T-duality of current algebras and their quantization

TL;DR

This paper demonstrates how T-duality transforms can establish isomorphisms between current algebras and vertex algebras on T-dual spacetimes with circle bundle compactifications and H-flux.

Contribution

It extends T-duality to relate current and vertex algebras on topologically distinct spaces, providing a new mathematical framework.

Findings

T-duality induces isomorphisms of current algebras

T-duality relates vertex algebras on dual spaces

Application to circle bundles with H-flux

Abstract

In this paper we show that the T-duality transform of Bouwknegt, Evslin and Mathai applies to determine isomorphisms of certain current algebras and their associated vertex algebras on topologically distinct T-dual spacetimes compactified to circle bundles with $H$-flux.