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Minisuperspace Quantization of "Bubbling AdS" and Free Fermion Droplets

Lars Grant·Liat Maoz·Joseph Marsano·Kyriakos Papadodimas·Vyacheslav S. Rychkov
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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.

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Lars Grant, Liat Maoz, Joseph Marsano, Kyriakos Papadodimas, Vyacheslav S. Rychkov. 2005-08-17. Minisuperspace Quantization of "Bubbling AdS" and Free Fermion Droplets. https://doi.org/10.1088/1126-6708%2F2005%2F08%2F025

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