
Coupling of Yang-Mills to N=4, d=4 supergravity
International Nuclear Information System (INIS)
Bergshoeff, E.; Koh, I.G.; Sezgin, E.
1985-01-01
We couple N=4, d=4 supersymmetric Yang-Mills theory to supergravity. The scalars of the theory parametrize the coset (SO(n,6)/[SO(n)xSO(6)])xSU(1,1)/U(1)). Keeping the composite local SO(n)xSO(6)xU(1) invariance intact, we gauge an (n+6) parameter subgroup of SO(n,6) which is either (i) SU(2)xSU(2)xH(dim H=n), (ii) SO(4,1)xH(dim H=n-4) or (iii) SO(6,1)xH(dim H=n-15). In all these cases the theory has an indefinite potential. (orig.)
Calculating the anomalous supersymmetry breaking in super Yang-Mills theories with local coupling
International Nuclear Information System (INIS)
Kraus, E.
2002-01-01
Supersymmetric Yang-Mills theories with local gauge coupling have a new type of anomalous breaking, which appears as a breaking of supersymmetry in the Wess-Zumino gauge. The anomalous breaking generates the two-loop order of the gauge β function in terms of the one-loop β function and the anomaly coefficient. We determine the anomaly coefficient in the Wess-Zumino gauge by solving the relevant supersymmetry identities. For this purpose we use a background gauge and show that the anomaly coefficient is uniquely determined by convergent one-loop integrals. When evaluating the one-loop diagrams in the background gauge, it is seen that the anomaly coefficient is determined by the Feynman-gauge value of the one-loop vertex function to G μν G-tilde μν at vanishing momenta
Duality symmetry of N=4 Yang-Mills theory on T3
International Nuclear Information System (INIS)
Hacquebord, F.; Verlinde, H.
1997-01-01
We study the spectrum of BPS states in N=4 supersymmetric U(N) Yang-Mills theory. This theory has been proposed to describe M-theory on T 3 in the discrete light-cone formalism. We find that the degeneracy of irreducible BPS bound states in this model exhibits a (partially hidden) SL(5,Z) duality symmetry. Besides the electro-magnetic symmetry, this duality group also contains Nahm-like transformations that interchange the rank N of the gauge group with some of the magnetic or electric fluxes. In the M-theory interpretation, this mapping amounts to a reflection that interchanges the longitudinal direction with one of the transverse directions. (orig.)
N=4 Super Yang-Mills: the harmonic oscillator of interacting quantum field theories
International Nuclear Information System (INIS)
Minahan, Joseph A.
2012-01-01
Full text: In this talk I discuss progress over the last ten years in solving N=4 Super Yang-Mills in the planar limit, where the number of colors is taken to infinity. The key to the solution is mapping the theory to an integrable one-dimensional spin chain. At the leading perturbative level the spin-chain in question is the Heisenberg chain which was solved by Bethe in 1931. We discuss how the analysis of spin-chains ultimately allows to compute the spectrum of observables in the theory for any value of the coupling constant. I then discuss ongoing work to find the so-called three-point functions, which when combined with the spectrum would completely solve the theory in the planar limit. (author)
Open spin chains in super Yang-Mills at higher loops: some potential problems with integrability
International Nuclear Information System (INIS)
Agarwal, Abhishek
2006-01-01
The super Yang-Mills duals of open strings attached to maximal giant gravitons are studied in perturbation theory. It is shown that non-BPS baryonic excitations of the gauge theory can be studied within the paradigm of open quantum spin chains even beyond the leading order in perturbation theory. The open spin chain describing the two loop mixing of non-BPS giant gravitons charged under an su(2) of the so(6) R symmetry group is explicitly constructed. It is also shown that although the corresponding open spin chain is integrable at the one loop order, there is a potential breakdown of integrability at two and higher loops. The study of integrability is performed using coordinate Bethe ansatz techniques
Integrable open spin chain in Super Yang-Mills and the plane-wave/SYM duality
International Nuclear Information System (INIS)
Chen Bin; Wang Xiaojun; Wu Yongshi
2004-01-01
We investigate the integrable structures in an N = 2 superconfomal Sp(N) Yang-Mills theory with matter, which is dual to an open+closed string system. We restrict ourselves to the BMN operators that correspond to free string states. In the closed string sector, an integrable structure is inherited from its parent theory, N = 4 SYM. For the open string sector, the planar one-loop mixing matrix for gauge invariant holomorphic operators is identified with the Hamiltonian of an integrable SU(3) open spin chain. Using the K-matrix formalism we identify the integrable open-chain boundary conditions that correspond to string boundary conditions. The solutions to the algebraic Bethe ansatz equations (ABAE) with a few impurities are shown to recover the anomalous dimensions that exactly match the spectrum of free open string in the plane-wave background. We also discuss the properties of the solutions of ABAE beyond the BMN regime. (author)
Maxwell, Yang-Mills, Weyl and eikonal fields defined by any null shear-free congruence
Kassandrov, Vladimir V.; Rizcallah, Joseph A.
We show that (specifically scaled) equations of shear-free null geodesic congruences on the Minkowski space-time possess intrinsic self-dual, restricted gauge and algebraic structures. The complex eikonal, Weyl 2-spinor, SL(2, ℂ) Yang-Mills and complex Maxwell fields, the latter produced by integer-valued electric charges (“elementary” for the Kerr-like congruences), can all be explicitly associated with any shear-free null geodesic congruence. Using twistor variables, we derive the general solution of the equations of the shear-free null geodesic congruence (as a modification of the Kerr theorem) and analyze the corresponding “particle-like” field distributions, with bounded singularities of the associated physical fields. These can be obtained in a straightforward algebraic way and exhibit nontrivial collective dynamics simulating physical interactions.
Towards a unified treatment of Yang-Mills and Higgs fields
International Nuclear Information System (INIS)
Balakrishna, B.S.; Guersey, F.; Wali, K.C.
1991-01-01
Starting from a noncommutative algebra scrA of the form scrC direct-product scrM, where scrC is the algebra of smooth functions on space-time and scrM is the algebra of nxn Hermitian matrices, we construct an exterior algebra of differential forms over scrA. We use the one-forms of this algebra to describe Yang-Mills and Higgs fields on a similar footing and construct a Lagrangian from its two-forms. We show how, in the resulting geometrical description, a Higgs potential that leads to spontaneous symmetry breaking arises naturally. We discuss the application of this formalism to the bosonic sectors of the standard electroweak theory and a grand-unified model based on SU(5)direct-product U(1)
Evolution of nonlinear perturbations inside Einstein-Yang-Mills black holes
International Nuclear Information System (INIS)
Donets, E.E.; Tentyukov, M.N.; Tsulaya, M.M.
1998-01-01
We present our results on numerical study of evolution of nonlinear perturbations inside spherically symmetric black holes in the SU(2) Einstein-Yang-Mills (EYM) theory. Recent developments demonstrate a new type of the behaviour of the metric for EYM black hole interiors; the generic metric exhibits an infinitely oscillating approach to the singularity, which is a spacelike but not of the mixmaster type. The evolution of various types of spherically symmetric perturbations, propagating from the internal vicinity of the external horizon towards the singularity is investigated in a self-consistent way using an adaptive numerical algorithm. The obtained results give strong numerical evidence in favor of nonlinear stability of the generic EYM black hole interiors. Alternatively, the EYM black hole interiors of S (schwarzschild)-type, which form only a zero measure subset in the space of all internal solutions are found to be unstable and transform to the generic type as perturbations are developed
On the restoration of supersymmetry in twisted two-dimensional lattice Yang-Mills theory
International Nuclear Information System (INIS)
Catterall, Simon
2007-01-01
We study a discretization of N = 2 super Yang-Mills theory which possesses a single exact supersymmetry at non-zero lattice spacing. This supersymmetry arises after a reformulation of the theory in terms of twisted fields. In this paper we derive the action of the other twisted supersymmetries on the component fields and study, using Monte Carlo simulation, a series of corresponding Ward identities. Our results for SU(2) and SU(3) support a restoration of these additional supersymmetries without fine tuning in the infinite volume continuum limit. Additionally we present evidence supporting a restoration of (twisted) rotational invariance in the same limit. Finally we have examined the distribution of scalar field eigenvalues and find evidence for power law tails extending out to large eigenvalue. We argue that these tails indicate that the classical moduli space does not survive in the quantum theory
The 1+1 SU(2) Yang-Mills path integral
International Nuclear Information System (INIS)
Swanson, Mark S
2004-01-01
The path integral for SU(2) invariant two-dimensional Yang-Mills theory is recast in terms of the chromoelectric field strength by integrating the gauge fields from the theory. Implementing Gauss's law as a constraint in this process induces a topological term in the action that is no longer invariant under large gauge transformations. For the case that the partition function is considered over a circular spatial degree of freedom, it is shown that the effective action of the path integral is quantum mechanically WKB exact and localizes onto a set of chromoelectric zero modes satisfying antiperiodic boundary conditions. Summing over the zero modes yields a partition function that can be reexpressed using the Poisson resummation technique, allowing an easy determination of the energy spectrum, which is found to be identical to that given by other approaches
Supercurrent and the Adler-Bardeen theorem in coupled supersymmetric Yang-Mills theories
International Nuclear Information System (INIS)
Ensign, P.; Mahanthappa, K.T.
1987-01-01
We construct the supercurrent and a supersymmetric current which satisfies the Adler-Bardeen theorem in supersymmetric Yang-Mills theory coupled to non-self-interacting chiral matter. Using the formulation recently developed by Grisaru, Milewski, and Zanon, supersymmetry and gauge invariance are maintained with supersymmetric background-field theory and regularization by dimensional reduction. We verify the finiteness of the supercurrent to one loop, and the Adler-Bardeen theorem to two loops by explicit calculations in the minimal-subtraction scheme. We then demonstrate the subtraction-scheme independence of the one-loop Adler-Bardeen anomaly and prove the existence of a subtraction scheme in which the Adler-Bardeen theorem is satisfied to all orders in perturbation theory
Regge meets collinear in strongly-coupled N=4 super Yang-Mills
Energy Technology Data Exchange (ETDEWEB)
Sprenger, Martin [Institut für Theoretische Physik, Eidgenössische Technische Hochschule Zürich,Wolfgang-Pauli-Strasse 27, 8093 Zürich (Switzerland)
2017-01-10
We revisit the calculation of the six-gluon remainder function in planar N=4 super Yang-Mills theory from the strong coupling TBA in the multi-Regge limit and identify an infinite set of kinematically subleading terms. These new terms can be compared to the strong coupling limit of the finite-coupling expressions for the impact factor and the BFKL eigenvalue proposed by Basso et al. in https://www.doi.org/10.1007/JHEP01(2015)027, which were obtained from an analytic continuation of the Wilson loop OPE. After comparing the results order by order in those subleading terms, we show that it is possible to precisely map both formalisms onto each other. A similar calculation can be carried out for the seven-gluon amplitude, the result of which shows that the central emission vertex does not become trivial at strong coupling.
Emergent gravity and noncommutative branes from Yang-Mills matrix models
International Nuclear Information System (INIS)
Steinacker, Harold
2009-01-01
The framework of emergent gravity arising from Yang-Mills matrix models is developed further, for general noncommutative branes embedded in R D . The effective metric on the brane turns out to have a universal form reminiscent of the open string metric, depending on the dynamical Poisson structure and the embedding metric in R D . A covariant form of the tree-level equations of motion is derived, and the Newtonian limit is discussed. This points to the necessity of branes in higher dimensions. The quantization is discussed qualitatively, which singles out the IKKT model as a prime candidate for a quantum theory of gravity coupled to matter. The Planck scale is then identified with the scale of N=4 SUSY breaking. A mechanism for avoiding the cosmological constant problem is exhibited
Spectral parameters for scattering amplitudes in N=4 super Yang-Mills theory
International Nuclear Information System (INIS)
Ferro, Livia; Łukowski, Tomasz; Meneghelli, Carlo; Plefka, Jan; Staudacher, Matthias
2014-01-01
Planar N=4 Super Yang-Mills theory appears to be a quantum integrable four-dimensional conformal theory. This has been used to find equations believed to describe its exact spectrum of anomalous dimensions. Integrability seemingly also extends to the planar space-time scattering amplitudes of the N=4 model, which show strong signs of Yangian invariance. However, in contradistinction to the spectral problem, this has not yet led to equations determining the exact amplitudes. We propose that the missing element is the spectral parameter, ubiquitous in integrable models. We show that it may indeed be included into recent on-shell approaches to scattering amplitude integrands, providing a natural deformation of the latter. Under some constraints, Yangian symmetry is preserved. Finally we speculate that the spectral parameter might also be the regulator of choice for controlling the infrared divergences appearing when integrating the integrands in exactly four dimensions
Coupling of Yang-Mills to N=4, d=4 supergravity
International Nuclear Information System (INIS)
Bergshoeff, E.; Koh, I.G.; Sezgin, E.
1985-01-01
We couple N=4, d=4 supersymmetric Yang-Mills theory to supergravity. The scalars of the theory parametrize the coset ((SO(n,6)/SO(n)xSO(6))x((SU(1,1)/U(1)). Keeping the composite local SO(n)xSO(6)xU(1) invariance intact, we gauge an (n+6) parameter subgroup of SO(n,6) which is either (i) SU(2)xSU(2)xH (dim H=n), (ii) SO(4,1)xH (dim H=n-4) or (iii) SO(6,1)xH (dim H=n-15). In all these cases the theory has an indefinite potential. (author)
Lattice simulation of a center symmetric three dimensional effective theory for SU(2) Yang-Mills
International Nuclear Information System (INIS)
Smith, Dominik
2010-01-01
We present lattice simulations of a center symmetric dimensionally reduced effective field theory for SU(2) Yang Mills which employ thermal Wilson lines and three-dimensional magnetic fields as fundamental degrees of freedom. The action is composed of a gauge invariant kinetic term, spatial gauge fields and a potential for theWilson line which includes a ''fuzzy'' bag term to generate non-perturbative fluctuations between Z(2) degenerate ground states. The model is studied in the limit where the gauge fields are set to zero as well as the full model with gauge fields. We confirm that, at moderately weak coupling, the ''fuzzy'' bag term leads to eigenvalue repulsion in a finite region above the deconfining phase transition which shrinks in the extreme weak-coupling limit. A non-trivial Z(N) symmetric vacuum arises in the confined phase. The effective potential for the Polyakov loop in the theory with gauge fields is extracted from the simulations including all modes of the loop as well as for cooled configurations where the hard modes have been averaged out. The former is found to exhibit a non-analytic contribution while the latter can be described by a mean-field like ansatz with quadratic and quartic terms, plus a Vandermonde potential which depends upon the location within the phase diagram. Other results include the exact location of the phase boundary in the plane spanned by the coupling parameters, correlation lengths of several operators in the magnetic and electric sectors and the spatial string tension. We also present results from simulations of the full 4D Yang-Mills theory and attempt to make a qualitative comparison to the 3D effective theory. (orig.)
Lattice simulation of a center symmetric three dimensional effective theory for SU(2) Yang-Mills
Energy Technology Data Exchange (ETDEWEB)
Smith, Dominik
2010-11-17
We present lattice simulations of a center symmetric dimensionally reduced effective field theory for SU(2) Yang Mills which employ thermal Wilson lines and three-dimensional magnetic fields as fundamental degrees of freedom. The action is composed of a gauge invariant kinetic term, spatial gauge fields and a potential for theWilson line which includes a ''fuzzy'' bag term to generate non-perturbative fluctuations between Z(2) degenerate ground states. The model is studied in the limit where the gauge fields are set to zero as well as the full model with gauge fields. We confirm that, at moderately weak coupling, the ''fuzzy'' bag term leads to eigenvalue repulsion in a finite region above the deconfining phase transition which shrinks in the extreme weak-coupling limit. A non-trivial Z(N) symmetric vacuum arises in the confined phase. The effective potential for the Polyakov loop in the theory with gauge fields is extracted from the simulations including all modes of the loop as well as for cooled configurations where the hard modes have been averaged out. The former is found to exhibit a non-analytic contribution while the latter can be described by a mean-field like ansatz with quadratic and quartic terms, plus a Vandermonde potential which depends upon the location within the phase diagram. Other results include the exact location of the phase boundary in the plane spanned by the coupling parameters, correlation lengths of several operators in the magnetic and electric sectors and the spatial string tension. We also present results from simulations of the full 4D Yang-Mills theory and attempt to make a qualitative comparison to the 3D effective theory. (orig.)
Space/time non-commutative field theories and causality
International Nuclear Information System (INIS)
Bozkaya, H.; Fischer, P.; Pitschmann, M.; Schweda, M.; Grosse, H.; Putz, V.; Wulkenhaar, R.
2003-01-01
As argued previously, amplitudes of quantum field theories on non-commutative space and time cannot be computed using naive path integral Feynman rules. One of the proposals is to use the Gell-Mann-Low formula with time-ordering applied before performing the integrations. We point out that the previously given prescription should rather be regarded as an interaction-point time-ordering. Causality is explicitly violated inside the region of interaction. It is nevertheless a consistent procedure, which seems to be related to the interaction picture of quantum mechanics. In this framework we compute the one-loop self-energy for a space/time non-commutative φ 4 theory. Although in all intermediate steps only three-momenta play a role, the final result is manifestly Lorentz covariant and agrees with the naive calculation. Deriving the Feynman rules for general graphs, we show, however, that such a picture holds for tadpole lines only. (orig.)
Stability of a non-commutative Jackiw-Teitelboim gravity
Energy Technology Data Exchange (ETDEWEB)
Vassilevich, D.V. [Universitaet Leipzig, Institut fuer Theoretische Physik, Postfach 100 920, Leipzig (Germany); St. Petersburg University, V.A. Fock Institute of Physics, St. Petersburg (Russian Federation); Fresneda, R.; Gitman, D.M. [Sao Paulo Univ. (Brazil). Inst. de Fisica
2006-07-15
We start with a non-commutative version of the Jackiw-Teitelboim gravity in two dimensions which has a linear potential for the dilaton fields. We study whether it is possible to deform this model by adding quadratic terms to the potential but preserving the number of gauge symmetries. We find that no such deformation exists (provided one does not twist the gauge symmetries). (orig.)
Semiclassical and quantum motions on the non-commutative plane
International Nuclear Information System (INIS)
Baldiotti, M.C.; Gazeau, J.P.; Gitman, D.M.
2009-01-01
We study the canonical and the coherent state quantizations of a particle moving in a magnetic field on the non-commutative plane. Using a θ-modified action, we perform the canonical quantization and analyze the gauge dependence of the theory. We compare coherent states quantizations obtained through Malkin-Man'ko states and circular squeezed states. The relation between these states and the 'classical' trajectories is investigated, and we present numerical explorations of some semiclassical quantities.
Semiclassical and quantum motions on the non-commutative plane
Energy Technology Data Exchange (ETDEWEB)
Baldiotti, M.C., E-mail: baldiott@fma.if.usp.b [Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318-CEP, 05315-970 Sao Paulo, S.P. (Brazil); Gazeau, J.P., E-mail: gazeau@apc.univ-paris7.f [Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318-CEP, 05315-970 Sao Paulo, S.P. (Brazil); Gitman, D.M., E-mail: gitman@dfn.if.usp.b [Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318-CEP, 05315-970 Sao Paulo, S.P. (Brazil)
2009-10-19
We study the canonical and the coherent state quantizations of a particle moving in a magnetic field on the non-commutative plane. Using a theta-modified action, we perform the canonical quantization and analyze the gauge dependence of the theory. We compare coherent states quantizations obtained through Malkin-Man'ko states and circular squeezed states. The relation between these states and the 'classical' trajectories is investigated, and we present numerical explorations of some semiclassical quantities.
Commutative and Non-commutative Parallelogram Geometry: an Experimental Approach
Bertram, Wolfgang
2013-01-01
By "parallelogram geometry" we mean the elementary, "commutative", geometry corresponding to vector addition, and by "trapezoid geometry" a certain "non-commutative deformation" of the former. This text presents an elementary approach via exercises using dynamical software (such as geogebra), hopefully accessible to a wide mathematical audience, from undergraduate students and high school teachers to researchers, proceeding in three steps: (1) experimental geometry, (2) algebra (linear algebr...
Euler Polynomials and Identities for Non-Commutative Operators
De Angelis, V.; Vignat, C.
2015-01-01
Three kinds of identities involving non-commutating operators and Euler and Bernoulli polynomials are studied. The first identity, as given by Bender and Bettencourt, expresses the nested commutator of the Hamiltonian and momentum operators as the commutator of the momentum and the shifted Euler polynomial of the Hamiltonian. The second one, due to J.-C. Pain, links the commutators and anti-commutators of the monomials of the position and momentum operators. The third appears in a work by Fig...
Non-topological non-commutativity in string theory
International Nuclear Information System (INIS)
Guttenberg, S.; Herbst, M.; Kreuzer, M.; Rashkov, R.
2008-01-01
Quantization of coordinates leads to the non-commutative product of deformation quantization, but is also at the roots of string theory, for which space-time coordinates become the dynamical fields of a two-dimensional conformal quantum field theory. Appositely, open string diagrams provided the inspiration for Kontsevich's solution of the long-standing problem of quantization of Poisson geometry by virtue of his formality theorem. In the context of D-brane physics non-commutativity is not limited, however, to the topological sector. We show that non-commutative effective actions still make sense when associativity is lost and establish a generalized Connes-Flato-Sternheimer condition through second order in a derivative expansion. The measure in general curved backgrounds is naturally provided by the Born-Infeld action and reduces to the symplectic measure in the topological limit, but remains non-singular even for degenerate Poisson structures. Analogous superspace deformations by RR-fields are also discussed. (Abstract Copyright [2008], Wiley Periodicals, Inc.)
The Analytic Structure of Scattering Amplitudes in N = 4 Super-Yang-Mills Theory
Litsey, Sean Christopher
We begin the dissertation in Chapter 1 with a discussion of tree-level amplitudes in Yang-. Mills theories. The DDM and BCJ decompositions of the amplitudes are described and. related to one another by the introduction of a transformation matrix. This is related to the. Kleiss-Kuijf and BCJ amplitude identities, and we conjecture a connection to the existence. of a BCJ representation via a condition on the generalized inverse of that matrix. Under. two widely-believed assumptions, this relationship is proved. Switching gears somewhat, we introduce the RSVW formulation of the amplitude, and the extension of BCJ-like features to residues of the RSVW integrand is proposed. Using the previously proven connection of BCJ representations to the generalized inverse condition, this extension is validated, including a version of gravitational double copy. The remainder of the dissertation involves an analysis of the analytic properties of loop. amplitudes in N = 4 super-Yang-Mills theory. Chapter 2 contains a review of the planar case, including an exposition of dual variables and momentum twistors, dual conformal symmetry, and their implications for the amplitude. After defining the integrand and on-shell diagrams, we explain the crucial properties that the amplitude has no poles at infinite momentum and that its leading singularities are dual-conformally-invariant cross ratios, and can therefore be normalized to unity. We define the concept of a dlog form, and show that it is a feature of the planar integrand as well. This leads to the definition of a pure integrand basis. The proceeding setup is connected to the amplituhedron formulation, and we put forward the hypothesis that the amplitude is determined by zero conditions. Chapter 3 contains the primary computations of the dissertation. This chapter treats. amplitudes in fully nonplanar N = 4 super-Yang-Mills, analyzing the conjecture that they. follow the pattern of having no poles at infinity, can be written in dlog
Non-commutative and commutative vacua effects in a scalar torsion scenario
Energy Technology Data Exchange (ETDEWEB)
Sheikhahmadi, Haidar, E-mail: h.sh.ahmadi@gmail.com [Department of Physics, Faculty of Science, University of Kurdistan, Sanandaj (Iran, Islamic Republic of); Aghamohammadi, Ali, E-mail: a.aghamohamadi@iausdj.ac.ir [Sanandaj Branch, Islamic Azad University, Sanandaj (Iran, Islamic Republic of); Saaidi, Khaled, E-mail: ksaaidi@uok.ac.ir [Department of Physics, Faculty of Science, University of Kurdistan, Sanandaj (Iran, Islamic Republic of)
2015-10-07
In this work, the effects of non-commutative and commutative vacua on the phase space generated by a scalar field in a scalar torsion scenario are investigated. For both classical and quantum regimes, the commutative and non-commutative cases are compared. To take account the effects of non-commutativity, two well known non-commutative parameters, θ and β, are introduced. It should be emphasized, the effects of β which is related to momentum sector has more key role in comparison to θ which is related to space sector. Also the different boundary conditions and mathematical interpretations of non-commutativity are explored.
Non-commutative and commutative vacua effects in a scalar torsion scenario
International Nuclear Information System (INIS)
Sheikhahmadi, Haidar; Aghamohammadi, Ali; Saaidi, Khaled
2015-01-01
In this work, the effects of non-commutative and commutative vacua on the phase space generated by a scalar field in a scalar torsion scenario are investigated. For both classical and quantum regimes, the commutative and non-commutative cases are compared. To take account the effects of non-commutativity, two well known non-commutative parameters, θ and β, are introduced. It should be emphasized, the effects of β which is related to momentum sector has more key role in comparison to θ which is related to space sector. Also the different boundary conditions and mathematical interpretations of non-commutativity are explored.
Non-commutative and commutative vacua effects in a scalar torsion scenario
Directory of Open Access Journals (Sweden)
Haidar Sheikhahmadi
2015-10-01
Full Text Available In this work, the effects of non-commutative and commutative vacua on the phase space generated by a scalar field in a scalar torsion scenario are investigated. For both classical and quantum regimes, the commutative and non-commutative cases are compared. To take account the effects of non-commutativity, two well known non-commutative parameters, θ and β, are introduced. It should be emphasized, the effects of β which is related to momentum sector has more key role in comparison to θ which is related to space sector. Also the different boundary conditions and mathematical interpretations of non-commutativity are explored.
International Nuclear Information System (INIS)
Nunez, Alvaro; Starinets, Andrei O.
2003-01-01
We use the Lorentzian AdS/CFT prescription to find the poles of the retarded thermal Green's functions of N=4 SU(N) supersymmetric Yang-Mills theory in the limit of large N and large 't Hooft coupling. In the process, we propose a natural definition for quasinormal modes in an asymptotically AdS spacetime, with boundary conditions dictated by the AdS/CFT correspondence. The corresponding frequencies determine the dispersion laws for the quasiparticle excitations in the dual finite-temperature gauge theory. Correlation functions of operators dual to massive scalar, vector and gravitational perturbations in a five-dimensional AdS-Schwarzschild background are considered. We find asymptotic formulas for quasinormal frequencies in the massive scalar and tensor cases, and an exact expression for vector perturbations. In the long-distance, low-frequency limit we recover results of the hydrodynamic approximation to thermal Yang-Mills theory
Núñez, Alvaro; Starinets, Andrei O.
2003-06-01
We use the Lorentzian AdS/CFT prescription to find the poles of the retarded thermal Green’s functions of N=4 SU(N) supersymmetric Yang-Mills theory in the limit of large N and large ’t Hooft coupling. In the process, we propose a natural definition for quasinormal modes in an asymptotically AdS spacetime, with boundary conditions dictated by the AdS/CFT correspondence. The corresponding frequencies determine the dispersion laws for the quasiparticle excitations in the dual finite-temperature gauge theory. Correlation functions of operators dual to massive scalar, vector and gravitational perturbations in a five-dimensional AdS-Schwarzschild background are considered. We find asymptotic formulas for quasinormal frequencies in the massive scalar and tensor cases, and an exact expression for vector perturbations. In the long-distance, low-frequency limit we recover results of the hydrodynamic approximation to thermal Yang-Mills theory.
D = 4 Yang-Mills correlators from NSR strings on AdS5 x S5
International Nuclear Information System (INIS)
Polyakov, D.
1999-07-01
In our previous work (hep-th/9812044) we have proposed the sigma-model action, conjectured to be the NSR analogue of superstring theory on AdS 5 x S 5 . This sigma-model is the NSR superstring action with potential term corresponding to the exotic 5-form vertex operator (branelike state). This 5-form potential plays the role of cosmological term, effectively curving the flat space-time geometry to that of AdS 5 x S 5 . In this paper we study this ansatz in more detail and provide the derivation of the correlators of the four-dimensional super Yang-Mills theory from the above mentioned sigma-model. In particular, we show that the correlation function of two dilaton vertex operators in such a model reproduces the well-known result for the two-point function in N = 4 four-dimensional super Yang-Mills theory. (author)
International Nuclear Information System (INIS)
Bogolubov, N.N. Jr.; Prykarpatsky, A.K.; Taneri, U.; Prykarpatsky, Y.A.
2009-01-01
Based on analysis of reduced geometric structures on fibered manifolds, invariant under action of a certain symmetry group, we construct the symplectic structures associated with connection forms on suitable principal fiber bundles. The application to the non-standard Hamiltonian analysis of the Maxwell and Yang-Mills type dynamical systems is presented. A symplectic reduction theory of the classical Maxwell electromagnetic field equations is formulated, the important Lorentz condition, ensuring the existence of electromagnetic waves, is naturally included into the Hamiltonian picture, thereby solving the well known Dirac, Fock and Podolsky problem. The symplectically reduced Poissonian structures and the related classical minimal interaction principle, concerning the Yang-Mills type equations, are considered. (author)
International Nuclear Information System (INIS)
Naito, S.
1976-01-01
We derive commutation relations (CR's) between gauge-invariant quantities in the Yang-Mills field theory by applying the Peierls method. The CR's obtained are different from those given by Mandelstam in his gauge-independent, path-dependent formalism. However, our CR's are shown to give a consistently quantized field theory, while his CR's do not. In fact, there exist systematic errors in Mandelstam's treatment of the covariant Green's functions. On the other hand, if we correctly treat covariant Green's functions guided by his procedure, our CR's are shown to lead to the same Feynman rules for the Yang-Mills field as prescribed by Feynman, DeWitt, Faddeev and Popov, and Mandelstam
The one-loop partition function of N=4 super-Yang-Mills theory on RxS3
International Nuclear Information System (INIS)
Spradlin, Marcus; Volovich, Anastasia
2005-01-01
We study weakly coupled SU(N)N=4 super-Yang-Mills theory on RxS 3 at infinite N, which has interesting thermodynamics, including a Hagedorn transition, even at zero Yang-Mills coupling. We calculate the exact one-loop partition function below the Hagedorn temperature. Our calculation employs the representation of the one-loop dilatation operator as a spin chain Hamiltonian acting on neighboring sites and a generalization of Polya's counting of necklaces (gauge-invariant operators) to include necklaces with a 'pendant' (an operator which acts on neighboring beads). We find that the one-loop correction to the Hagedorn temperature is δlnT H =+λ/8π 2
On the field/string theory approach to theta dependence in large N Yang-Mills theory
International Nuclear Information System (INIS)
Gabadadze, Gregory
1999-01-01
The theta dependence of the vacuum energy in large N Yang-Mills theory has been studied some time ago by Witten using a duality of large N gauge theories with the string theory compactified on a certain space-time. We show that within the field theory context vacuum fluctuations of the topological charge give rise to the vacuum energy consistent with the string theory computation. Furthermore, we calculate 1/N suppressed corrections to the string theory result. The reconciliation of the string and field theory approaches is based on the fact that the gauge theory instantons carry zerobrane charge in the corresponding D-brane construction of Yang-Mills theory. Given the formula for the vacuum energy we study certain aspects of stability of the false vacua of the model for different realizations of the initial conditions. The vacuum structure appears to be different depending on whether N is infinite or, alternatively, large but finite
On N=8 supergravity in AdS5 and N=4 superconformal Yang-Mills theory
International Nuclear Information System (INIS)
Ferrara, S.; Zaffaroni, A.; Froensdal, C.
1998-01-01
We discuss the spectrum of states of IIB supergravity on AdS 5 x S 5 in a manifest SU(2,2/4) invariant setting. The boundary fields are described in terms of N=4 superconformal Yang-Mills theory and the proposed correspondence between supergravity in AdS 5 and superconformal invariant singleton theory at the boundary is formulated in a N=4 superfield covariant language. (orig.)
Three-loop renormalization of the N=1, N=2, N=4 supersymmetric Yang-Mills theories
International Nuclear Information System (INIS)
Velizhanin, V.N.
2009-01-01
We calculate the renormalization constants of the N=1, N=2, N=4 supersymmetric Yang-Mills theories in an arbitrary covariant gauge in the dimensional reduction scheme up to three loops. We have found, that the beta-functions for N=1 and N=4 SYM theories are the same from the different triple vertices. This means that the dimensional reduction scheme works correctly in these models up to third order of perturbative theory.
International Nuclear Information System (INIS)
Fucito, F.
1997-01-01
The aim of this talk is to give a brief introduction to the problem of confinement in QCD and N = 2 globally supersymmetric Yang-Mills gauge theories (SYM). While avoiding technicalities as much as possible I will try to emphasize the physical ideas which lie behind the picture of confinement as a consequence of the vacua of QCD to be a dual superconductor. Finally I review the implementation of this picture in the framework of N = 2 SYM. (author)
((F, D1), D3) bound state, S-duality and noncommutative open string/Yang-Mills theory
International Nuclear Information System (INIS)
Lu, J.X.; Roy, S.; Singh, H.
2000-01-01
We study decoupling limits and S-dualities for noncommutative open string/Yang-Mills theory in a gravity setup by considering an SL(2,Z) invariant supergravity solution of the form ((F, D1), D3) bound state of type IIB string theory. This configuration can be regarded as D3-branes with both electric and magnetic fields turned on along one of the spatial directions of the brane and preserves half of the space-time supersymmetries of the string theory. Our study indicates that there exists a decoupling limit for which the resulting theory is an open string theory defined in a geometry with noncommutativity in both space-time and space-space directions. We study S-duality of this noncommutative open string (NCOS) and find that the same decoupling limit in the S-dual description gives rise to a space-space noncommutative Yang-Mills theory (NCYM). We also discuss independently the decoupling limit for NCYM in this D3 brane background. Here we find that S-duality of NCYM theory does not always give a NCOS theory. Instead, it can give an ordinary Yang-Mills with a singular metric and an infinitely large coupling. We also find that the open string coupling relation between the two S-duality related theories is modified such that S-duality of a strongly coupled open-string/Yang-Mills theory does not necessarily give a weakly coupled theory. The relevant gravity dual descriptions of NCOS/NCYM are also given. (author)
International Nuclear Information System (INIS)
Nikolaevskij, E.S.; Shchur, L.N.
1983-01-01
A perticular case of the Yang-Mills (YM) equations has been studied. For this system a transversal intersection of separatrices of unstable periodical trajectories is discovered, hence, it follows that there are no first real-analytical integrals of motion additional to the Hamiltonian. As a result, a complete set of integrals does not exist for the system describing the classical YM fields. Numerical methods of constructing separatrices, double-asymptotical solutions and of determining the angles between separatrices have been described
Solitons in a six-dimensional super Yang-Mills-tensor system and non-critical strings
International Nuclear Information System (INIS)
Nair, V.P.; Randjbar-Daemi, S.
1997-11-01
In this letter we study a coupled system of six-dimensional N = 1 tensor and super Yang-Mills multiplets. We identify some of the solitonic states of this system which exhibit stringy behaviour in six dimensions. A discussion of the supercharges and energy for the tensor multiples as well as zero modes is also given. We speculate about the possible relationship between our solution and what is known as tensionless strings. (author)
The light bound states of N=1 supersymmetric SU(3) Yang-Mills theory on the lattice
Ali, Sajid; Bergner, Georg; Gerber, Henning; Giudice, Pietro; Montvay, Istvan; Münster, Gernot; Piemonte, Stefano; Scior, Philipp
2018-03-01
In this article we summarise our results from numerical simulations of N=1 supersymmetric Yang-Mills theory with gauge group SU(3). We use the formulation of Curci and Veneziano with clover-improved Wilson fermions. The masses of various bound states have been obtained at different values of the gluino mass and gauge coupling. Extrapolations to the limit of vanishing gluino mass indicate that the bound states form mass-degenerate supermultiplets.
Non-existence of black-hole solutions for the electroweak Einstein-Dirac-Yang/Mills equations
International Nuclear Information System (INIS)
Bernard, Yann
2006-01-01
We consider a static, spherically symmetric system of a Dirac particle interacting with classical gravity and an electroweak Yang-Mills field. It is shown that the only black-hole solutions of the corresponding coupled equations must be the extreme Reissner-Nordstroem solutions, locally near the event horizon. This work generalizes a series of papers published by F Finster, J Smoller and S-T Yau
Energy Technology Data Exchange (ETDEWEB)
Narita, Makoto [Department of Mathematics, National Taiwan University, 1, Sec. 4, Roosevelt Rd., Taipei 106, Taiwan (China)
2006-12-21
We discuss the strong cosmic censorship conjecture for cosmological spacetimes in the Einstein-Yang-Mills-dilaton system. Locally rotational symmetric Bianchi I spacetimes are considered. We show local and global existence theorems for the system. Asymptotic behaviour for the spacetimes is also investigated. The curvature invariant is blowup at the initial singularities and the spacetimes are future geodesic complete. Thus, the strong cosmic censorship conjecture for the spacetimes holds.
International Nuclear Information System (INIS)
Narita, Makoto
2006-01-01
We discuss the strong cosmic censorship conjecture for cosmological spacetimes in the Einstein-Yang-Mills-dilaton system. Locally rotational symmetric Bianchi I spacetimes are considered. We show local and global existence theorems for the system. Asymptotic behaviour for the spacetimes is also investigated. The curvature invariant is blowup at the initial singularities and the spacetimes are future geodesic complete. Thus, the strong cosmic censorship conjecture for the spacetimes holds
On Yang--Mills Theories with Chiral Matter at Strong Coupling
Energy Technology Data Exchange (ETDEWEB)
Shifman, M.; /Minnesota U., Theor. Phys. Inst. /Saclay, SPhT; Unsal, Mithat; /SLAC /Stanford U., Phys. Dept.
2008-08-20
Strong coupling dynamics of Yang-Mills theories with chiral fermion content remained largely elusive despite much effort over the years. In this work, we propose a dynamical framework in which we can address non-perturbative properties of chiral, non-supersymmetric gauge theories, in particular, chiral quiver theories on S{sub 1} x R{sub 3}. Double-trace deformations are used to stabilize the center-symmetric vacuum. This allows one to smoothly connect smaller(S{sub 1}) to larger(S{sub 1}) physics (R{sub 4} is the limiting case) where the double-trace deformations are switched off. In particular, occurrence of the mass gap in the gauge sector and linear confinement due to bions are analytically demonstrated. We find the pattern of the chiral symmetry realization which depends on the structure of the ring operators, a novel class of topological excitations. The deformed chiral theory, unlike the undeformed one, satisfies volume independence down to arbitrarily small volumes (a working Eguchi-Kawai reduction) in the large N limit. This equivalence, may open new perspectives on strong coupling chiral gauge theories on R{sub 4}.
On string solutions of Bethe equations in N=4 supersymmetric Yang-Mills theory
International Nuclear Information System (INIS)
Bytsko, A.G.; Shenderovich, I.E.
2007-12-01
The Bethe equations, arising in description of the spectrum of the dilatation operator for the su(2) sector of the N=4 supersymmetric Yang-Mills theory, are considered in the anti-ferromagnetic regime. These equations are deformation of those for the Heisenberg XXX magnet. It is proven that in the thermodynamic limit roots of the deformed equations group into strings. It is proven that the corresponding Yang's action is convex, which implies uniqueness of solution for centers of the strings. The state formed of strings of length (2n+1) is considered and the density of their distribution is found. It is shown that the energy of such a state decreases as n grows. It is observed that non-analyticity of the left hand side of the Bethe equations leads to an additional contribution to the density and energy of strings of even length. Whence it is concluded that the structure of the anti-ferromagnetic vacuum is determined by the behaviour of exponential corrections to string solutions in the thermodynamic limit and possibly involves strings of length 2. (orig.)
Lattice super-Yang-Mills: a virial approach to operator dimensions
International Nuclear Information System (INIS)
Callan, Curtis G.; Heckman, Jonathan; McLoughlin, Tristan; Swanson, Ian
2004-01-01
The task of calculating operator dimensions in the planar limit of N=4 super-Yang-Mills theory can be vastly simplified by mapping the dilatation generator to the Hamiltonian of an integrable spin chain. The Bethe ansatz has been used in this context to compute the spectra of spin chains associated with various sectors of the theory which are known to decouple in the planar (large-Nc) limit. These techniques are powerful at leading order in perturbation theory but become increasingly complicated beyond one loop in the 't Hooft parameter λ=gYM2Nc, where spin chains typically acquire long-range (non-nearest-neighbor) interactions. In certain sectors of the theory, moreover, higher-loop Bethe ansatze do not even exist. We develop a virial expansion of the spin chain Hamiltonian as an alternative to the Bethe ansatz methodology, a method which simplifies the computation of dimensions of multi-impurity operators at higher loops in λ. We use these methods to extract previously reported numerical gauge theory predictions near the BMN limit for comparison with corresponding results on the string theory side of the AdS/CFT correspondence. For completeness, we compare our virial results with predictions that can be derived from current Bethe ansatz technology
Deriving CSW rules for massive scalar legs and pure Yang-Mills loops
International Nuclear Information System (INIS)
Boels, Rutger; Schwinn, Christian
2008-01-01
This article provides two complementary detailed derivations of Cachazo-Svrcek-Witten-style Feynman rules for Yang-Mills gauge theory coupled to a massive coloured scalar as presented in earlier work. These proceed through a direct canonical transformation method on space-time and through a gauge transformation in an action constructed on twistor space. It is shown explicitly that the field transformations are identical in both cases. Some simple tree-level examples of our rules are given and we comment on the application of them to the calculation of the rational part of one-loop pure glue amplitudes. A possible direct quantum completion of pure glue CSW rules based on dimensional regularisation motivated by these results is sketched. Finally, it is shown how to derive CSW rules for effective Higgs-gluon and Higgs-matter couplings proposed in the literature directly from the action. This derivation yields additional towers of vertices which generate a subset of the contributions to effective multi-Higgs scattering amplitudes.
Hamiltonian approach to 1 + 1 dimensional Yang-Mills theory in Coulomb gauge
International Nuclear Information System (INIS)
Reinhardt, H.; Schleifenbaum, W.
2009-01-01
We study the Hamiltonian approach to 1 + 1 dimensional Yang-Mills theory in Coulomb gauge, considering both the pure Coulomb gauge and the gauge where in addition the remaining constant gauge field is restricted to the Cartan algebra. We evaluate the corresponding Faddeev-Popov determinants, resolve Gauss' law and derive the Hamiltonians, which differ in both gauges due to additional zero modes of the Faddeev-Popov kernel in the pure Coulomb gauge. By Gauss' law the zero modes of the Faddeev-Popov kernel constrain the physical wave functionals to zero colour charge states. We solve the Schroedinger equation in the pure Coulomb gauge and determine the vacuum wave functional. The gluon and ghost propagators and the static colour Coulomb potential are calculated in the first Gribov region as well as in the fundamental modular region, and Gribov copy effects are studied. We explicitly demonstrate that the Dyson-Schwinger equations do not specify the Gribov region while the propagators and vertices do depend on the Gribov region chosen. In this sense, the Dyson-Schwinger equations alone do not provide the full non-abelian quantum gauge theory, but subsidiary conditions must be required. Implications of Gribov copy effects for lattice calculations of the infrared behaviour of gauge-fixed propagators are discussed. We compute the ghost-gluon vertex and provide a sensible truncation of Dyson-Schwinger equations. Approximations of the variational approach to the 3 + 1 dimensional theory are checked by comparison to the 1 + 1 dimensional case
Self-dual phase space for (3 +1 )-dimensional lattice Yang-Mills theory
Riello, Aldo
2018-01-01
I propose a self-dual deformation of the classical phase space of lattice Yang-Mills theory, in which both the electric and magnetic fluxes take value in the compact gauge Lie group. A local construction of the deformed phase space requires the machinery of "quasi-Hamiltonian spaces" by Alekseev et al., which is reviewed here. The results is a full-fledged finite-dimensional and gauge-invariant phase space, the self-duality properties of which are largely enhanced in (3 +1 ) spacetime dimensions. This enhancement is due to a correspondence with the moduli space of an auxiliary noncommutative flat connection living on a Riemann surface defined from the lattice itself, which in turn equips the duality between electric and magnetic fluxes with a neat geometrical interpretation in terms of a Heegaard splitting of the space manifold. Finally, I discuss the consequences of the proposed deformation on the quantization of the phase space, its quantum gravitational interpretation, as well as its relevance for the construction of (3 +1 )-dimensional topological field theories with defects.
On string solutions of Bethe equations in N=4 supersymmetric Yang-Mills theory
Energy Technology Data Exchange (ETDEWEB)
Bytsko, A.G. [Rossijskaya Akademiya Nauk, St. Petersburg (Russian Federation). Inst. Matematiki]|[Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Shenderovich, I.E. [St. Petersburg State Univ. (Russian Federation). Physics Dept.
2007-12-15
The Bethe equations, arising in description of the spectrum of the dilatation operator for the su(2) sector of the N=4 supersymmetric Yang-Mills theory, are considered in the anti-ferromagnetic regime. These equations are deformation of those for the Heisenberg XXX magnet. It is proven that in the thermodynamic limit roots of the deformed equations group into strings. It is proven that the corresponding Yang's action is convex, which implies uniqueness of solution for centers of the strings. The state formed of strings of length (2n+1) is considered and the density of their distribution is found. It is shown that the energy of such a state decreases as n grows. It is observed that non-analyticity of the left hand side of the Bethe equations leads to an additional contribution to the density and energy of strings of even length. Whence it is concluded that the structure of the anti-ferromagnetic vacuum is determined by the behaviour of exponential corrections to string solutions in the thermodynamic limit and possibly involves strings of length 2. (orig.)
N=4 super-Yang-Mills in LHC superspace part I: classical and quantum theory
Energy Technology Data Exchange (ETDEWEB)
Chicherin, Dmitry [LAPTH, Université de Savoie,CNRS, B.P. 110, F-74941 Annecy-le-Vieux (France); Sokatchev, Emery [LAPTH, Université de Savoie,CNRS, B.P. 110, F-74941 Annecy-le-Vieux (France); Theoretical Physics Department, CERN,CH -1211, Geneva 23 (Switzerland)
2017-02-10
We present a formulation of the maximally supersymmetric N=4 gauge theory in Lorentz harmonic chiral (LHC) superspace. It is closely related to the twistor formulation of the theory but employs the simpler notion of Lorentz harmonic variables. They parametrize a two-sphere and allow us to handle efficiently infinite towers of higher-spin auxiliary fields defined on ordinary space-time. In this approach the chiral half of N=4 supersymmetry is manifest. The other half is realized non-linearly and the algebra closes on shell. We give a straightforward derivation of the Feynman rules in coordinate space. We show that the LHC formulation of the N=4 super-Yang-Mills theory is remarkably similar to the harmonic superspace formulation of the N=2 gauge and hypermultiplet matter theories. In the twin paper https://arxiv.org/abs/1601.06804 we apply the LHC formalism to the study of the non-chiral multipoint correlation functions of the N=4 stress-tensor supermultiplet.
Moduli dynamics as a predictive tool for thermal maximally supersymmetric Yang-Mills at large N
Energy Technology Data Exchange (ETDEWEB)
Morita, Takeshi [Department of Physics, Shizuoka University,836 Ohya, Suruga-ku, Shizuoka 422-8529 (Japan); Department of Physics and Astronomy, University of Kentucky,Lexington, KY 40506 (United States); Shiba, Shotaro [Maskawa Institute for Science and Culture, Kyoto Sangyo University,Kamigamo-Motoyama, Kita-ku, Kyoto 603-8555 (Japan); Wiseman, Toby [Theoretical Physics Group, Blackett Laboratory, Imperial College,Exhibition Road, London SW7 2AZ (United Kingdom); Withers, Benjamin [Mathematical Sciences and STAG Research Centre, University of Southampton,Highfield, Southampton SO17 1BJ (United Kingdom)
2015-07-09
Maximally supersymmetric (p+1)-dimensional Yang-Mills theory at large N and finite temperature, with possibly compact spatial directions, has a rich phase structure. Strongly coupled phases may have holographic descriptions as black branes in various string duality frames, or there may be no gravity dual. In this paper we provide tools in the gauge theory which give a simple and unified picture of the various strongly coupled phases, and transitions between them. Building on our previous work we consider the effective theory describing the moduli of the gauge theory, which can be computed precisely when it is weakly coupled far out on the Coulomb branch. Whilst for perturbation theory naive extrapolation from weak coupling to strong gives little information, for this moduli theory naive extrapolation from its weakly to its strongly coupled regime appears to encode a surprising amount of information about the various strongly coupled phases. We argue it encodes not only the parametric form of thermodynamic quantities for these strongly coupled phases, but also certain transcendental factors with a geometric origin, and allows one to deduce transitions between the phases. We emphasise it also gives predictions for the behaviour of other observables in these phases.
A further pathology of the Coulomb gauge in non-Abelian Yang-Mills theories
International Nuclear Information System (INIS)
Ademollo, M.; Napolitano, E.; Sciuto, S.
1978-01-01
In the first part the vacuum structure of SU(2) Yang-Mills theories in the Coulomb gauge is discussed. It is proved that the only transverse pure gauge field Asub(μ)(x) = U -1 deltasub(μ)U with U(x) → (as r→infinity) const., is the trivial one Asub(μ)(x) equivalent to 0; the features of other possible vacua with U(x) → (as r→infinity) U(theta, pli) are studied. In the second part, regular Euclidean configurations that connect a vacuum state at x 4 = -infinity to another at x 4 = +infinity are discussed. It is proved, always working in the Coulomb gauge, that the perturbative vacuum Asub(μ)(x) equivalent to 0 cannot tunnel into any other one and that regular configurations with non-vanishing Pontryagin number q cannot affect such a vacuum. Moreover, strong arguments are given to show that many-instanton configurations (mod(q)>=2) cannot be expressed at all in the Coulomb gauge, that is by a regular field Asub(μ) satisfying the transversality condition deltasub(i)Asub(i) (x, x 4 ) = 0. (Auth.)
Adventures of the coupled Yang-Mills oscillators: I. Semiclassical expansion
International Nuclear Information System (INIS)
Matinyan, Sergei G; Mueller, Berndt
2006-01-01
We study the quantum mechanical motion in the x 2 y 2 potentials with n 2, 3, which arise in the spatially homogeneous limit of the Yang-Mills (YM) equations. These systems show strong stochasticity in the classical limit (ℎ = 0) and exhibit a quantum mechanical confinement feature. We calculate the partition function Z(t) going beyond the Thomas-Fermi (TF) approximation by means of the semiclassical expansion using the Wigner-Kirkwood (WK) method. We derive a novel compact form of the differential equation for the WK function. After separating the motion in the channels of the equipotential surface from the motion in the central region, we show that the leading higher order corrections to the TF term vanish up to eighth order in ℎ, if we treat the quantum motion in the hyperbolic channels correctly by adiabatic separation of the degrees of freedom. Finally, we obtain an asymptotic expansion of the partition function in terms of the parameter g 2 ℎ 4 t 3
Local BRST cohomology in the antifield formalism. Pt. 2. Application to Yang-Mills theory
International Nuclear Information System (INIS)
Barnich, G.; Henneaux, M.
1995-01-01
Yang-Mills models with compact gauge group coupled to matter fields are considered. The general tools developed in a companion paper are applied to compute the local cohomology of the BRST differential s modulo the exterior spacetime derivative d for all values of the ghost number, in the space of polynomials in the fields, the ghosts, the antifields (=sources for the BRST variations) and their derivatives. New solutions to the consistency conditions sa+db=0 depending non-trivially on the antifields are exhibited. For a semi-simple gauge group, however, these new solutions arise only at ghost number two or higher. Thus at ghost number zero or one, the inclusion of the antifields does not bring in new solutions to the consistency condition sa+db=0 besides the already known ones. The analysis does not use power counting and is purely cohomological. It can be easily extended to more general actions containing higher derivatives of the curvature or Chern-Simons terms. (orig.)
Compact invariant sets of the static spherically symmetric Einstein-Yang-Mills equations
Energy Technology Data Exchange (ETDEWEB)
Starkov, Konstantin E., E-mail: konst@citedi.m [CITEDI-IPN, Av. del Parque 1310, Mesa de Otay, Tijuana, BC (Mexico)
2010-04-05
In this Letter we obtain results concerning compact invariant sets of the static spherically symmetric Einstein-Yang-Mills (EYM) equations with help of studies of its localization. Let a be a cosmological constant and s be another parameter entering into these equations which is used for considering the physical time as a temporal variable, with s=1, while s=-1 is used for considering the physical time as a spatial variable. We show that in case s=1; a<0 the location of any compact invariant set is described by some system of linear inequalities. Then we prove that in case s=1; a>0 the set of all compact invariant sets consists of two equilibrium points only. Further, we state that in cases s=-1; a<0 and s=-1; a>0 there are only two equilibrium points and there are no periodic orbits. In addition, we prove that in the last two cases there are neither homoclinic orbits nor heteroclinic orbits as well.
Yang-Mills gauge invariance of a space of Bose and Fermi coordinates
International Nuclear Information System (INIS)
Friedman, M.H.; Srivastava, Y.
1977-01-01
A complete formalism is developed for imposing Yang-Mills gauge invariance induced by general coordinate transformations on superspace (i.e., a space containing both commuting and anticommuting coordinates). The appropriate group is the graded pseudo-Lie group of real, general linear transformations on superspace analogous to the role played by GL(4,R) in general relativity. The construction of derivatives which transform covariantly under this group forces the introduction of a connection. In the usual gauge theories the connection is just the vector potential, whereas here we expect it to be a function of all the dynamical fields. In this purely affine theory, field strengths and our proposed equations of motion for them result in a self-sourced theory involving only the connection. However, we find that there exist solutions which permit us to define a metric for which an inverse does not exist. These solutions are associated with a spontaneous symmetry breakdown of the vacuum which yields only the Lorentz metric and with no restriction on the internal-symmetry group. This spontaneous symmetry breaking introduces a parameter with the dimensions of (mass) 2
Geometrical Lagrangian for a Supersymmetric Yang-Mills Theory on the Group Manifold
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Borges, M. F.
2002-01-01
Perhaps one of the main features of Einstein's General Theory of Relativity is that spacetime is not flat itself but curved. Nowadays, however, many of the unifying theories like superstrings on even alternative gravity theories such as teleparalell geometric theories assume flat spacetime for their calculations. This article, an extended account of an earlier author's contribution, it is assumed a curved group manifold as a geometrical background from which a Lagrangian for a supersymmetric N=2, d=5 Yang-Mills - SYM, N=2, d=5 - is built up. The spacetime is a hypersurface embedded in this geometrical scenario, and the geometrical action here obtained can be readily coupled to the five-dimensional supergravity action. The essential idea that underlies this work has its roots in the Einstein-Cartan formulation of gravity and in the 'group manifold approach to gravity and supergravity theories'. The group SYM, N=2, d=5, turns out to be the direct product of supergravity and a general gauge group G:G=GxSU(2,2/1)-bar
Integrability in dipole-deformed \\boldsymbol{N=4} super Yang-Mills
Guica, Monica; Levkovich Maslyuk, Fedor; Zarembo, Konstantin
2017-09-01
We study the null dipole deformation of N=4 super Yang-Mills theory, which is an example of a potentially solvable ‘dipole CFT’: a theory that is non-local along a null direction, has non-relativistic conformal invariance along the remaining ones, and is holographically dual to a Schrödinger space-time. We initiate the field-theoretical study of the spectrum in this model by using integrability inherited from the parent theory. The dipole deformation corresponds to a nondiagonal Drinfeld-Reshetikhin twist in the spin chain picture, which renders the traditional Bethe ansatz inapplicable from the very beginning. We use instead the Baxter equation supplemented with nontrivial asymptotics, which gives the full 1-loop spectrum in the sl(2) sector. We show that anomalous dimensions of long gauge theory operators perfectly match the string theory prediction, providing a quantitative test of Schrödinger holography. Dedicated to the memory of Petr Petrovich Kulish.
On non-primitively divergent vertices of Yang-Mills theory
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Huber, Markus Q. [Institute of Physics, University of Graz, NAWI Graz (Austria)
2017-11-15
Two correlation functions of Yang-Mills beyond the primitively divergent ones, the two-ghost-two-gluon and the four-ghost vertices, are calculated and their influence on lower vertices is examined. Their full (transverse) tensor structure is taken into account. As input, a solution of the full two-point equations - including two-loop terms - is used that respects the resummed perturbative ultraviolet behavior. A clear hierarchy is found with regard to the color structure that reduces the number of relevant dressing functions. The impact of the two-ghost-two-gluon vertex on the three-gluon vertex is negligible, which is explained by the fact that all non-small dressing functions drop out due to their color factors. Only in the ghost-gluon vertex a small net effect below 2% is seen. The four-ghost vertex is found to be extremely small in general. Since these two four-point functions do not enter into the propagator equations, these findings establish their small overall effect on lower correlation functions. (orig.)
Lattice Yang-Mills theory at finite densities of heavy quarks
International Nuclear Information System (INIS)
Langfeld, Kurt; Shin, Gwansoo
2000-01-01
SU(N c ) Yang-Mills theory is investigated at finite densities of N f heavy quark flavors. The calculation of the (continuum) quark determinant in the large-mass limit is performed by analytic methods and results in an effective gluonic action. This action is then subject to a lattice representation of the gluon fields and computer simulations. The approach maintains the same number of quark degrees of freedom as in the continuum formulation and a physical heavy quark limit (to be contrasted with the quenched approximation N f →0). The proper scaling towards the continuum limit is manifest. We study the partition function for given values of the chemical potential as well as the partition function which is projected onto a definite baryon number. First numerical results for an SU(2) gauge theory are presented. We briefly discuss the breaking of the color-electric string at finite densities and shed light onto the origin of the overlap problem inherent in the Glasgow approach
Dirac - Kaehler formalism and the Yang-Mills model with Supersymmetry
International Nuclear Information System (INIS)
Goto, M.
1985-01-01
It is used the differential Dirac-Kahler's formalism for transposing supersymmetric models for the lattice. Such a formalism has shown itself extremely useful for these purposes because there exists a complete mathematical duality in its versions in the continuum and in the lattice. This work treats specifically the Yang-Mills, model with extended supersymmetry N = 2 in the adjoint representation; the procedure which is adopted here consists in to rewrite the essential of the model in question in the new language, first in the continuum, getting it adequate for the lattice, because it is from the property of the supercharges Q 2 = H that the lattice supersymmetric Hamiltonian will be obtained. By the way, it was constructed a lattice gauge theory within the formalism of Dirac-Kahler, it is almost a natural consequence of the adopted definitions for the lattice gauge transformations of the fields in the adjoint representation and of the two types of covariant derivatives which are necessary in the lattice. In order to carry out some calculations, it was put emphasis on the matrix representation of the Dirac-Kahler's formalism, it was also extended to a lattice. (author) [pt
Non-intersecting Brownian walkers and Yang-Mills theory on the sphere
International Nuclear Information System (INIS)
Forrester, Peter J.; Majumdar, Satya N.; Schehr, Gregory
2011-01-01
We study a system of N non-intersecting Brownian motions on a line segment [0,L] with periodic, absorbing and reflecting boundary conditions. We show that the normalized reunion probabilities of these Brownian motions in the three models can be mapped to the partition function of two-dimensional continuum Yang-Mills theory on a sphere respectively with gauge groups U(N), Sp(2N) and SO(2N). Consequently, we show that in each of these Brownian motion models, as one varies the system size L, a third order phase transition occurs at a critical value L=L c (N)∼√(N) in the large N limit. Close to the critical point, the reunion probability, properly centered and scaled, is identical to the Tracy-Widom distribution describing the probability distribution of the largest eigenvalue of a random matrix. For the periodic case we obtain the Tracy-Widom distribution corresponding to the GUE random matrices, while for the absorbing and reflecting cases we get the Tracy-Widom distribution corresponding to GOE random matrices. In the absorbing case, the reunion probability is also identified as the maximal height of N non-intersecting Brownian excursions ('watermelons' with a wall) whose distribution in the asymptotic scaling limit is then described by GOE Tracy-Widom law. In addition, large deviation formulas for the maximum height are also computed.
The ultraviolet behaviour of N=4 Yang-Mills and the power counting of extended superspace
International Nuclear Information System (INIS)
Marcus, N.; Sagnotti, A.
1985-01-01
A two-loop calculation in the N=4 supersymmetric Yang-Mills theory is performed in various dimensions. The theory is found to be two-loop finite in six dimensions or less, but infinite in seven and nine dimensions. The six-dimensional result can be explained by a formulation of the theory in terms of N=2 superfields. The divergence in seven dimensions is naively compatible with both N=2 and N=4 superfield power counting rules, but is of a form that cannot be written as an on-shell N=4 superfield integral. The hypothesized N=4 extended superfield formalism therefore either does not exist, or at least has weaker consequences than would have been expected. This leads one to expect that four-dimensional supergravity theories diverge at three loops. Some general issues about the meaning of finiteness in nonrenormalizable theories are discussed. In particular, we discuss the use of field redefinitions, the generalization of wave function renormalization to nonrenormalizable theories, and whether counterterms should be used in calculations in finite theories. (orig.)
Local BRST cohomology in the antifield formalism. Pt. 2. Application to Yang-Mills theory
International Nuclear Information System (INIS)
Barnich, G.; Henneaux, M.; Brandt, F.
1994-01-01
Yang-Mills models with compact gauge group coupled to matter fields are considered. The general tools developed in a companion paper are applied to compute the local cohomology of the BRST differential s modulo the exterior spacetime derivative d for all values of the ghost number, in the space of polynomials in the fields, the ghosts, the antifields (= sources for the BRST variations) and their derivatives. New solutions to the consistency conditions sa+db = 0 depending non trivially on the antifields are exhibited. For a semi-simple gauge group, however, these new solutions arise only at ghost number two or higher. Thus at ghost number zero or one, the inclusion of the antifields does not bring in new solutions to the consistency condition sa+db 0 besides the already known ones. The analysis does not use power counting and is purely cohomological. It can be easily extended to more general actions containing higher derivatives of the curvature, or Chern-Simons terms. (orig.)
Moduli dynamics as a predictive tool for thermal maximally supersymmetric Yang-Mills at large N
International Nuclear Information System (INIS)
Morita, Takeshi; Shiba, Shotaro; Wiseman, Toby; Withers, Benjamin
2015-01-01
Maximally supersymmetric (p+1)-dimensional Yang-Mills theory at large N and finite temperature, with possibly compact spatial directions, has a rich phase structure. Strongly coupled phases may have holographic descriptions as black branes in various string duality frames, or there may be no gravity dual. In this paper we provide tools in the gauge theory which give a simple and unified picture of the various strongly coupled phases, and transitions between them. Building on our previous work we consider the effective theory describing the moduli of the gauge theory, which can be computed precisely when it is weakly coupled far out on the Coulomb branch. Whilst for perturbation theory naive extrapolation from weak coupling to strong gives little information, for this moduli theory naive extrapolation from its weakly to its strongly coupled regime appears to encode a surprising amount of information about the various strongly coupled phases. We argue it encodes not only the parametric form of thermodynamic quantities for these strongly coupled phases, but also certain transcendental factors with a geometric origin, and allows one to deduce transitions between the phases. We emphasise it also gives predictions for the behaviour of other observables in these phases.
Yang-Mills solutions and Spin(7)-instantons on cylinders over coset spaces with G2-structure
International Nuclear Information System (INIS)
Haupt, Alexander S.
2016-01-01
We study g-valued Yang-Mills fields on cylinders Z(G/H)=ℝ×G/H, where G/H is a compact seven-dimensional coset space with G 2 -structure, g is the Lie algebra of G, and Z(G/H) inherits a Spin(7)-structure. After imposing a general G-invariance condition, Yang-Mills theory with torsion on Z(G/H) reduces to Newtonian mechanics of a point particle moving in ℝ n under the influence of some quartic potential and possibly additional constraints. The kinematics and dynamics depends on the chosen coset space. We consider in detail three coset spaces with nearly parallel G 2 -structure and four coset spaces with SU(3)-structure. For each case, we analyze the critical points of the potential and present a range of finite-energy solutions. We also study a higher-dimensional analog of the instanton equation. Its solutions yield G-invariant Spin(7)-instanton configurations on Z(G/H), which are special cases of Yang-Mills configurations with torsion.
International Nuclear Information System (INIS)
Drechsler, W.; Havas, P.; Rosenblum, A.
1984-01-01
In two recent papers, the general form of the laws of motion for point particles which are multipole sources of the classical coupled Yang-Mills-Higgs fields was determined by Havas, and for the special case of monopole singularities of a Yang-Mills field an iteration procedure was developed by Drechsler and Rosenblum to obtain the equations of motion of mass points, i.e., the laws of motion including the explicit form of the fields of all interacting particles. In this paper we give a detailed derivation of the laws of motion of monopole-dipole singularities of the coupled Yang-Mills-Higgs fields for point particles with mass and spin, following a procedure first applied by Mathisson and developed by Havas. To obtain the equations of motion, a systematic approximation method is developed in the following paper for the solution of the nonlinear field equations and determination of the fields entering the laws of motion found here to any given order in the coupling constant g
A less-constrained (2,0) super-Yang-Mills model: the coupling to non-linear σ-models
International Nuclear Information System (INIS)
Almeida, C.A.S.; Doria, R.M.
1990-01-01
Considering a class of (2,0) super-Yang-Mills multiplets characterised by the appearance of a pair of independent gauge potentials, we present here their coupling to non-linear σ-models in (2,0)-superspace. Contrary to the case of the coupling to (2,0) matter superfields, the extra gauge potential present in the Yang-Mills sector does not decouple from the theory in the case one gauges isometry groups of σ-models. (author)
Directory of Open Access Journals (Sweden)
Suhendro I.
2008-01-01
Full Text Available In this work, we attempt at constructing a comprehensive four-dimensional unified field theory of gravity, electromagnetism, and the non-Abelian Yang-Mills gauge field in which the gravitational, electromagnetic, and material spin fields are unified as intrinsic geometric objects of the space-time manifold $S_4$ via the connection, with the generalized non-Abelian Yang-Mills gauge field appearing in particular as a sub-field of the geometrized electromagnetic interaction.
Non-commutative geometry inspired charged black holes
International Nuclear Information System (INIS)
Ansoldi, Stefano; Nicolini, Piero; Smailagic, Anais; Spallucci, Euro
2007-01-01
We find a new, non-commutative geometry inspired, solution of the coupled Einstein-Maxwell field equations describing a variety of charged, self-gravitating objects, including extremal and non-extremal black holes. The metric smoothly interpolates between de Sitter geometry, at short distance, and Reissner-Nordstrom geometry far away from the origin. Contrary to the ordinary Reissner-Nordstrom spacetime there is no curvature singularity in the origin neither 'naked' nor shielded by horizons. We investigate both Hawking process and pair creation in this new scenario
Can non-commutativity resolve the big-bang singularity?
Energy Technology Data Exchange (ETDEWEB)
Maceda, M.; Madore, J. [Laboratoire de Physique Theorique, Universite de Paris-Sud, Batiment 211, 91405, Orsay (France); Manousselis, P. [Department of Engineering Sciences, University of Patras, 26110, Patras (Greece); Physics Department, National Technical University, Zografou Campus, 157 80, Zografou, Athens (Greece); Zoupanos, G. [Physics Department, National Technical University, Zografou Campus, 157 80, Zografou, Athens (Greece); Theory Division, CERN, 1211, Geneva 23 (Switzerland)
2004-08-01
A possible way to resolve the singularities of general relativity is proposed based on the assumption that the description of space-time using commuting coordinates is not valid above a certain fundamental scale. Beyond that scale it is assumed that the space-time has non-commutative structure leading in turn to a resolution of the singularity. As a first attempt towards realizing the above programme a modification of the Kasner metric is constructed which is commutative only at large time scales. At small time scales, near the singularity, the commutation relations among the space coordinates diverge. We interpret this result as meaning that the singularity has been completely delocalized. (orig.)
Non-commutative field theory with twistor-like coordinates
International Nuclear Information System (INIS)
Taylor, Tomasz R.
2007-01-01
We consider quantum field theory in four-dimensional Minkowski spacetime, with the position coordinates represented by twistors instead of the usual world-vectors. Upon imposing canonical commutation relations between twistors and dual twistors, quantum theory of fields described by non-holomorphic functions of twistor variables becomes manifestly non-commutative, with Lorentz symmetry broken by a time-like vector. We discuss the free field propagation and its impact on the short- and long-distance behavior of physical amplitudes in perturbation theory. In the ultraviolet limit, quantum field theories in twistor space are generically less divergent than their commutative counterparts. Furthermore, there is no infrared-ultraviolet mixing problem
An object oriented code for simulating supersymmetric Yang-Mills theories
Catterall, Simon; Joseph, Anosh
2012-06-01
We present SUSY_LATTICE - a C++ program that can be used to simulate certain classes of supersymmetric Yang-Mills (SYM) theories, including the well known N=4 SYM in four dimensions, on a flat Euclidean space-time lattice. Discretization of SYM theories is an old problem in lattice field theory. It has resisted solution until recently when new ideas drawn from orbifold constructions and topological field theories have been brought to bear on the question. The result has been the creation of a new class of lattice gauge theories in which the lattice action is invariant under one or more supersymmetries. The resultant theories are local, free of doublers and also possess exact gauge-invariance. In principle they form the basis for a truly non-perturbative definition of the continuum SYM theories. In the continuum limit they reproduce versions of the SYM theories formulated in terms of twisted fields, which on a flat space-time is just a change of the field variables. In this paper, we briefly review these ideas and then go on to provide the details of the C++ code. We sketch the design of the code, with particular emphasis being placed on SYM theories with N=(2,2) in two dimensions and N=4 in three and four dimensions, making one-to-one comparisons between the essential components of the SYM theories and their corresponding counterparts appearing in the simulation code. The code may be used to compute several quantities associated with the SYM theories such as the Polyakov loop, mean energy, and the width of the scalar eigenvalue distributions. Program summaryProgram title: SUSY_LATTICE Catalogue identifier: AELS_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AELS_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 9315 No. of bytes in distributed program