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Gauge Theory (gauge + theory)
Selected AbstractsBrane tilings and their applicationsFORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 6 2008M. Yamazaki Abstract We review recent developments in the theory of brane tilings and four-dimensional ,, = 1 supersymmetric quiver gauge theories. This review consists of two parts. In part I, we describe foundations of brane tilings, emphasizing the physical interpretation of brane tilings as fivebrane systems. In part II, we discuss application of brane tilings to AdS/CFT correspondence and homological mirror symmetry. More topics, such as orientifold of brane tilings, phenomenological model building, similarities with BPS solitons in supersymmetric gauge theories, are also briefly discussed. This paper is a revised version of the author's master's thesis submitted to Department of Physics, Faculty of Science, the University of Tokyo on January 2008, and is based on his several papers and some works in progress [1,7]. [source] Gauge/string duality in confining theoriesFORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 7 2006J.D. Edelstein Abstract This is the content of a set of lectures given at the "XIII Jorge André Swieca Summer School on Particles and Fields", Campos do Jordão, Brazil in January 2005. They intend to be a basic introduction to the topic of gauge/gravity duality in confining theories. We start by reviewing some key aspects of the low energy physics of non-Abelian gauge theories. Then, we present the basics of the AdS/CFT correspondence and its extension both to gauge theories in different spacetime dimensions with sixteen supercharges and to more realistic situations with less supersymmetry. We discuss the different options of interest: placing D,branes at singularities and wrapping D,branes in calibrated cycles of special holonomy manifolds. We finally present an outline of a number of non-perturbative phenomena in non-Abelian gauge theories as seen from supergravity. [source] Higher spins and stringy AdS5 × S5,FORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 7-8 2005M. Bianchi Abstract In this lecture I review recent work done in collaboration with Beisert et al. [1-3] (For a concise summary see [4].). After a notational flash on the AdS/CFT correspondence, I will discuss higher spin (HS) symmetry enhancement at small radius and how this is holographically captured by free N = 4 SYM theory. I will then derive the spectrum of perturbative superstring excitations on AdS in this particular limit and successfully compare it with the spectrum of single-trace operators in free ,, = 4 SYM at large N, obtained by means of Polya(kov)'s counting. Decomposing the spectrum into HS multiplets allows one to precisely identify the 'massless' HS doubleton and the lower spin Goldstone multiplets which participate in the pantagruelic Higgs mechanism, termed "La Grande Bouffe". After recalling some basic features of Vasiliev's formulation of HS gauge theories, I will eventually sketch how to describe mass generation in the AdS bulk à la Sückelberg and its holographic implications such as the emergence of anomalous dimensions in the boundary ,, = 4 SYM theory. [source] Generalizations of the AdS/CFT correspondence,FORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 8 2004I. Kirsch Abstract We consider generalizations of the AdS/CFT correspondence in which probe branes are embedded in gravity backgrounds dual to either conformal or confining gauge theories. These correspond to defect conformal field theories (dCFT) or QCD-like theories with fundamental matter, respectively. Moreover, starting from the dCFT we discuss the deconstruction of intersecting M5-branes and M-theory. We obtain the following results: i) Holography of defect conformal field theories. We consider holography for a general D3-Dp brane intersection in type IIB string theory (p , {3,5,7}). The corresponding near-horizon geometry is given by a probe AdS-brane in AdS5 × S5. The dual defect conformal field theory describes ,, = 4 super Yang-Mills degrees of freedom coupled to fundamental matter on a lower-dimensional space-time defect. We derive the spectrum of fluctuations about the brane embedding and determine the behaviour of correlation functions involving defect operators. We also study the dual conformal field theory in the case of intersecting D3-branes. To this end, we develop a convenient superspace approach in which both two- and four-dimensional fields are described in a two-dimensional (2,2) superspace. We show that quantum corrections vanish to all orders in perturbation theory, such that the theory remains a (defect) conformal field theory when quantized. ii) Flavour in generalized AdS/CFT dualities. We present a holographic non-perturbative description of QCD-like theories with a large number of colours by embedding D7-brane probes into two non-supersymmetric gravity backgrounds. Both backgrounds exhibit confinement of fundamental matter and a discrete glueball and meson spectrum. We numerically compute the quark condensate and meson spectrum associated with these backgrounds. In the first background, we find some numerical evidence for a first order phase transition at a critical quark mass where the D7 embedding undergoes a geometric transition. In the second, we find a chiral symmetry breaking condensate as well as the associated Goldstone boson. iii) Deconstruction of extra dimensions. We apply the deconstruction method to the dCFT of intersecting D3-branes to obtain a field theory description for intersecting M5-branes. The resulting theory corresponds to two six-dimensional (2,0) superconformal field theories which we show to have tensionless strings on their four-dimensional intersection. Moreover, we argue that the SU(2)L R-symmetry of the dCFT matches the manifest SU(2) R-symmetry of the M5-M5 intersection. We finally explore the fascinating idea of deconstructing M-theory itself. We give arguments for an equivalence of M-theory on a certain background with the Higgs branch of a four-dimensional non-supersymmetric (quiver) gauge theory: in addition to a string theoretical motivation, we find wrapped M2-branes in the mass spectrum of the quiver theory at low energies. [source] Toric duality, Seiberg duality and Picard-Lefschetz transformationsFORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 7-8 2003S. Franco Toric Duality arises as an ambiguity in computing the quiver gauge theory living on a D3-brane which probes a toric singularity. It is reviewed how, in simple cases Toric Duality is Seiberg Duality. The set of all Seiberg Dualities on a single node in the quiver forms a group which is contained in a larger group given by a set of Picard-Lefschetz transformations. This leads to elements in the group (sometimes called fractional Seiberg Duals) which are not Seiberg Duality on a single node, thus providing a new set of gauge theories which flow to the same universality class in the Infra Red. [source] Gauge fixing procedure in the extended BRST theory.ANNALEN DER PHYSIK, Issue 3 2006The example of the abelian 2-forms Abstract The paper proposes a general procedure to find the form of the gauge fixing term in the extended BRST quantization of the gauge theories, a difficult problem in the standard approach. Our proposal is based on the many level structure of the extended spaces and leads to a simple form of the gauge fixing term. The abelian 2-form model is completely analyzed as an example. [source] The quantum supersymmetric vector multiplet and some problems in non-Abelian supergauge theoryANNALEN DER PHYSIK, Issue 11-12 2003D.R. Grigore Abstract We consider the supersymmetric vector multiplet in a purely quantum framework. We obtain some discrepancies with respect to the literature in the expression of the super-propagator and we prove that the model is consistent only for positive mass. The gauge structure is constructed purely deductive and leads to the introduction of scalar ghost superfields, in analogy to the usual gauge theories. The construction of a consistent supersymmetric gauge theory based on the vector model depends crucially on the definition of gauge invariance. We find some significant difficulties to impose a supersymmetric gauge invariance condition for the usual expressions from the literature. [source] Scattering of charged tensor bosons in gauge and superstring theoriesFORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 7-9 2010I. Antoniadis Abstract We calculate the leading-order scattering amplitude of one vector and two tensor gauge bosons in a recently proposed non-Abelian tensor gauge field theory and open superstring theory. The linear in momenta part of the superstring amplitude has identical Lorentz structure with the gauge theory, while its cubic in momenta part can be identified with an effective Lagrangian which is constructed using generalized non-Abelian field strength tensors. [source] Unquenched flavors in the Klebanov-Strassler theoryFORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 7-9 2008Article first published online: 21 JUL 200, S. Cremonesi Abstract We present an analytic solution of type IIB supergravity plus D7-branes, describing the addition of any number of flavors to the Klebanov-Strassler background. The dual field theory and its self-similar RG flow, described by a cascade of Seiberg dualities also in the presence of flavors, are discussed. The solution indicates that the dual gauge theory enjoys a duality wall in the UV. We stress the correspondence between Seiberg duality on the field theory side, and large gauge transformations on the RR and NSNS potentials on the gravity side. This contribution is mostly based on [1]. [source] Emergent 4D gravity from matrix modelsFORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 4-5 2008Article first published online: 8 APR 200, H. Steinacker Abstract Recent progress in the understanding of gravity on noncommutative spaces is discussed. A gravity theory naturally emerges from matrix models of noncommutative gauge theory. The effective metric depends on the dynamical Poisson structure, absorbing the degrees of freedom of the would-be U(1) gauge field. The gravity action is induced upon quantization. [source] Generalizations of the AdS/CFT correspondence,FORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 8 2004I. Kirsch Abstract We consider generalizations of the AdS/CFT correspondence in which probe branes are embedded in gravity backgrounds dual to either conformal or confining gauge theories. These correspond to defect conformal field theories (dCFT) or QCD-like theories with fundamental matter, respectively. Moreover, starting from the dCFT we discuss the deconstruction of intersecting M5-branes and M-theory. We obtain the following results: i) Holography of defect conformal field theories. We consider holography for a general D3-Dp brane intersection in type IIB string theory (p , {3,5,7}). The corresponding near-horizon geometry is given by a probe AdS-brane in AdS5 × S5. The dual defect conformal field theory describes ,, = 4 super Yang-Mills degrees of freedom coupled to fundamental matter on a lower-dimensional space-time defect. We derive the spectrum of fluctuations about the brane embedding and determine the behaviour of correlation functions involving defect operators. We also study the dual conformal field theory in the case of intersecting D3-branes. To this end, we develop a convenient superspace approach in which both two- and four-dimensional fields are described in a two-dimensional (2,2) superspace. We show that quantum corrections vanish to all orders in perturbation theory, such that the theory remains a (defect) conformal field theory when quantized. ii) Flavour in generalized AdS/CFT dualities. We present a holographic non-perturbative description of QCD-like theories with a large number of colours by embedding D7-brane probes into two non-supersymmetric gravity backgrounds. Both backgrounds exhibit confinement of fundamental matter and a discrete glueball and meson spectrum. We numerically compute the quark condensate and meson spectrum associated with these backgrounds. In the first background, we find some numerical evidence for a first order phase transition at a critical quark mass where the D7 embedding undergoes a geometric transition. In the second, we find a chiral symmetry breaking condensate as well as the associated Goldstone boson. iii) Deconstruction of extra dimensions. We apply the deconstruction method to the dCFT of intersecting D3-branes to obtain a field theory description for intersecting M5-branes. The resulting theory corresponds to two six-dimensional (2,0) superconformal field theories which we show to have tensionless strings on their four-dimensional intersection. Moreover, we argue that the SU(2)L R-symmetry of the dCFT matches the manifest SU(2) R-symmetry of the M5-M5 intersection. We finally explore the fascinating idea of deconstructing M-theory itself. We give arguments for an equivalence of M-theory on a certain background with the Higgs branch of a four-dimensional non-supersymmetric (quiver) gauge theory: in addition to a string theoretical motivation, we find wrapped M2-branes in the mass spectrum of the quiver theory at low energies. [source] Exact results in a non-supersymmetric gauge theoryFORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 6-7 2004A. Armoni We consider non-supersymmetric large N orientifold field theories. Specifically, we discuss a gauge theory with a Dirac fermion in the anti-symmetric tensor representation. We argue that, at large N and in a large part of its bosonic sector, this theory is non-perturbatively equivalent to ,, = 1 SYM, so that exact results established in the latter (parent) theory also hold in the daughter orientifold theory. In particular, the non-supersymmetric theory has an exactly calculable bifermion condensate, exactly degenerate parity doublets, and a vanishing cosmological constant (all this to leading order in 1 / N). [source] Field theory on a non-commutative plane: a non-perturbative studyFORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 5 2004F. Hofheinz Abstract The 2d gauge theory on the lattice is equivalent to the twisted Eguchi,Kawai model, which we simulated at N ranging from 25 to 515. We observe a clear large N scaling for the 1- and 2-point function of Wilson loops, as well as the 2-point function of Polyakov lines. The 2-point functions agree with a universal wave function renormalization. The large N double scaling limit corresponds to the continuum limit of non-commutative gauge theory, so the observed large N scaling demonstrates the non-perturbative renormalizability of this non-commutative field theory. The area law for the Wilson loops holds at small physical area as in commutative 2d planar gauge theory, but at large areas we find an oscillating behavior instead. In that regime the phase of the Wilson loop grows linearly with the area. This agrees with the Aharonov-Bohm effect in the presence of a constant magnetic field, identified with the inverse non-commutativity parameter. Next we investigate the 3d ,,4 model with two non-commutative coordinates and explore its phase diagram. Our results agree with a conjecture by Gubser and Sondhi in d = 4, who predicted that the ordered regime splits into a uniform phase and a phase dominated by stripe patterns. We further present results for the correlators and the dispersion relation. In non-commutative field theory the Lorentz invariance is explicitly broken, which leads to a deformation of the dispersion relation. In one loop perturbation theory this deformation involves an additional infrared divergent term. Our data agree with this perturbative result. We also confirm the recent observation by Ambjø rn and Catterall that stripes occur even in d = 2, although they imply the spontaneous breaking of the translation symmetry. [source] Lectures on the plane-wave string/gauge theory dualityFORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 2-3 2004J.C. Plefka Abstract These lectures give an introduction to the novel duality relating type IIB string theory in a maximally supersymmetric plane-wave background to ,, = 4, d = 4, U(N) super Yang-Mills theory in a particular large N and large R-charge limit due to Berenstein, Maldacena and Nastase. In the first part of these lectures the duality is derived from the AdS/CFT correspondence by taking a Penrose limit of the AdS5 × S5 geometry and studying the corresponding double-scaling limit on the gauge theory side. The resulting free plane-wave superstring is then quantized in light-cone gauge. On the gauge theory side of the correspondence the composite super Yang-Mills operators dual to string excitations are identified, and it is shown how the string spectrum can be mapped to the planar scaling dimensions of these operators. In the second part of these lectures we study the correspondence at the interacting respectively non-planar level. On the gauge theory side it is demonstrated that the large N large R-charge limit in question preserves contributions from Feynman graphs of all genera through the emergence of a new genus counting parameter , in agreement with the string genus expansion for non-zero gs. Effective quantum mechanical tools to compute higher genus contributions to the scaling dimensions of composite operators are developed and explicitly applied in a genus one computation. We then turn to the interacting string theory side and give an elementary introduction into light-cone superstring field theory in a plane-wave background and point out how the genus one prediction from gauge theory can be reproduced. Finally, we summarize the present status of the plane-wave string/gauge theory duality. [source] Toric duality, Seiberg duality and Picard-Lefschetz transformationsFORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 7-8 2003S. Franco Toric Duality arises as an ambiguity in computing the quiver gauge theory living on a D3-brane which probes a toric singularity. It is reviewed how, in simple cases Toric Duality is Seiberg Duality. The set of all Seiberg Dualities on a single node in the quiver forms a group which is contained in a larger group given by a set of Picard-Lefschetz transformations. This leads to elements in the group (sometimes called fractional Seiberg Duals) which are not Seiberg Duality on a single node, thus providing a new set of gauge theories which flow to the same universality class in the Infra Red. [source] Non-commutative field theories beyond perturbation theoryFORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 7-8 2003W. Bietenholz We investigate two models in non-commutative (NC) field theory by means of Monte Carlo simulations. Even if we start from the Euclidean lattice formulation, such simulations are only feasible after mapping the systems onto dimensionally reduced matrix models. Using this technique, we measure Wilson loops in 2d NC gauge theory of rank 1. It turns out that they are non-perturbatively renormalizable, and the phase follows an Aharonov-Bohm effect if we identify , = 1/B. Next we study the 3d , ,4 model with two NC coordinates, where we present new results for the correlators and the dispersion relation. We further reveal the explicit phase diagram. The ordered regime splits into a uniform and a striped phase, as it was qualitatively conjectured before. We also confirm the recent observation by Ambjø rn and Catterall that such stripes occur even in d = 2, although they imply the spontaneous breaking of translation symmetry. However, in d = 3 and d = 2 we observe only patterns of two stripes to be stable in the range of parameters investigated. [source] Stripe fractionalization: the quantum spin nematic and the Abrikosov latticePHYSICA STATUS SOLIDI (B) BASIC SOLID STATE PHYSICS, Issue 2 2003J. Zaanen Abstract In part (I) of this two paper series on stripe fractionalization [J. Phys. IV (France) 12, Prg-245 (2002)], we argued that in principle the "domain wall-ness" of the stripe phase could persist in the spin and charge disordered superconductors, and we demonstrated how this physics is in one-to-one correspondence with Ising gauge theory. Here we focus on yet another type of order suggested by the gauge theory: the quantum spin nematic. Although it is not easy to measure this order directly, we argue that the superconducting vortices act as perturbations destroying the gauge symmetry locally. This turns out to give rise to a simple example of a gauge-theoretical phenomenon known as topological interaction. As a consequence, at any finite vortex density a globally ordered antiferromagnet emerges. This offers a potential explanation for recent observations in the underdoped 214 system. [source] Duality between constraints and gauge conditionsANNALEN DER PHYSIK, Issue 7-8 2007M.N. Stoilov Abstract There are two important sets of seemingly absolutely different objects in any gauge theory: the set of constraints, which generate the local symmetry and the set of gauge conditions, which fix this symmetry; the first one is determined by the Lagrangean of the model, the second is a matter of choice. However, in the transition amplitude constraints and gauge conditions participate in exactly the same way. This suggests the possibility for existence of a model with the same transition amplitude and in which gauge conditions and constraints are interchanged. We investigate the conditions that gauge fixing terms should satisfy so that this dual picture is allowed. En route, we propose to add new terms in the constraints which would generate the gauge transformation of the Lagrange multipliers and construct two BRST charges , one, as usual, for the constraints, and one for the gauge conditions. [source] Electric/magnetic flux tube on the background of magnetic/electric fieldANNALEN DER PHYSIK, Issue 5 2004V. Dzhunushaliev Abstract It is argued that the phenomenon of a flux tube in quantum chromodynamics is closely connected with a spontaneously symmetry breakdown of gauge theory. It is shown that in the presence of a mass term in the SU(2) gauge theory the Nielsen-Olesen equations describe the flux tube surrounded by an external field. [source] The quantum supersymmetric vector multiplet and some problems in non-Abelian supergauge theoryANNALEN DER PHYSIK, Issue 11-12 2003D.R. Grigore Abstract We consider the supersymmetric vector multiplet in a purely quantum framework. We obtain some discrepancies with respect to the literature in the expression of the super-propagator and we prove that the model is consistent only for positive mass. The gauge structure is constructed purely deductive and leads to the introduction of scalar ghost superfields, in analogy to the usual gauge theories. The construction of a consistent supersymmetric gauge theory based on the vector model depends crucially on the definition of gauge invariance. We find some significant difficulties to impose a supersymmetric gauge invariance condition for the usual expressions from the literature. [source] A supersymmetric extension of quantum gauge theoryANNALEN DER PHYSIK, Issue 1-2 2003D.R. Grigore Abstract We consider a supersymmetric extension of quantum gauge theory based on a vector multiplet containing supersymmetric partners of spin 3/2 for the vector fields. The constructions of the model follows closely the usual construction of gauge models in the Epstein-Glaser framework for perturbative field theory. Accordingly, all the arguments are completely of quantum nature without reference to a classical supersymmetric theory. As an application we consider the supersymmetric electroweak theory. The resulting self-couplings of the gauge bosons agree with the standard model up to a divergence. [source] | ||||||||||