Branes at Angles and Black Holes

TL;DR

This paper constructs and analyzes the most general supersymmetric D-brane configurations on a 6-torus, revealing their supergravity solutions, supersymmetry properties, and microscopic black hole entropy, consistent with duality predictions.

Contribution

It provides the first explicit construction of general supersymmetric D2-D6 brane configurations with arbitrary angles and relates these to extremal black hole solutions and their microscopic entropy.

Findings

Supergravity solutions are expressed in a simple form using complex geometry.

Configurations correspond to a 16-parameter family of extremal black holes.

Microscopic entropy matches duality group predictions.

Abstract

We construct the most general supersymmetric configuration of D2-branes and D6-branes on a 6-torus. It contains arbitrary numbers of branes at relative U(3) angles. The corresponding supergravity solutions are constructed and expressed in a remarkably simple form, using the complex geometry of the compact space. The spacetime supersymmetry of the configuration is verified explicitly, by solution of the Killing spinor equations. Our configurations can be interpreted as a 16-parameter family of regular extremal black holes in four dimensions. Their entropy is interpreted microscopically by counting the degeneracy of bound states of D-branes. Our result agrees in detail with the prediction for the degeneracy of BPS states in terms of the quartic invariant of the E(7,7) duality group.