Minisuperspace quantization of bubbling AdS$_2\times$S$^2$ geometries

TL;DR

This paper performs a quantization of the moduli space of supersymmetric microstates for 4D black holes with AdS2×S2 geometry, revealing the underlying quantum structure of these microstates.

Contribution

It introduces a method to quantize the moduli space of microstates using the symplectic form derived from Type IIB supergravity, focusing on solutions parameterized by harmonic functions.

Findings

Derived the symplectic form for the moduli space

Established commutation relations for microstate parameters

Enhanced understanding of quantum microstates of black holes

Abstract

We quantize the moduli space of supersymmetric microstates describing four-dimensional black holes with AdS$_2$$\times$S$^2$ asymptotics. To acquire the commutation relations of quantization, we find the symplectic form that is imposed in the Type IIB SUGRA and defined in the space of solutions parameterized by one complex harmonic function in ${R}^3$ with sources distributed along closed curves.