Twisted reduction of quiver W-algebras

TL;DR

This paper explores the twisted Nekrasov-Shatashvili limit of 5d and 6d quiver gauge theories, revealing the structure of associated q-deformed W-algebras and their relation to quantum affine algebra representations.

Contribution

It introduces a formalism to compute the extended center of twisted q-deformed quiver W-algebras, linking gauge theory limits to quantum affine algebra representations.

Findings

Extended center of q-deformed quiver W-algebras obtained.

Gauge theoretic proof of the relation to quantum affine algebra.

Connection established between twisted gauge theories and algebraic structures.

Abstract

We consider the $k$-twisted Nekrasov-Shatashvili limit (NS$_k$ limit) of 5d (K-theoretic) and 6d (elliptic) quiver gauge theory, where one of the multiplicative equivariant parameters is taken to be the $k$-th root of unity. We obtain the extended center of the associated $q$-deformed quiver W-algebras constructed by our formalism [arXiv:1512.08533; arXiv:1608.04651; arXiv:1705.04410], which provides gauge theoretic proof of Bouwknegt-Pilch's statement on the relation to the representation ring of quantum affine algebra.