Localization of affine W-algebras

TL;DR

This paper develops a new framework for affine W-algebras using chiral differential operators, establishing a localization theorem at the critical level through geometric and algebraic constructions.

Contribution

It introduces the concept of asymptotic algebras of chiral differential operators and constructs a localization theorem for affine W-algebras at the critical level.

Findings

Constructed an asymptotic algebra of chiral differential operators.

Proved a localization theorem for affine W-algebras at the critical level.

Computed the space of global sections of the constructed algebra.

Abstract

We introduce the notion of an asymptotic algebra of chiral differential operators. We then construct, via a chiral Hamiltonian reduction, one such algebra over a resolution of the intersection of the Slodowy slice with the nilpotent cone. We compute the space of global sections of this algebra thereby proving a localization theorem for affine W-algebras at the critical level.