Exact QFT duals of AdS black holes

Abstract

Abstract We construct large N saddle points of the matrix model for the $$ \mathcal{N} $$ N = 4 Yang- Mills index dual to the BPS black holes in AdS5 × S5, in two different setups. When the two complex chemical potentials for the angular momenta are collinear, we find linear eigenvalue distributions which solve the large N saddle point equation. When the chemical potentials are not collinear, we find novel solutions given by areal eigenvalue distributions after slightly reformulating the saddle point problem. We also construct a class of multi-cut saddle points, showing that they sometimes admit nontrivial filling fractions. As a byproduct, we find that the Bethe ansatz equation emerges from our saddle point equation.