Quantum coordinate ring in WZW model and affine vertex algebra extensions

TL;DR

This paper constructs new simple vertex superalgebras as extensions of affine vertex algebras using quantum group twists, confirming conjectures and connecting to WZW models and chiral differential operators.

Contribution

It introduces a method to build vertex superalgebras via abelian cocycle twists, solving conjectures for type ABC and linking to physical models.

Findings

Constructed simple vertex superalgebras as extensions of affine vertex algebras.

Solved Creutzig and Gaiotto conjectures for type ABC.

Connected algebraic constructions to WZW models and chiral differential operators.

Abstract

In this paper, we construct various simple vertex superalgebras which are extensions of affine vertex algebras, by using abelian cocycle twists of representation categories of quantum groups. This solves the Creutzig and Gaiotto conjectures in the case of type ABC. If the twist is trivial, the resulting algebras correspond to chiral differential operators in the chiral case, and to WZW models in the non-chiral case.