Deformations of calibrated D-branes in flux generalized complex manifolds

TL;DR

This paper investigates the deformations of supersymmetric D-branes within flux backgrounds using generalized complex geometry, revealing their classification via Lie algebroid cohomology and exploring various examples and flux effects.

Contribution

It introduces a classification of massless D-brane deformations through Lie algebroid cohomology in generalized complex manifolds, including flux effects and specific examples.

Findings

Deformations classified by first Lie algebroid cohomology.

Examples provided in SU(3) and generalized complex structures.

Fluxes can lift certain massless modes.

Abstract

We study massless deformations of generalized calibrated cycles, which describe, in the language of generalized complex geometry, supersymmetric D-branes in N=1 supersymmetric compactifications with fluxes. We find that the deformations are classified by the first cohomology group of a Lie algebroid canonically associated to the generalized calibrated cycle, seen as a generalized complex submanifold with respect to the integrable generalized complex structure of the bulk. We provide examples in the SU(3) structure case and in a `genuine' generalized complex structure case. We discuss cases of lifting of massless modes due to world-volume fluxes, background fluxes and a generalized complex structure that changes type.