Affine sl(N) conformal blocks from N=2 SU(N) gauge theories

TL;DR

This paper extends the Alday-Tachikawa relation from affine sl(2) to affine sl(N) conformal blocks, linking them to instanton partition functions in N=2 SU(N) gauge theories with surface operators.

Contribution

It generalizes the known correspondence between affine sl(2) conformal blocks and gauge theory partition functions to affine sl(N) cases, including non-conformal theories.

Findings

Established a relation between affine sl(N) conformal blocks and gauge theory instanton functions.

Extended the correspondence to non-conformal N=2 SU(N) theories.

Discussed implications for surface operator insertions in gauge theories.

Abstract

Recently Alday and Tachikawa proposed a relation between conformal blocks in a two-dimensional theory with affine sl(2) symmetry and instanton partition functions in four-dimensional conformal N=2 SU(2) quiver gauge theories in the presence of a certain surface operator. In this paper we extend this proposal to a relation between conformal blocks in theories with affine sl(N) symmetry and instanton partition functions in conformal N=2 SU(N) quiver gauge theories in the presence of a surface operator. We also discuss the extension to non-conformal N=2 SU(N) theories.