Comments on Quiver Gauge Theories and Matrix Models

TL;DR

This paper explores the Dijkgraaf-Vafa conjecture linking topological strings, gauge theories, and matrix models to compute quantum deformations of Calabi-Yau threefolds with ADE singularities and derive effective superpotentials.

Contribution

It provides a method to calculate quantum deformations and superpotentials for ADE singularities using multi-matrix models and geometric engineering.

Findings

Derived effective superpotentials for dual quiver gauge theories.

Identified Veneziano-Yankielowicz terms in the superpotentials.

Connected geometric deformations with matrix model calculations.

Abstract

Dijkgraaf and Vafa have conjectured the correspondences between topological string theories, ${\cal N}=1$ gauge theories and matrix models. By the use of this conjecture, we calculate the quantum deformations of Calabi-Yau threefolds with ADE singularities from ADE multi-matrix models. We obtain the effective superpotentials of the dual quiver gauge theories in terms of the geometric engineering for the deformed geometries. We find the Veneziano-Yankielowicz terms in the effective superpotentials.