Exts and the AGT Relations

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. Keywords: Nekrasov partition function, AGT relations, Ext operators, shuffle algebra