The Coulomb branch of the Leigh-Strassler deformation and matrix models

TL;DR

This paper employs the Dijkgraaf-Vafa matrix model approach to analyze the Coulomb branch of the Leigh-Strassler deformation of N=4 SYM, revealing a family of generalized Seiberg-Witten curves and explicit relations between potentials and vacua.

Contribution

It introduces a novel matrix model analysis of the Leigh-Strassler deformation, characterizing the Coulomb branch via multi-valued functions and explicit curve descriptions.

Findings

Derived the family of generalized Seiberg-Witten curves.

Established the relation between potentials and vacua.

Presented resolvents for expectation values of chiral operators.

Abstract

The Dijkgraaf-Vafa approach is used in order to study the Coulomb branch of the Leigh-Strassler massive deformation of N=4 SYM with gauge group U(N). The theory has N=1 SUSY and an N-dimensional Coulomb branch of vacua, which can be described by a family of ``generalized'' Seiberg-Witten curves. The matrix model analysis is performed by adding a tree level potential that selects particular vacua. The family of curves is found: it consists of order N branched coverings of a base torus, and it is described by multi-valued functions on the latter. The relation between the potential and the vacuum is made explicit. The gauge group SU(N) is also considered. Finally the resolvents from which expectation values of chiral operators can be extracted are presented.