Half-integrable modules over algebras of twisted chiral differential operators

TL;DR

This paper investigates half-integrable modules over sheaves of twisted chiral differential operators on smooth varieties, establishing an equivalence with categories of twisted D-modules, thus linking vertex algebra modules with differential operators.

Contribution

It introduces a new equivalence between categories of half-integrable modules over TCDO and twisted D-modules on smooth varieties.

Findings

Established an equivalence between half-integrable TCDO modules and twisted D-modules.

Characterized the structure of half-integrable modules over TCDO.

Provided new insights into the representation theory of vertex algebras.

Abstract

A module M over a vertex algebra V is half-integrable if a_n act locally nilpotently on M for all a in V, m in M, n>0. We study half-integrable modules over sheaves of twisted chiral differential operators (TCDO) on a smooth variety X. We prove an equivalence between certain categories of half-integrable modules over TCDO and categories of (twisted) D-modules on X.