Two-Black-Hole Bound States

TL;DR

This paper studies the quantum mechanics of multiple BPS black holes in five dimensions, revealing a superconformal structure and computing an index that counts supersymmetric bound states, with explicit results for two black holes.

Contribution

It introduces a superconformal framework for analyzing bound states of black holes and computes an index based on cohomology, providing new insights into black hole bound state counting.

Findings

Identifies a divergent continuum of bound states with near-zero excitation energy.

Establishes a superconformal structure at low energies for black hole systems.

Calculates a finite index for the two-black-hole case, confirming the existence of supersymmetric bound states.

Abstract

The quantum mechanics of $N$ slowly-moving BPS black holes in five dimensions is considered. A divergent continuum of states describing arbitrarily closely bound black holes with arbitrarily small excitation energies is found. A superconformal structure appears at low energies and can be used to define an index counting the weighted number of supersymmetric bound states. It is shown that the index is determined from the dimensions of certain cohomology classes on the symmetric product of $N$ copies of $R^4$. An explicit computation for the case of N=2 with no angular momentum yields a finite nonzero result.