Seiberg-Witten curve via generalized matrix model

TL;DR

This paper derives the Seiberg-Witten curve for N=2 SU(2)^n gauge theory using a generalized matrix model linked to the AGT correspondence, connecting conformal blocks and gauge theory spectral curves.

Contribution

It introduces a generalized matrix model framework for the n-point toric Virasoro conformal block and derives the associated Seiberg-Witten curve.

Findings

Verification from Liouville correlation functions

Derivation of the Seiberg-Witten spectral curve

Connection between matrix models and gauge theory geometry

Abstract

We study the generalized matrix model which corresponds to the n-point toric Virasoro conformal block. This describes four-dimensional N=2 SU(2)^n gauge theory with circular quiver diagram by the AGT relation. We first verify that it is obtained from the perturbative calculation of the Liouville correlation function. We derive the Seiberg-Witten curve for N=2 gauge theory as a spectral curve of the generalized matrix model.