Small AdS black holes from SYM

TL;DR

This work identifies configurations in N=4 SYM that correspond to small AdS black holes by isolating an approximately thermal SU(M) subsector whose degrees of freedom are insulated from the rest of the gauge theory. The construction uses emergent geometry from large-N dynamics to map the MxM block to a localized state on S^5 and models black-hole formation via collapse of a dense gas of string bits connecting eigenvalues. Thermodynamics within the trapped sector follow $E ~ M^2 T^4$ and $S ~ M^2 T^3$, with a saturation-based relation giving $T ~ N^{3/10} M^{-3/10}$ and $S ~ N^{-3/4} E^{11/8}$; the entropy-energy scaling differs modestly from the classic Schwarzschild result, reflecting crude approximations and potential DBI corrections. The results provide a concrete microstate picture for small AdS black holes in AdS/CFT, illustrating how emergent geometry, fast thermalization, and backreaction considerations shape black-hole formation and absorption in the dual field theory.

Abstract

We provide a characterization of the set of configurations in N=4 SYM theory that are dual to small AdS black holes. Our construction shows that the black hole dual states are approximately thermal on a SU(M) subset of degrees of freedom of a SU(N) gauge theory. M is determined dynamically and the black hole degrees of freedom are dynamically insulated from the rest. These states are localized on the S^5 and have dynamical processes that correspond to matter absorption that make them behave as black objects.