Tachyon condensation and D-branes in generalized geometries

TL;DR

This paper explores the description of D-branes within generalized complex geometry, examining their stability, T-duality relations, and tachyon condensation, and linking geometric and K-theoretic classifications.

Contribution

It provides a novel framework connecting D-branes as generalized complex submanifolds with tachyon condensation and K-theory in generalized geometries.

Findings

D-branes correspond to pure spinors in generalized complex geometry

Tachyon condensation relates to stability and classification of D-branes

T-duality transformations are linked to the geometric description of D-branes

Abstract

In generalized complex geometry, D-branes can be seen as maximally isotropic spaces and are thus in one-to-one correspondence with pure spinors. When considered on the sum of the tangent and cotangent bundles to the ambient space, all the branes are of the same dimension and the transverse scalars enter on par with the gauge fields; the split between the longitudinal and transverse directions is done in accordance with the type of the pure spinor corresponding to the given D-brane. We elaborate on the relation of this picture to the T-duality transformations and stability of D-branes. A discussion of tachyon condensation in the context of the generalized complex geometry is given, linking the description of D-branes as generalized complex submanifolds to their K-theoretic classification.