Virasoro constraint for Nekrasov instanton partition function

TL;DR

This paper demonstrates that the Nekrasov instanton partition function for SU(N) gauge theories obeys recursion relations akin to Virasoro constraints at , providing evidence for the AGT conjecture in quiver gauge theories.

Contribution

It establishes Virasoro constraints for Nekrasov functions at , supporting the AGT correspondence for general quiver gauge theories.

Findings

Nekrasov partition function satisfies Virasoro constraints at 

Constraints support the AGT conjecture for quiver gauge theories

Recursion relations are explicitly derived for SU(N) gauge theories

Abstract

We show that Nekrasov instanton partition function for SU(N) gauge theories satisfies recursion relations in the form of U(1)+Virasoro constraints when {\beta} = 1. The constraints give a direct support for AGT conjecture for general quiver gauge theories.