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

We perform 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 <= T <= 1.0. As a way to test the gauge/gravity duality conjecture we compute the internal energy of the black hole as a function of the temperature directly from the gauge theory. We obtain a leading behavior that is compatible with the supergravity result E/N-2 = 7.41T(14/5): the coefficient is estimated to be 7.4 +/- 0.5 when the exponent is fixed and stringy corrections are included. 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.