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.Comment: 22 Pages + 2 Appendices, JHEP3; v3: explanation of factor 2 mismatch
added, references reordered, published versio