Double field theory for the A/B-models and topological S-duality in generalized geometry

TL;DR

This paper develops a double field theory framework for topological A- and B-models, revealing a topological S-duality and introducing new Courant algebroids linked to generalized complex geometry.

Contribution

It introduces a novel double field theory approach to topological models, connecting them via S-duality and expanding the mathematical structures involved.

Findings

Establishes a relation between AKSZ BV constructions and Courant sigma-models.

Defines a topological S-duality exchanging A- and B-models.

Proposes new classes of Courant algebroids associated with generalized complex structures.

Abstract

We study AKSZ-type BV constructions for the topological A- and B-models within a double field theory formulation that incorporates backgrounds with geometric and non-geometric fluxes. We relate them to a Courant sigma-model, on an open membrane, corresponding to a generalized complex structure, which reduces to the A- or B-models on the boundary. We introduce S-duality at the level of the membrane sigma-model based on the generalized complex structure, which exchanges the related AKSZ field theories, and interpret it as topological S-duality of the A- and B-models. Our approach leads to new classes of Courant algebroids associated to (generalized) complex geometry.