5d Gauge Theories Research Articles

Comment on Dirac spectral sum rules for QCD in three dimensions

Recently Magnea hep-th/9907096 , hep-th/9912207 [Phys.Rev.D61, 056005 (2000); Phys.Rev.D62, 016005 (2000)] claimed to have computed the first sum rules for Dirac operators in 3D gauge theories from 0D non-linear sigma models. I point out that these computations are incorrect, and that they contradict with the exact results for the spectral densities unambiguously derived from random matrix theory by Nagao and myself.

Chiral compactifications of 6D superconformal theories

We construct chiral N=1 gauge theories in 4D by compactifying the 6D Blum–Intriligator (1,0) theories of 5-branes at Ak singularities on T2 with a nontrivial bundle of the global U(1) symmetry of these theories.

Nonabelian duality and solvable large lattice systems

We introduce the basics of the nonabelian duality transformation of SU(N) or U(N) vector-field models defined on a lattice. The dual degrees of freedom are certain species of the integer-valued fields complemented by the symmetric groups' \otimes_{n} S(n) variables. While the former parametrize relevant irreducible representations, the latter play the role of the Lagrange multipliers facilitating the fusion rules involved. As an application, I construct a novel solvable family of SU(N) D-matrix systems graded by the rank 1\leq{k}\leq{(D-1)} of the manifest [U(N)]^{\oplus k} conjugation-symmetry. Their large N solvability is due to a hidden invariance (explicit in the dual formulation) which allows for a mapping onto the recently proposed eigenvalue-models \cite{Dub1} with the largest k=D symmetry. Extending \cite{Dub1}, we reconstruct a D-dimensional gauge theory with the large N free energy given (modulo the volume factor) by the free energy of a given proposed 1\leq{k}\leq{(D-1)} D-matrix system. It is emphasized that the developed formalism provides with the basis for higher-dimensional generalizations of the Gross-Taylor stringy representation of strongly coupled 2d gauge theories.

The Hagedorn transition, deconfinement and [formula omitted] SYM theory

N=4 Super Yang–Mills theory supplies us with a non-Abelian 4D gauge theory with a meaningful perturbation expansion, both in the UV and in the IR. We calculate the free energy on a 3-sphere and observe a deconfinement transition for large N at zero coupling. The same thermodynamic behaviour is found for a wide class of toy models, possibly also including the case of nonzero coupling. Below the transition we also find Hagedorn behaviour, which is identified with fluctuations signaling the approach to the deconfined phase. The Hagedorn and the deconfinement temperatures are identical. Application of the AdS/CFT correspondence gives a connection between string Hagedorn behaviour and black holes.

Non-supersymmetric large N gauge theories from type 0 brane configurations

We use dyonic brane configurations of type 0 string theory to study large N non-supersymmetric 4d gauge theories. The brane configurations define theories similar to the supersymmetric ones which arise in type II. We find the non-SUSY analogues of N=2 and N=1. In particular we suggest new non-SUSY CFT's and a brane realization of a non-SUSY Seiberg duality.

5d and 6d supersymmetric gauge theories: prepotentials from integrable systems

We discuss 5d and 6d supersymmetric gauge theories in the target-space with compactified directions and with the matter hypermultiplets in fundamental representations in the framework of integrable systems. In particular, we consider the prepotentials of these theories and derive explicit formulas for their perturbative parts.

Softly broken SQCD: in the continuum, on the lattice, on the brane

We review progress in studying the solutions of SQCD in the presence of explicit, soft SUSY breaking terms. Massive N = 1 SQCD in the presece of a small gaugino mass leads to a controlled solution which has interesting phase structure with changing θ angle reminiscent of the QCD chiral Lagrangian. Current attempts to test the solutions of pure glue SQCD on the lattice require a theoretical understandinf of the theory with small gaugino mass in order to understand the approach to the SUSY point. We provide such a description making predictions for the gaugino condensate and lightest bound state masses. Finally we briefly review recent D-brane constructions of 4D gauge theories in string theory including a non-supersymmetric configuration. We identify this configuration with softly broken N = 2 SQCD.

Orientifolds, branes, and duality of 4D gauge theories

Recently, a D-brane construction in type IIA string theory was shown to yield the electric/magnetic duality of four-dimensional N = 1 supersymmetric U( N c ) gauge theories with N f flavours of quark. We present here an extension of that construction which yields the electric/magnetic duality for the SO( N c ) and USp( N c ) gauge theories with N f quarks, by adding an orientifold plane which is consistent with the supersymmetry. Due to the intersection of the orientifold plane with the NS-NS fivebranes already present, new features arise which are crucial in determining the correct final structure of the dualities.

Type IIA superstrings, chiral symmetry, and N = 1 4D gauge theory dualities

We study N = 1 four-dimensional gauge theories as the world-volume theory of D4-branes between NS 5-branes. We find constructions for a number of known field theory dualities involving SU( N c ) × SU( N′ c ) groups, coupled by matter fields F in the (N c, N − c) representation, in terms of branes of type IIA string theory. The dual gauge group follows from simply reversing the ordering of the NS 5-branes and the D6-branes while conserving magnetic charge on the world-volume of the branes. We interpret many field theory phenomena such as deformation of the superpotential W = Tr (F F ̃ ) k+1 in terms of the position of branes. By looking to D-branes for guidance, we find new N = 1 dualities involving arbitrary numbers of gauge groups. We propose a mechanism for enhanced chiral symmetry in the brane construction which, we conjecture, is associated with tensionless 3-branes in six dimensions.

SO(3) monopoles, vortices and confinement in SU(2) gauge theory

We report on further progress in our programme of understanding confinement in 3d and 4d SU(2) gauge theory in terms of Z(2) monopoles. A sufficient condition for confinement was previously translated into Z(2) monopole correlation inequalities in a related SO(3) gauge theory. We shall discuss the physical picture underlying this scenario and present some Monte Carlo evidence concerning the monopole correlation inequalities.

Width of long colour flux tubes in lattice gauge systems

In the confining phase of any gauge system the mean squared width of the colour flux tube joining a pair of quarks should grow logarithmically as a function of their distance, according to the effective string description of its infrared properties. New data on 3D 7L2 gauge theory, combined with high precision data on the interface physics of the 3D Ising model, nicely fit this behaviour over a range of more than two orders of magnitude.

Chiral symmetry breaking and the thermodynamics of 2d gauge theories

Chiral symmetry breaking and the thermodynamics of 2d gauge theories

Temperature- and curvature dependence of the chiral symmetry breaking in 2D gauge theories

The partition functions for a family of 2-dimensional interacting theories containing the gauged Thirring model are computed. We obtain non-perturbative expressions for the dependence of the chiral condensate on the temperature and the curvature. Both, high temperature and big curvature suppress the condensate exponentially and we can associate an effective temperature to the curvature.

Gell-mann-low function of the chiral model on the homogeneous berger space

The asymptotic freedon of two-dimensional nonlinear sigma models (chiral models) is one of the most important properties on which the analogy between 2d sigma models and 4d gauge theories is based. For the two-dimensional nonlinear sigma model on the homogeneous space Sp(2)/SU(2) (Berger manifold) the method of sectional curvatures is used to find the Gell-Mann-Low beta function in the single-loop approximation. The result indicates that the model is an asymptotically free renormalizable nonlinear model.

Analytic determination of theSU 2 lattice gauge theory stable under Migdal-Kadanoff renormalization

The Migdal-Kadanoff recursion relations are applied to the most general plaquette action. The stable action, determined by a weak-coupling expansion, lies between the Manton and the heat kernel ones, in agreement with previous numerical investigations. Moreover, it is shown that certain contributions to the renormalization of the coupling constant exactly coincide with the perturbative ones; this happens for those terms of pure group-theoretical origin, which are the same in the perturbative expansions of the 4D gauge theory and of the corresponding 2D chiral model.

Duality, vortices and flux tubes in two-dimensional spin and chiral models

Duality transformations of abelian spin systems are arranged from the “field strength” point of view, a way which allows a straightforward extension to the non-abelian continuum chiral models. A proof of the equivalence of the field strength and the more standard formulation of chiral models is given, and for SU(2), the dual partition function is worked out explicitly. It is essentially an O(3) model. We also review some facts about vortices in the U(1) and SU( N)/Z N models. Then it is shown how these objects are naturally incorporated in the dual representation of these models. Next, the dual representation of the invariant correlation function in any chiral model is derived. We discuss, making use of the string singularity in this representation how the behavior of the function can be understood in terms of the confinement of the models conserved current to a tube. For the periodic gaussian model this is seen explicitly in the saddle-point approximation, the confinement being due to a solenoid of vortices. We also elaborate on the analogues between 4d gauge theories and 2d chiral models, including a comparison of the duality transformation for each.

Closed-form bound-state effective potential and exact solutions for dynamical symmetry breaking in a 4D gauge theory

We have found a closed-form expression for the bound-state effective potential or a large class of models of dynamical symmetry breaking. Exact solutions to a Schwinger-Dyson equation and the corresponding Bethe-Salpeter equations are found. This enables one to cómpute the effective potential in a non-trivial four-dimensional gauge model of chiral breaking for an arbitrary coupling constant and gauge parameter.

First and second order phase transitions in gauge theories at finite temperature

We consider in general the nature of the phase transition which occurs in 4D gauge theories coupled to scalar and spinor fields at finite temperature. It is shown that the critical behavior can be isolated in an effective 3D theory of the zero frequency mode whose lagrangian may be calculated explicitly in weak coupling perturbation theory. This lagrangian, in turn, may be investigated by means of standard ϵ-expansion techniques. Theories with an asymptotically free gauge coupling constant possess no stable fixed point in the ϵ-expansion and are inferred to have weakly first-order phase transitions; theories not satisfying this condition may have second-order transitions.

Quantum Langlands dualities of boundary conditions, $D$-modules, and conformal blocks

We review and extend the vertex algebra framework linking gauge theory constructions and a quantum deformation of the Geometric Langlands Program. The relevant vertex algebras are associated to junctions of two boundary conditions in a 4d gauge theory and can be constructed from the basic ones by following certain standard procedures. Conformal blocks of modules over these vertex algebras give rise to twisted D-modules on the moduli stacks of G-bundles on Riemann surfaces which have applications to the Langlands Program. In particular, we construct a series of vertex algebras for every simple Lie group G which we expect to yield D-module kernels of various quantum Geometric Langlands dualities. We pay particular attention to the full duality group of gauge theory, which enables us to extend the standard qGL duality to a larger duality groupoid. We also discuss various subtleties related to the spin and gerbe structures and present a detailed analysis for the U(1) and SU(2) gauge theories.

Givental $J$-functions, quantum integrable systems, AGT relation with surface operator

We study 4d $\mathcal{N}=2$ gauge theories with a co-dimension two full surface operator, which exhibit a fascinating interplay of supersymmetric gauge theories, equivariant Gromov-Witten theory and geometric representation theory. For pure Yang-Mills and $\mathcal{N}=2^*$ theory, we describe a full surface operator as the 4d gauge theory coupled to a 2d $\mathcal{N}=(2,2)$ gauge theory. By supersymmetric localizations, we present the exact partition functions of both 4d and 2d theories which satisfy integrable equations. In addition, the form of the structure constants with a semi-degenerate field in SL(N,R) WZNW model is predicted from one-loop determinants of 4d gauge theories with a full surface operator via the AGT relation.