The ABCDEFG of Instantons and W-algebras

TL;DR

This paper verifies a correspondence between Nekrasov partition functions and W-algebra coherent states for various gauge groups, including non-simply-laced cases, at the one-instanton level.

Contribution

It extends the instanton/W-algebra correspondence to arbitrary gauge groups and confirms the twisted sector for non-simply-laced groups.

Findings

Nekrasov partition function equals W-algebra coherent state norm at one-instanton level.

Confirmed the twisted sector for non-simply-laced gauge groups.

Validated the correspondence for arbitrary gauge groups.

Abstract

For arbitrary gauge groups, we check at the one-instanton level that the Nekrasov partition function of pure N=2 super Yang-Mills is equal to the norm of a certain coherent state of the corresponding W-algebra. For non-simply-laced gauge groups, we confirm in particular that the coherent state is in the twisted sector of a simply-laced W-algebra.