Superconformal Multi-Black Hole Quantum Mechanics

Abstract

The quantum mechanics of N slowly-moving charged BPS black holes in five-dimensional $\mathcal{N}=1$ 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 $2L_0=H+K$, 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.

17 pages AMSLaTeX with JHEP.cls, using epsf.tex for 3 eps figures. Typos corrected. References added

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