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

TL;DR

This paper analyzes the vacuum structure of a marginally deformed N=4 SUSY Yang-Mills theory, revealing complex sub-branches governed by algebraic curves and establishing connections to integrable systems and five-dimensional gauge theories.

Contribution

It determines the exact Coulomb branch structure of the deformed theory using matrix models and instanton calculations, linking it to spectral curves of integrable systems and 5D gauge theories.

Findings

Coulomb branch consists of multiple sub-branches with algebraic curve descriptions.

Each sub-branch intersects with Higgs and confining branches permuted by SL(2,Z).

The spectral curve matches that of the Ruijsenaars-Schneider system.

Abstract

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.