Precision lattice test of the gauge/gravity duality at large N

Abstract

We pioneer a systematic, large-scale lattice simulation of D0-brane quantum mechanics. The large-$N$ and continuum limits of the gauge theory are taken for the first time at various temperatures $0.4 \leq T \leq 1.0$. As a way to directly test the gauge/gravity duality conjecture we compute the internal energy of the black hole directly from the gauge theory and reproduce the coefficient of the supergravity result $E/N^2=7.41T^14/5$. This is the first confirmation of the supergravity prediction for the internal energy of a black hole at finite temperature coming directly from the dual gauge theory. We also constrain stringy corrections to the internal energy.