A sigma model field theoretic realization of Hitchin's generalized complex geometry

TL;DR

This paper develops a sigma model framework that captures Hitchin's generalized complex geometry, linking it to string theory flux compactifications and revealing deep geometric and cohomological structures.

Contribution

It introduces a sigma model realization of Hitchin's geometry, connecting integrability conditions to BV formalism and generalized Dolbeault cohomology.

Findings

Establishes a correspondence between integrability conditions and BV master equation restrictions.

Relates BV cohomology to generalized Dolbeault cohomology.

Provides a geometric framework relevant for string theory compactifications.

Abstract

We present a sigma model field theoretic realization of Hitchin's generalized complex geometry, which recently has been shown to be relevant in compactifications of superstring theory with fluxes. Hitchin sigma model is closely related to the well known Poisson sigma model, of which it has the same field content. The construction shows a remarkable correspondence between the (twisted) integrability conditions of generalized almost complex structures and the restrictions on target space geometry implied by the Batalin--Vilkovisky classical master equation. Further, the (twisted) classical Batalin--Vilkovisky cohomology is related non trivially to a generalized Dolbeault cohomology.