Exts and the AGT relations

TL;DR

This paper establishes a geometric proof connecting Nekrasov partition functions in N=2 supersymmetric gauge theories with Virasoro conformal blocks, confirming the AGT relations through intersection theory on moduli spaces.

Contribution

It introduces a new geometric method for intersection-theoretic computations of Ext operators, linking gauge theory partition functions with conformal field theory.

Findings

Proves the AGT relation for U(2) gauge theory with adjoint matter.

Relates the Carlsson-Okounkov Ext vector bundle to Virasoro vertex operators.

Develops a novel geometric approach for Ext operator computations.

Abstract

We prove the connection between the Nekrasov partition function of N=2 super-symmetric U(2) gauge theory with adjoint matter and conformal blocks for the Virasoro algebra, as predicted by the Alday-Gaiotto-Tachikawa relations. Mathematically, this is achieved by relating the Carlsson-Okounkov Ext vector bundle on the moduli space of rank 2 sheaves with Liouville vertex operators.Our approach is geometric in nature, and uses a new method for intersection-theoretic computations of the Ext operator.