Generalized complex geometry, generalized branes and the Hitchin sigma model

TL;DR

This paper extends the Hitchin sigma model to include branes modeled as generalized complex submanifolds, revealing new cohomological structures relevant for string theory compactifications and mirror symmetry.

Contribution

It introduces a field theoretic realization of generalized complex geometry with branes, analyzing boundary conditions and uncovering new cohomological sectors.

Findings

Incorporation of branes into the Hitchin sigma model.

Identification of an extra cohomology sector related to branes.

Implications for string theory compactifications and mirror symmetry.

Abstract

Hitchin's generalized complex geometry has been shown to be relevant in compactifications of superstring theory with fluxes and is expected to lead to a deeper understanding of mirror symmetry. Gualtieri's notion of generalized complex submanifold seems to be a natural candidate for the description of branes in this context. Recently, we introduced a field theoretic realization of generalized complex geometry, the Hitchin sigma model, extending the well known Poisson sigma model. In this paper, exploiting Gualtieri's formalism, we incorporate branes into the model. A detailed study of the boundary conditions obeyed by the world sheet fields is provided. Finally, it is found that, when branes are present, the classical Batalin--Vilkovisky cohomology contains an extra sector that is related non trivially to a novel cohomology associated with the branes as generalized complex submanifolds.