Minisuperspace Quantization of "Bubbling AdS" and Free Fermion Droplets

TL;DR

This paper quantizes 1/2 BPS configurations in Type IIB supergravity, revealing a U(1) Kac-Moody algebra that matches free fermion system quantization, confirming the AdS/CFT correspondence.

Contribution

It introduces a covariant supergravity quantization method for BPS configurations, explicitly deriving the symplectic form and confirming the fermion system correspondence.

Findings

Derived the symplectic form around AdS_5 x S^5.

Found a U(1) Kac-Moody algebra in the quantized solutions.

Confirmed results with an independent perturbation spectrum analysis.

Abstract

We quantize the space of 1/2 BPS configurations of Type IIB SUGRA found by Lin, Lunin and Maldacena (hep-th/0409174), directly in supergravity. We use the Crnkovic-Witten-Zuckerman covariant quantization method to write down the expression for the symplectic structure on this entire space of solutions. We find the symplectic form explicitly around AdS_5 x S^5 and obtain a U(1) Kac-Moody algebra, in precise agreement with the quantization of a system of N free fermions in a harmonic oscillator potential, as expected from AdS/CFT. As a cross check, we also perform the quantization around AdS_5 x S^5 by another method, using the known spectrum of physical perturbations around this background and find precise agreement with our previous calculation.