Twisted modules for Toroidal vertex algebras

TL;DR

This paper develops a theory of twisted modules for toroidal vertex algebras, generalizing their construction and establishing connections to twisted toroidal Lie algebras and extended affine Lie algebras.

Contribution

It introduces a notion of twisted modules for toroidal vertex algebras and provides a general construction linking these modules to twisted toroidal Lie algebras.

Findings

Established a natural association between toroidal vertex algebras and twisted toroidal Lie algebras.

Extended the framework to include almost all extended affine Lie algebras.

Provided a systematic construction method for twisted modules in the toroidal setting.

Abstract

This is a paper in a series systematically to study toroidal vertex algebras. Previously, a theory of toroidal vertex algebras and modules was developed and toroidal vertex algebras were explicitly associated to toroidal Lie algebras. In this paper, we study twisted modules for toroidal vertex algebras. More specifically, we introduce a notion of twisted module for a general toroidal vertex algebra with a finite order automorphism and we give a general construction of toroidal vertex algebras and twisted modules. We then use this construction to establish a natural association of toroidal vertex algebras and twisted modules to twisted toroidal Lie algebras. This together with some other known results implies that almost all extended affine Lie algebras can be associated to toroidal vertex algebras.