Quantizing N=2 Multicenter Solutions

TL;DR

The paper develops a program to quantize the moduli spaces of BPS multicenter solutions in N=2 supergravity, using a symplectic form derived from quiver QM and toric/Kähler geometry to perform geometric quantization. It demonstrates concrete state counts for two- and three-center configurations, including fermionic corrections, and establishes consistency with wall-crossing via split attractor flow. The analysis reveals that quantum effects cap off classically infinite throats in scaling solutions, predicting a finite mass gap in the dual CFT and offering a microscopic, non-perturbative window into black hole microstates and the fuzzball paradigm. Through halo/dipole halo constructions and AdS3 contexts, the work provides a detailed map from phase-space quantization to degeneracies, illustrating how quantum geometry reorganizes semiclassical intuition at macroscopic scales.

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.