Proving the AGT relation for N_f = 0,1,2 antifundamentals

TL;DR

This paper proves the AGT correspondence for N=2 superconformal SU(2) quiver gauge theories with up to two antifundamental hypermultiplets using recursive relations of Nekrasov functions and irregular conformal blocks.

Contribution

It provides a rigorous proof of the AGT relation for specific cases of N_f=0,1,2 antifundamental hypermultiplets in superconformal gauge theories.

Findings

Confirmed AGT correspondence for N_f=0,1,2 cases

Established recursive relations for Nekrasov partition functions

Linked irregular conformal blocks with gauge theory partition functions

Abstract

Using recursive relations satisfied by Nekrasov partition functions and by irregular conformal blocks we prove the AGT correspondence in the case of N=2 superconformal SU(2) quiver gauge theories with N_f = 0,1,2 antifundamental hypermultiplets