On the Coulomb branch of a marginal deformation of N = 4 SUSY Yang-Mills

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 Σn1∪Σn2∪Σn3 of genus N ≤ n1+n2+n3. Each sub-branch intersects with a family of Higgs and Confining branches permuted by SL(2,double struck Z sign) 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 Σn 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. © SISSA 2005.