Topological sigma-models with H-flux and twisted generalized complex manifolds

TL;DR

This paper explores the topological aspects of N=2 sigma-models with H-flux, revealing their geometric structure through twisted generalized complex geometry and establishing new models and mirror symmetry insights.

Contribution

It introduces a novel description of the target-space geometry using twisted generalized complex structures and defines analogues of A and B-models for these sigma-models.

Findings

Topological observables correspond to Lie algebroid cohomology.

The algebra of observables forms a Frobenius algebra.

Mirror symmetry extends to twisted generalized Calabi-Yau manifolds.

Abstract

We study the topological sector of N=2 sigma-models with H-flux. It has been known for a long time that the target-space geometry of these theories is not Kahler and can be described in terms of a pair of complex structures, which do not commute, in general, and are parallel with respect to two different connections with torsion. Recently an alternative description of this geometry was found, which involves a pair of commuting twisted generalized complex structures on the target space. In this paper we define and study the analogues of A and B-models for N=2 sigma-models with H-flux and show that the results are naturally expressed in the language of twisted generalized complex geometry. For example, the space of topological observables is given by the cohomology of a Lie algebroid associated to one of the two twisted generalized complex structures. We determine the topological scalar product, which endows the algebra of observables with the structure of a Frobenius algebra. We also discuss mirror symmetry for twisted generalized Calabi-Yau manifolds.