Showing papers on "Supersymmetric gauge theory published in 2000"
TL;DR: In this article, the cohomology groups of the differential introduced by Becchi, Rouet, Stora and Tyutin are computed in a self-contained manner, with the sources of the BRST variations of the fields included in the problem.
611 citations
TL;DR: In this paper, a formulation of gauge theory on noncommutative spaces based on the concept of covariant coordinates is introduced, and a Seiberg-Witten map is established in all cases.
Abstract: We introduce a formulation of gauge theory on noncommutative spaces based on the concept of covariant coordinates. Some important examples are discussed in detail. A Seiberg-Witten map is established in all cases.
453 citations
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TL;DR: In this article, the mass spectrum of the Kaluza-Klein (KK) excitations of the gauge fields and their couplings to the boundaries of the fifth dimension were studied.
377 citations
TL;DR: In this article, the authors studied brane configurations that give rise to large-N gauge theories with eight supersymmetries and no hypermultiplets, and they found that this singularity is removed by a distinctive mechanism, leaving a smooth geometry with a core having an enhanced gauge symmetry.
Abstract: We study brane configurations that give rise to large-N gauge theories with eight supersymmetries and no hypermultiplets. These configurations include a variety of wrapped, fractional, and stretched branes or strings. The corresponding spacetime geometries which we study have a distinct kind of singularity known as a repulson. We find that this singularity is removed by a distinctive mechanism, leaving a smooth geometry with a core having an enhanced gauge symmetry. The spacetime geometry can be related to large-N Seiberg-Witten theory.
359 citations
TL;DR: In this paper, an enveloping algebra-valued gauge field is constructed with the Seiberg-Witten map, which allows the formulation of a dynamics for a finite number of gauge field components on non-commutative spaces.
Abstract: An enveloping algebra-valued gauge field is constructed, its components are functions of the Lie algebra-valued gauge field and can be constructed with the Seiberg-Witten map. This allows the formulation of a dynamics for a finite number of gauge field components on non-commutative spaces.
328 citations
TL;DR: In this article, a lattice formulation of non-commutative Yang-Mills theory in arbitrary even dimensionality is presented, and a discrete Morita equivalence between the two models is established.
Abstract: We present a lattice formulation of non-commutative Yang-Mills theory in arbitrary even dimensionality. The UV/IR mixing characteristic of non-commutative field theories is demonstrated at a completely non-perturbative level. We prove a discrete Morita equivalence between ordinary Yang-Mills theory with multi-valued gauge fields and non-commutative Yang-Mills theory with periodic gauge fields. Using this equivalence, we show that generic non-commutative gauge theories in the continuum can be regularized non perturbatively by means of ordinary lattice gauge theory with 't Hooft flux. In the case of irrational non-commutativity parameters, the rank of the gauge group of the commutative lattice theory must be sent to infinity in the continuum limit. As a special case, the construction includes the recent description of non-commutative Yang-Mills theories using twisted large-N reduced models. We study the coupling of non-commutative gauge fields to matter fields in the fundamental representation of the gauge group using the lattice formalism. The large mass expansion is used to describe the physical meaning of Wilson loops in non-commutative gauge theories. We also demonstrate Morita equivalence in the presence of fundamental matter fields and use this property to comment on the calculation of the beta-function in non-commutative quantum electrodynamics.
242 citations
TL;DR: In this paper, the Moyal-Weyl deformations of superspace and their compatibility with supersymmetry were investigated and a supersymmetric version of the Born-Infeld action with a B-field turned on was given.
Abstract: We investigate some aspects of Moyal-Weyl deformations of superspace and their compatibility with supersymmetry. For the simplest case, when only bosonic coordinates are deformed, we consider a four-dimensional supersymmetric field theory which is the deformation of the Wess-Zumino renormalizable theory of a chiral superfield. We then consider the deformation of a free theory of an abelian vector multiplet, which is a non-commutative version of the rank 1 Yang-Mills theory. We finally give the supersymmetric version of the α'0 limit of the Born-Infeld action with a B-field turned on, which is believed to be related to the non-commutative U(1) gauge theory.
194 citations
TL;DR: In this article, the authors derive nonperturbative classical solutions of noncommutative U(1) gauge theory with or without Higgs field, representing static magnetic flux tubes with arbitrary cross-section.
182 citations
TL;DR: In this paper, the authors study non-perturbative aspects of non-commutative U(1) gauge theories and identify the string with the projection of a D-string ending on a D3-brane in the presence of a constant B-field.
Abstract: We study some non-perturbative aspects of non-commutative gauge theories. We find analytic solutions of the equations of motion, for non-commutative U(1) gauge theory, that describe magnetic monopoles with a finite tension string attached. These solutions are non singular, finite and sourceless. We identify the string with the projection of a D-string ending on a D3-brane in the presence of a constant B-field.
181 citations
TL;DR: In this paper, the authors studied the general gaugings of N =2 Maxwell-Einstein supergravity theories (MESGT) in five dimensions, extending and generalizing previous work, and showed that the presence of tensor fields transforming non-trivially under the Yang-Mills gauge group leads to the introduction of a potential which does not admit an AdS ground state.
TL;DR: In this paper, various dualities, relating integrable systems and show that these dualities are explained in the framework of hamiltonian and Poisson reductions, are discussed and discussed.
Abstract: We discuss various dualities, relating integrable systems and show that these dualities are explained in the framework of hamiltonian and Poisson reductions. The dualities we study shed some light on the known integrable systems as well as allow to construct new ones, double elliptic among them. We also discuss applications to the (supersymmetric) gauge theories in various dimensions.
TL;DR: In this article, the semi-classical and full quantum version of the map from the ordinary gauge theory to the noncommutative gauge theory (Seiberg-Witten map) is given explicitly to all orders for any Poisson manifold in the Abelian case.
TL;DR: In this article, the noncommutative counterparts of chiral gauge theories are discussed and the associated anomalies are computed, and the non-commutativity of the anomalies is analyzed.
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TL;DR: In this article, the authors studied the large N limit of SO(N) and Chern-Simons gauge theory on S^3 and identified its closed string dual as topological strings on an orientifold of the small resolution of the conifold.
Abstract: We study the large N limit of SO(N) and Sp(N) Chern-Simons gauge theory on S^3 and identify its closed string dual as topological strings on an orientifold of the small resolution of the conifold. Applications to large N dualities for N=1 supersymmetric gauge systems in 4 dimensions are also discussed.
TL;DR: In this paper, a pedagogical introduction into noncommutative gauge theories, their stringy origin, and nonperturbative effects, including monopole and instanton solutions, is presented.
Abstract: We present a pedagogical introduction into noncommutative gauge theories, their stringy origin, and non-perturbative effects, including monopole and instanton solutions
TL;DR: The T-duality of field theories on noncommutative spaces has simpler counterparts in the dipole-theories as discussed by the authors, where the dipoles represent dipoles of constant magnitude.
Abstract: T-duality of gauge theories on a noncommutative $T^d$ can be extended to include fields with twisted boundary conditions. The resulting T-dual theories contain novel nonlocal fields. These fields represent dipoles of constant magnitude. Several unique properties of field theories on noncommutative spaces have simpler counterparts in the dipole-theories.
TL;DR: In this article, a general construction of chiral gauge theories on the lattice is described, and local and global anomalies are easily discussed in this framework and a closed expression for the effective action can be obtained.
TL;DR: In this article, the authors studied the generalization of noncommutative gauge theories to the case of orthogonal and symplectic groups and showed that the corresponding noncommuttative picture from low energy string theory is obtained via orientifold projection in the presence of a non-trivial NSNS B field.
TL;DR: In this article, the symmetry properties of the full theory are restored in the limit where the cut-off is removed, and the symmetries of the effective action under gauge transformations for both the gauge field and the auxiliary background field are separately evaluated.
TL;DR: A new mechanism for formation of topological defects in a U(1) model with a local gauge symmetry is proposed, which leads to definite predictions, which are qualitatively different from those of the Kibble-Zurek mechanism of global theories.
Abstract: We propose a new mechanism for formation of topological defects in a U(1) model with a local gauge symmetry. This mechanism leads to definite predictions, which are qualitatively different from those of the Kibble-Zurek mechanism of global theories. We confirm these predictions in numerical simulations, and they can also be tested in superconductor experiments. We believe that the mechanism generalizes to more complicated theories.
TL;DR: In this paper, a simple BPS solution of N = 4 U(1) non-commutative gauge theory in 4 dimensions is presented, which describes N infinite D1 strings that pierce a D3 brane at various points, in the presence of a background B-field in the Seiberg-Witten limit.
Abstract: We continue our study of solitons in noncommutative gauge theories and present an extremely simple BPS solution of N=4 U(1) noncommutative gauge theory in 4 dimensions, which describes N infinite D1 strings that pierce a D3 brane at various points, in the presence of a background B-field in the Seiberg-Witten limit. We call this solution the N-fluxon. For N=1 we calculate the complete spectrum of small fluctuations about the fluxon and find three kinds of modes: the fluctuations of the superstring in 10 dimensions arising from fundamental strings attached to the D1strings, the ordinary particles of the gauge theory in 4 dimensions and a set of states with discrete spectrum, localized at the intersection point--- corresponding to fundamental strings stretched between the D1string and the D3 brane. We discuss the fluctuations about theN-fluxon as well and derive explicit expressions for the amplitudes of interactions between these various modes. We show that translations in noncommutative gauge theories are equivalent to gauge transformations (plus a constant shift of the gauge field) and discuss the implications for the translational zeromodes of our solitons. We also find the dyonic versions of N-fluxon, as well as of our previous string-monopole solution.
TL;DR: In this paper, the central extensions of the N = 1 superalgebras relevant to the soliton solutions with the axial geometry are studied and a general expression valid in any four-dimensional gauge theory is obtained.
Abstract: We study the central extensions of the N=1 superalgebras relevant to the soliton solutions with the axial geometry--strings, wall junctions, etc. A general expression valid in any four-dimensional gauge theory is obtained. We prove that the only gauge theory admitting BPS strings at weak coupling is supersymmetric electrodynamics with the Fayet-Iliopoulos term. The problem of the ambiguity of the (1/2,1/2) central charge in the generalized Wess-Zumino models and gauge theories with matter is addressed and solved. A possibility of existence of the BPS strings at strong coupling in N=2 theories is discussed. A representation of different strings within the brane picture is presented. (c) 2000 The American Physical Society.
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TL;DR: In this article, the supersymmetric index Tr (-1)^F for Yang-Mills theory with any simple gauge group G is discussed. And the results of the analysis are confirmed via microscopic calculations.
Abstract: This paper is devoted to a systematic discussion of the supersymmetric index Tr (-1)^F for the minimal supersymmetric Yang-Mills theory -- with any simple gauge group G -- primarily in four spacetime dimensions. The index has refinements that probe confinement and oblique confinement and the possible spontaneous breaking of chiral symmetry and of global symmetries, such as charge conjugation, that are derived from outer automorphisms of the gauge group. Predictions for the index and its refinements are obtained on the basis of standard hypotheses about the infrared behavior of gauge theories. The predictions are confirmed via microscopic calculations which involve a Born-Oppenheimer computation of the spectrum as well as mathematical formulas involving triples of commuting elements of G and the Chern-Simons invariants of flat bundles on the three-torus.
TL;DR: In this article, the authors show that higher order terms in the effective action of non-commutative gauge theories exhibit generalizations of the star-product (e.g. star' and star3).
Abstract: Higher order terms in the effective action of non-commutative gauge theories exhibit generalizations of the star-product (e.g. star' and star3). These terms do not manifestly respect the non-commutative gauge invariance of the tree level action. In U(1) gauge theories, we note that these generalized star-products occur in the expansion of some quantities that are invariant under non-commutative gauge transformations, but contain an infinite number of powers of the non-commutative gauge field. One example is an open Wilson line. Another is the expression for a commutative field strength tensor Fab in terms of the non-commutative gauge field hat Aa. Seiberg and Witten derived differential equations that relate commutative and non-commutative gauge transformations, gauge fields and field strengths. In the U(1) case we solve these equations neglecting terms of fourth order in hat A but keeping all orders in the non-commutative parameter θkl.
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TL;DR: In this article, the authors consider chiral gauge theories defined over a four-dimensional spacetime manifold with a Cartesian product structure for at least one compact spatial dimension, and calculate the effective gauge field action by integrating out the chiral fermions, while maintaining gauge invariance.
TL;DR: In this paper, the supersymmetric field theories on the noncommutative $R^4$ using the superspace formalism on the commutative space were considered, and the terms depending on the parameter of the non-commutativity $\Theta$ are regarded as the interactions.
Abstract: We consider the supersymmetric field theories on the noncommutative $R^4$ using the superspace formalism on the commutative space. The terms depending on the parameter of the noncommutativity $\Theta$ are regarded as the interactions. In this way we construct the N=1 supersymmetric action for the U(N) vector multiplets and chiral multiplets of the fundamental, anti-fundamental and adjoint representations of the gauge group. The action for vector multiplets of the products gauge group and its bi-fundamental matters is also obtained. We discuss the problem of the derivative terms of the auxiliary fields.
TL;DR: In this article, the Coulomb and Higgs branches of 3D gauge theories with = 2 supersymmetry were studied, and it was shown that Coulomb branches of such theories may be rendered compact by the dynamical generation of Chern-Simons terms.
Abstract: We study three dimensional gauge theories with = 2 supersymmetry. We show that the Coulomb branches of such theories may be rendered compact by the dynamical generation of Chern-Simons terms and present a new class of mirror symmetric theories in which both Coulomb and Higgs branches have a natural description in terms of toric geometry.
TL;DR: In this article, the authors apply Dirac's Hamiltonian approach to study the canonical structure of the teleparallel form of general relativity without matter fields, and show that the Hamiltonian has the generalized Dirac-ADM form, and constraints satisfy all the consistency requirements.
Abstract: We apply Dirac's Hamiltonian approach to study the canonical structure of the teleparallel form of general relativity without matter fields. It is shown, without any gauge fixing, that the Hamiltonian has the generalized Dirac-ADM form, and constraints satisfy all the consistency requirements. The set of constraints involves some extra first-class constraints, which are used to find additional gauge symmetries and clarify the gauge structure of the theory.
TL;DR: In this paper, it was shown that the gauge groups SU(N), SO(N) and Sp(N)) cannot be realized on a flat noncommutative manifold, while it is possible for U(N).