Quantum moduli spaces from matrix models

TL;DR

This paper extends matrix model techniques to compute quantum deformed moduli spaces of vacua in 4D supersymmetric gauge theories, especially involving D-branes and fractional branes at singularities.

Contribution

It introduces a method to apply Dijkgraaf-Vafa matrix models to analyze quantum moduli spaces in complex supersymmetric gauge theories.

Findings

Successfully computes quantum deformed moduli spaces in specific examples.

Connects matrix models with geometric engineering of gauge theories.

Provides a framework for studying D-brane probes in singular geometries.

Abstract

In this paper we show that the matrix model techniques developed by Dijkgraaf and Vafa can be extended to compute quantum deformed moduli spaces of vacua in four dimensional supersymmetric gauge theories. The examples studied give the moduli space of a bulk D-brane probe in geometrically engineered theories, in the presence of fractional branes at singularities.