On the Coulomb Branch of a Marginal Deformation of N=4 SUSY Yang-Mills

We determine the exact vacuum structure of a marginal deformation of N=4 SUSY Yang-Mills with gauge group U(N). The Coulomb branch of the theory consists of several sub-branches which are governed by complex curves of the form Sigma_{n_{1}} U Sigma_{n_{2}} U Sigma_{n_{3}} of genus N=n_{1}+n_{2}+n_{3}. Each sub-branch intersects with a family of Higgs and Confining branches permuted by SL(2,Z) transformations. We determine the curve by solving a related matrix model in the planar limit according to the prescription of Dijkgraaf and Vafa, and also by explicit instanton calculations using a form of localization on the instanton moduli space. We find that Sigma_{n} coincides with the spectral curve of the n-body Ruijsenaars-Schneider system. Our results imply that the theory on each sub-branch is holomorphically equivalent to certain five-dimensional gauge theory with eight supercharges. This equivalence also implies the existence of novel confining branches in five dimensions.Comment: LaTeX file. 48 page

The BPS Spectra of Two-Dimensional Supersymmetric Gauge Theories with Twisted Mass Terms

The vacuum structure and spectra of two-dimensional gauge theories with N=(2,2) supersymmetry are investigated. These theories admit a twisted mass term for charged chiral matter multiplets. In the case of a U(1) gauge theory with N chiral multiplets of equal charge, an exact description of the BPS spectrum is obtained for all values of the twisted masses. The BPS spectrum has two dual descriptions which apply in the Higgs and Coulomb phases of the theory respectively. The two descriptions are related by a massive analog of mirror symmetry: the exact mass formula which is given by a one-loop calculation in the Coulomb phase gives predictions for an infinite series of instanton corrections in the Higgs phase. The theory is shown to exhibit many phenomena which are usually associated with N=2 theories in four dimensions. These include BPS-saturated dyons which carry both topological and Noether charges, non-trivial monodromies of the spectrum in the complex parameter space, curves of marginal stability on which BPS states can decay and strongly coupled vacua with massless solitons and dyons.Comment: 51 page, LaTeX, Typos correcte

Exact Superpotentials from Matrix Models

Dijkgraaf and Vafa (DV) have conjectured that the exact superpotential for a large class of N=1 SUSY gauge theories can be extracted from the planar limit of a certain holomorphic matrix integral. We test their proposal against existing knowledge for a family of deformations of N=4 SUSY Yang-Mills theory involving an arbitrary polynomial superpotential for one of the three adjoint chiral superfields. Specifically, we compare the DV prediction for these models with earlier results based on the connection between SUSY gauge theories and integrable systems. We find complete agreement between the two approaches. In particular we show how the DV proposal allows the extraction of the exact eigenvalues of the adjoint scalar in the confining vacuum and hence computes all related condensates of the finite-N gauge theory. We extend these results to include Leigh-Strassler deformations of the N=4 theory.Comment: 28 pages, 1 figure, latex with JHEP.cls, replaced with typos corrected and one clarifying commen

Wall Crossing and Instantons in Compactified Gauge Theory

We calculate the leading weak-coupling instanton contribution to the moduli-space metric of N=2 supersymmetric Yang-Mills theory with gauge group SU(2) compactified on R^3 x S^1. The results are in precise agreement with the semiclassical expansion of the exact metric recently conjectured by Gaiotto, Moore and Neitzke based on considerations related to wall-crossing in the corresponding four-dimensional theory.Comment: 24 pages, no figure

The Phase Structure of Mass-Deformed SU(2)xSU(2) Quiver Theory

The phase structure of the finite SU(2)xSU(2) theory with N=2 supersymmetry, broken to N=1 by mass terms for the adjoint-valued chiral multiplets, is determined exactly by compactifying the theory on a circle of finite radius. The exact low-energy superpotential is constructed by identifying it as a linear combination of the Hamiltonians of a certain symplectic reduction of the spin generalized elliptic Calogero-Moser integrable system. It is shown that the theory has four confining, two Higgs and two massless Coulomb vacua which agrees with a simple analysis of the tree-level superpotential of the four-dimensional theory. In each vacuum, we calculate all the condensates of the adjoint-valued scalars.Comment: 12 pages, JHEP.cl

A New 2d/4d Duality via Integrability

We prove a duality, recently conjectured in arXiv:1103.5726, which relates the F-terms of supersymmetric gauge theories defined in two and four dimensions respectively. The proof proceeds by a saddle point analysis of the four-dimensional partition function in the Nekrasov-Shatashvili limit. At special quantized values of the Coulomb branch moduli, the saddle point condition becomes the Bethe Ansatz Equation of the SL(2) Heisenberg spin chain which coincides with the F-term equation of the dual two-dimensional theory. The on-shell values of the superpotential in the two theories are shown to coincide in corresponding vacua. We also identify two-dimensional duals for a large set of quiver gauge theories in four dimensions and generalize our proof to these cases.Comment: 19 pages, 2 figures, minor corrections and references adde

Spiky Strings and Giant Holes

We analyse semiclassical strings in AdS in the limit of one large spin. In this limit, classical string dynamics is described by a finite number of collective coordinates corresponding to spikes or cusps of the string. The semiclassical spectrum consists of two branches of excitations corresponding to "large" and "small" spikes respectively. We propose that these states are dual to the excitations known as large and small holes in the spin chain description of N=4 SUSY Yang-Mills. The dynamics of large spikes in classical string theory can be mapped to that of a classical spin chain of fixed length. In turn, small spikes correspond to classical solitons propagating on the background formed by the large spikes. We derive the dispersion relation for these excitations directly in the finite gap formalism.Comment: 36 pages, 9 figure

New Results from Glueball Superpotentials and Matrix Models: the Leigh-Strassler Deformation

Using the result of a matrix model computation of the exact glueball superpotential, we investigate the relevant mass perturbations of the Leigh-Strassler marginal ``q'' deformation of N=4 supersymmetric gauge theory. We recall a conjecture for the elliptic superpotential that describes the theory compactified on a circle and identify this superpotential as one of the Hamiltonians of the elliptic Ruijsenaars-Schneider integrable system. In the limit that the Leigh-Strassler deformation is turned off, the integrable system reduces to the elliptic Calogero-Moser system which describes the N=1^* theory. Based on these results, we identify the Coulomb branch of the partially mass-deformed Leigh-Strassler theory as the spectral curve of the Ruijsenaars-Schneider system. We also show how the Leigh-Strassler deformation may be obtained by suitably modifying Witten's M theory brane construction of N=2 theories.Comment: 13 pages, JHEP, amstex, changed JHEP to JHEP