Superconformal Multi-Black Hole Quantum Mechanics

TL;DR

This paper studies the quantum mechanics of multiple charged BPS black holes in five-dimensional supergravity, revealing a superconformal symmetry and a discrete spectrum for their near-horizon states.

Contribution

It derives the moduli space metric for N black holes, uncovers superconformal symmetry, and proposes a new approach to define a well-behaved Hilbert space for black hole dynamics.

Findings

Moduli space metric admits 4 supersymmetries.

Near-horizon limit decouples black hole interactions.

Eigenstates of 2L_0 have a discrete spectrum.

Abstract

The quantum mechanics of N slowly-moving charged BPS black holes in five-dimensional ${\cal N}=1$ supergravity is considered. The moduli space metric of the N black holes is derived and shown to admit 4 supersymmetries. A near-horizon limit is found in which the dynamics of widely separated black holes decouples from that of strongly-interacting, near-coincident black holes. This decoupling suggests that the quantum states supported in the near-horizon moduli space can be interpreted as internal states of a single composite black hole carrying all of the charge. The near-horizon theory is shown to have an enhanced D(2,1;0) superconformal symmetry. Eigenstates of the Hamiltonian H of the near-horizon theory are ill-defined due to noncompact regions of the moduli space corresponding to highly redshifted near-coincident black holes. It is argued that one should consider, instead of H eigenstates, eigenstates of $2 L_0 = H+K$, where K is the generator of special conformal transformations. The result is a well-defined Hilbert space with a discrete spectrum describing the N-black hole dynamics.