The ABCDEFG of Instantons and W-algebras
Christoph A. Keller, Noppadol Mekareeya, Jaewon Song, Yuji Tachikawa

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.
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