D-Branes in Para-Hermitian Geometries

TL;DR

This paper develops a T-duality invariant framework for D-branes within doubled geometry using para-Hermitian structures, generalizing traditional branes as maximally isotropic bundles and linking them to Dirac structures.

Contribution

It introduces a covariant, para-Hermitian geometric approach to D-branes, extending their description beyond standard submanifold pictures and connecting to topological A/B-branes.

Findings

Defines D-branes as conformal boundary conditions in doubled geometry.

Shows how to recover standard D-branes via reduction from doubled nilmanifolds.

Introduces generalized para-complex D-branes as para-complex analogs of topological branes.

Abstract

We introduce T-duality invariant versions of D-branes in doubled geometry using a global covariant framework based on para-Hermitian geometry and metric algebroids. We define D-branes as conformal boundary conditions for the open string version of the Born sigma-model, where they are given by maximally isotropic vector bundles which do not generally admit the standard geometric picture in terms of submanifolds. When reduced to the conventional sigma-model description of a physical string background as the leaf space of a foliated para-Hermitian manifold, integrable branes yield D-branes as leaves of foliations which are interpreted as Dirac structures on the physical spacetime. We define a notion of generalised para-complex D-brane, which realises our D-branes as para-complex versions of topological A/B-branes. We illustrate how our formalism recovers standard D-branes in the explicit example of reductions from doubled nilmanifolds.