Chiral differential operators on abelian varieties

TL;DR

This paper explores the construction of chiral differential operators on abelian varieties and their duals, and introduces sigma-models and Wess-Zumino-Witten models from this perspective.

Contribution

It provides a novel method to derive chiral differential operators on dual abelian varieties and connects these operators to sigma-models and Wess-Zumino-Witten models.

Findings

Established a correspondence between cdo on abelian varieties and their duals

Linked chiral differential operators to sigma-models on tori

Provided insights into the structure of Wess-Zumino-Witten models from a cdo perspective

Abstract

The paper consists of two parts. In the first, we describe a way of getting from an algebra of chiral differential operators (cdo) on an abelian variety a cdo on the dual variety. The second is an introduction to the sigma-model on a torus and to the Wess-Zumino-Witten model from the cdo perspective.