Superconformal multi-black hole quantum mechanics

TLDR: In this article, the quantum mechanics of slowly-moving charged BPS black holes in five-dimensional = 1 supergravity is considered and the moduli space metric of the N black holes is derived and shown to admit 4 supersymmetries.

Abstract: The quantum mechanics of N slowly-moving charged BPS black holes in five-dimensional = 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 2L0 = 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.

Figures

Figure 3: (a) Regions of the two-black hole moduli space. (b) The near-horizon limit.

Figure 1: The AdS2 time coordinate conjugate to H is badly behaved at the horizon, but the time conjugate to H +K is a good global coordinate.

Figure 2: (a) Widely separated black holes. (b) Near-coincident black holes. (c) The nearhorizon limit.