D-brane networks in flux vacua, generalized cycles and calibrations

TL;DR

This paper develops a homology theory for generalized cycles in flux vacua, showing how D-brane networks must wrap these cycles and introducing calibrations to identify supersymmetric configurations.

Contribution

It introduces a new homology framework for generalized cycles in flux compactifications and defines calibrations for supersymmetric D-brane networks.

Findings

Generalized cycles form a homology theory relevant for D-brane configurations.

D-brane networks must wrap these generalized cycles for gauge invariance.

Explicit examples on toroidal orientifold and Klebanov-Strassler geometries.

Abstract

We consider chains of generalized submanifolds, as defined by Gualtieri in the context of generalized complex geometry, and define a boundary operator that acts on them. This allows us to define generalized cycles and the corresponding homology theory. Gauge invariance demands that D-brane networks on flux vacua must wrap these generalized cycles, while deformations of generalized cycles inside of a certain homology class describe physical processes such as the dissolution of D-branes in higher-dimensional D-branes and MMS-like instantonic transitions. We introduce calibrations that identify the supersymmetric D-brane networks, which minimize their energy inside of the corresponding homology class of generalized cycles. Such a calibration is explicitly presented for type II N=1 flux compactifications to four dimensions. In particular networks of walls and strings in compactifications on warped Calabi-Yau's are treated, with explicit examples on a toroidal orientifold vacuum and on the Klebanov-Strassler geometry.