Generalized matrix models and AGT correspondence at all genera

TL;DR

This paper develops generalized matrix models for n-point Virasoro conformal blocks on Riemann surfaces of any genus, connecting them to 4D N=2 gauge theories via AGT correspondence and deriving Seiberg-Witten curves.

Contribution

It introduces a comprehensive framework for matrix models at arbitrary genus and verifies the AGT correspondence through spectral curve derivation.

Findings

Generalized matrix models describe conformal blocks at all genera.

Seiberg-Witten curves are obtained as spectral curves of these models.

Consistency is verified through surface degeneration analysis.

Abstract

We study generalized matrix models corresponding to n-point Virasoro conformal blocks on Riemann surfaces with arbitrary genus g. Upon AGT correspondence, these describe four dimensional N=2 SU(2)^{n+3g-3} gauge theories with generalized quiver diagrams. We obtain the generalized matrix models from the perturbative evaluation of the Liouville correlation functions and verify the consistency of the description with respect to degenerations of the Riemann surface. Moreover, we derive the Seiberg-Witten curve for the N=2 gauge theory as the spectral curve of the generalized matrix model, thus providing a check of AGT correspondence at all genera.