How To Count the States of Extremal Black Holes in N=8 Supergravity

TL;DR

This paper verifies the duality prediction that the entropy of extremal black holes in N=8 supergravity relates to the E(7,7) quartic invariant by constructing explicit bound states of branes and matching microscopic degeneracy with black hole entropy.

Contribution

It constructs explicit supersymmetric bound states of branes in N=8 supergravity and demonstrates their entropy matches the duality-predicted invariant, providing a detailed verification.

Findings

Microscopic degeneracy matches black hole entropy.

Bound states are constructed with arbitrary brane rotations.

The entire charge spectrum forms an orbit under duality.

Abstract

N=8 supergravity has a rich spectrum of black holes charged under the 56 U(1) gauge fields of the theory. Duality predicts that the entropy of these black holes is related to the quartic invariant of the E(7,7) group. We verify this prediction in detail by constructing black holes that correspond to supersymmetric bound states of 2-branes at angles and 6-branes. The general bound state contains an arbitrary number of branes rotated relative to each other, and we derive the condition for these rotations to preserve supersymmetry. The microscopic bound state degeneracy matches the black hole entropy in detail. The entire 56 charge spectrum of extremal black holes in N=8 supergravity can be displayed as the orbit under duality of a five parameter generating solution. We exhibit a new generating configuration consisting of D3-branes at angles and discuss its entropy.