Instanton partition functions in N=2 SU(N) gauge theories with a general surface operator, and their W-algebra duals

TL;DR

This paper conjectures explicit formulas for instanton partition functions in 4d N=2 SU(N) gauge theories with various surface operators, linking them to W-algebras and generalizing known results.

Contribution

It provides a unified conjecture for instanton partition functions with surface operators classified by partitions of N, connecting to W-algebras and extending previous special cases.

Findings

Recover Nekrasov formalism for N=N

Match Feigin et al. results for N=1+...+1

Show consistency with W-algebra formulations for N=1+...+1+2

Abstract

We write down an explicit conjecture for the instanton partition functions in 4d N=2 SU(N) gauge theories in the presence of a certain type of surface operator. These surface operators are classified by partitions of N, and for each partition there is an associated partition function. For the partition N=N we recover the Nekrasov formalism, and when N=1+...+1 we reproduce the result of Feigin et. al. For the case N=1+(N-1) our expression is consistent with an alternative formulation in terms of a restricted SU(N)xSU(N) instanton partition function. When N=1+...+1+2 the partition functions can also be obtained perturbatively from certain W-algebras known as quasi-superconformal algebras, in agreement with a recent general proposal.