RESUMEN

We study D0-brane quantum mechanics in the 't Hooft large N limit. Itzhaki et al. have proposed that the strong coupling limit is dual to a particular ten-dimensional uncharged black hole. To study this proposal we develop a mean field approximation for the quantum mechanics. We find the entropy of microstates agrees with the Bekenstein-Hawking prediction, and obtain the density of microstates. By studying potentials for test branes in this background, we reconstruct the spacetime metric from the large N quantum mechanics. Quasi-particles of the mean field approximation match the frequency and decay rate of the lowest quasi-normal modes of the black hole. We use this matching to compute the horizon area directly in the quantum mechanics, establishing both sides of the formula S=A/4 from a non-perturbative string theory calculation.