Quantizing N=2 Multicenter Solutions

TL;DR

This paper studies the quantization of BPS solutions in N=2 supergravity, deriving wavefunctions, explaining wall-crossing phenomena, and revealing quantum effects that resolve classical paradoxes and cap off deep throats.

Contribution

It provides a detailed quantization of moduli spaces of multicenter solutions, deriving wavefunctions and explaining quantum resolutions of classical singularities.

Findings

Derived the symplectic form of moduli spaces

Reproduced wall-crossing formulae through wavefunction counting

Quantum effects cap off deep gravitational throats

Abstract

N=2 supergravity in four dimensions, or equivalently N=1 supergravity in five dimensions, has an interesting set of BPS solutions that each correspond to a number of charged centers. This set contains black holes, black rings and their bound states, as well as many smooth solutions. Moduli spaces of such solutions carry a natural symplectic form which we determine, and which allows us to study their quantization. By counting the resulting wavefunctions we come to an independent derivation of some of the wall-crossing formulae. Knowledge of the explicit form of these wavefunctions allows us to find quantum resolutions to some apparent classical paradoxes such as solutions with barely bound centers and those with an infinitely deep throat. We show that quantum effects seem to cap off the throat at a finite depth and we give an estimate for the corresponding mass gap in the dual CFT. This is an interesting example of a system where quantum effects cannot be neglected at macroscopic scales even though the curvature is everywhere small.