S-duality of the Leigh-Strassler Deformation via Matrix Models

TL;DR

This paper explores the S-duality properties of the Leigh-Strassler deformation of N=4 supersymmetric Yang-Mills theory using matrix models, revealing how vacua are related by modular transformations and proposing an exact superpotential.

Contribution

It introduces a matrix model approach to compute the superpotential of the Leigh-Strassler deformation and demonstrates the SL(2,Z) duality acting on the vacua.

Findings

SL(2,Z) modular group relates different vacua.

Exact superpotential derived via matrix model.

Identification of parameter points with diverging condensates.

Abstract

We investigate an exactly marginal N=1 supersymmetric deformation of SU(N) N=4 supersymmetric Yang-Mills theory discovered by Leigh and Strassler. We use a matrix model to compute the exact superpotential for a further massive deformation of the U(N) Leigh-Strassler theory. We then show how the exact superpotential and eigenvalue spectrum for the SU(N) theory follows by a process of integrating-in. We find that different vacua are related by an action of the SL(2,Z) modular group on the bare couplings of the theory extending the action of electric-magnetic duality away from the N=4 theory. We perform non-trivial tests of the matrix model results against semiclassical field theory analysis. We also show that there are interesting points in parameter space where condensates can diverge and vacua disappear. Based on the matrix model results, we propose an exact elliptic superpotential to describe the theory compactified on a circle of finite radius.