Electrified branes

TL;DR

Electrified branes develops a geometric framework to formulate and analyze the supersymmetry conditions and BPS bounds for D-branes and fundamental strings on general type II backgrounds. By employing generalized geometry, it expresses SUSY constraints covariantly through background data (K, $\omega$, $\Psi$) and world-volume fluxes, and derives corresponding conserved currents, charges, and topological BPS energies. The work provides a unified treatment of static and non-static configurations, including cases with non-vanishing electric flux, and demonstrates the extensions of calibrations to these general settings. It also offers concrete examples—magnetized branes, BIons, and supertubes—to illustrate how brane energetics are governed by topological invariants tied to the background, with potential implications for black holes and fully coupled bulk-brane systems.

Abstract

A geometrical form of the supersymmetry conditions for D-branes on arbitrary type II supersymmetric backgrounds is derived, as well as the associated BPS bounds. The treatment is general and allows to consider, for instance, non-static configurations or D-branes supporting a non-vanishing electric flux, hence completing previous partial results. In particular, our discussion clarifies how the notion of calibration can be extended in order to be applicable to the most general supersymmetric configurations. As an exemplifying preliminary step, the procedure followed is first applied to fundamental strings.