Geometry Quantization from Supergravity: the case of "Bubbling AdS"

TL;DR

This paper quantizes the moduli space of 1/2 BPS supergravity solutions in type IIB theory using a covariant method, demonstrating the symplectic form matches the dual fermion description for arbitrary droplet configurations.

Contribution

It provides a direct supergravity-based quantization of the moduli space, confirming the dual fermion symplectic structure for all droplet shapes and topologies.

Findings

Symplectic form matches dual fermion picture.

Quantization applies to arbitrary droplet configurations.

Generalizes previous results and resolves earlier puzzles.

Abstract

We consider the moduli space of 1/2 BPS configurations of type IIB SUGRA found by Lin, Lunin and Maldacena (hep-th/0409174), and quantize it directly from the supergravity action, around any point in the moduli space. This quantization is done using the Crnkovic-Witten-Zuckerman covariant method. We make some remarks on the applicability and validity of this general on-shell quantization method. We then obtain an expression for the symplectic form on the moduli space of LLM configurations, and show that it exactly coincides with the one expected from the dual fermion picture. This equivalence is shown for any shape and topology of the droplets and for any number of droplets. This work therefore generalizes the previous work (hep-th/0505079) and resolves the puzzle encountered there.