T-duality through BV Morphisms and BV Pushforwards in Topological Field Theories

TL;DR

This paper formalizes T-duality in topological field theories using BV morphisms and pushforwards, connecting string theory dualities with mathematical structures like Courant algebroids.

Contribution

It introduces a BV formalism framework for dualities, especially T-duality, linking physical dualities with mathematical structures in topological sigma models.

Findings

T-duality is characterized as a BV morphism affecting target space.

Topological aspects of T-duality relate to curvature, H-flux, and Courant algebroids.

Dualities of topological sigma models correspond to string theory T-duality.

Abstract

We introduce the concept of duality between quantum field theories in the Batalin-Vilkovisky formalism, which is interpreted either as a BV morphism, the result of dual BV pushforwards or a combination of both. When a BV morphism affects only the target space of a given model, we call it T-duality. To justify this name, we demonstrate how topological aspects of T-duality in string theory such as the relation between curvature and H-flux or isomorphisms of Courant algebroids are equivalent to dualities of topological sigma models in two and three dimensions.