Constructing Gauge Theory Geometries from Matrix Models

TL;DR

This paper constructs the geometry associated with the exact superpotential of certain N=1 gauge theories using matrix models, revealing detailed geometric structures and 1/N corrections related to string theory effects.

Contribution

It introduces a method to derive the geometry encoding the superpotential for gauge theories with complex matter content from matrix models, including subleading 1/N corrections.

Findings

Extraction of non-hyperelliptic Riemann surfaces from loop equations.

Identification of 1/N corrections via logarithmic deformations.

Explicit encoding of orientifolded string theory geometries.

Abstract

We use the matrix model -- gauge theory correspondence of Dijkgraaf and Vafa in order to construct the geometry encoding the exact gaugino condensate superpotential for the N=1 U(N) gauge theory with adjoint and symmetric or anti-symmetric matter, broken by a tree level superpotential to a product subgroup involving U(N_i) and SO(N_i) or Sp(N_i/2) factors. The relevant geometry is encoded by a non-hyperelliptic Riemann surface, which we extract from the exact loop equations. We also show that O(1/N) corrections can be extracted from a logarithmic deformation of this surface. The loop equations contain explicitly subleading terms of order 1/N, which encode information of string theory on an orientifolded local quiver geometry.