On Geometry and Matrix Models

TL;DR

This paper explores extensions of the relationship between matrix models, topological strings, and supersymmetric gauge theories, revealing new dualities and computational methods for gauge theory solutions using matrix models.

Contribution

It introduces double scaling limits of unitary matrix models to derive large N duals of local Calabi-Yau geometries and connects multi-matrix models to effective superpotentials in N=1 ADE quiver gauge theories.

Findings

Double scaling limits of matrix models yield large N duals of Calabi-Yau geometries.

Multi-matrix models compute superpotentials for N=1 ADE quiver gauge theories.

Spectral curves are described as branched covers via Virasoro and W-constraints.

Abstract

We point out two extensions of the relation between matrix models, topological strings and N=1 supersymmetric gauge theories. First, we note that by considering double scaling limits of unitary matrix models one can obtain large N duals of the local Calabi-Yau geometries that engineer N=2 gauge theories. In particular, a double scaling limit of the Gross-Witten one-plaquette lattice model gives the SU(2) Seiberg-Witten solution, including its induced gravitational corrections. Secondly, we point out that the effective superpotential terms for N=1 ADE quiver gauge theories is similarly computed by large multi-matrix models, that have been considered in the context of ADE minimal models on random surfaces. The associated spectral curves are multiple branched covers obtained as Virasoro and W-constraints of the partition function.