Towards a proof of AGT conjecture by methods of matrix models

TL;DR

This paper reviews a matrix model approach to proving the AGT relation, connecting conformal blocks, Nekrasov functions, and Seiberg-Witten prepotentials through integrability and resolvent techniques.

Contribution

It proposes a novel matrix model framework to establish the AGT conjecture by linking conformal blocks and Nekrasov functions via integrability methods.

Findings

Matrix model approach to AGT relation outlined

Connection between conformal blocks and Nekrasov functions established

Potential for proof via integrability and resolvent techniques

Abstract

A matrix model approach to proof of the AGT relation is briefly reviewed. It starts from the substitution of conformal blocks by the Dotsenko-Fateev beta-ensemble averages and Nekrasov functions by a double deformation of the exponentiated Seiberg-Witten prepotential in beta \neq 1 and g_s \neq 0 directions. Establishing the equality of these two quantities is a typical matrix model problem, and it presumably can be ascertained by investigation of integrability properties and developing an associated Harer-Zagier technique for evaluation of the exact resolvent.