Supersymmetric D-branes and calibrations on general N=1 backgrounds

TL;DR

This paper investigates the conditions for supersymmetric D-branes in general N=1 backgrounds with fluxes, using pure spinors and generalized complex geometry, and relates these to calibration conditions and mirror symmetry.

Contribution

It formulates supersymmetry conditions for D-branes in flux backgrounds using pure spinors and generalized calibrations, extending understanding of mirror symmetry in string theory.

Findings

Supersymmetric D-branes wrap generalized complex submanifolds.

Conditions expressed via pure spinors split into integrable and non-integrable parts.

Results support the generalized mirror symmetry between type IIA and IIB backgrounds.

Abstract

We study the conditions to have supersymmetric D-branes on general {\cal N}=1 backgrounds with Ramond-Ramond fluxes. These conditions can be written in terms of the two pure spinors associated to the SU(3)\times SU(3) structure on T_M\oplus T^\star_M, and can be split into two parts each involving a different pure spinor. The first involves the integrable pure spinor and requires the D-brane to wrap a generalised complex submanifold with respect to the generalised complex structure associated to it. The second contains the non-integrable pure spinor and is related to the stability of the brane. The two conditions can be rephrased as a generalised calibration condition for the brane. The results preserve the generalised mirror symmetry relating the type IIA and IIB backgrounds considered, giving further evidence for this duality.