Higher Derivative Corrections to Black Hole Thermodynamics from Supersymmetric Matrix Quantum Mechanics

We perform a direct test of the gauge-gravity duality associated with the system of $N$ $D0$-branes in type IIA superstring theory at finite temperature. Based on the fact that higher derivative corrections to the type IIA supergravity action start at the order of ${\alpha }^{\prime 3}$, we derive the internal energy in expansion around infinite ’t Hooft coupling up to the subleading term with one unknown coefficient. The power of the subleading term is shown to be nicely reproduced by the Monte Carlo data obtained nonperturbatively on the gauge theory side at finite but large effective (dimensionless) ’t Hooft coupling constant. This suggests, in particular, that the open strings attached to the $D0$-branes provide the microscopic origin of the black hole thermodynamics of the dual geometry including ${\alpha }^{\prime }$ corrections. The coefficient of the subleading term extracted from the fit to the Monte Carlo data provides a prediction for the gravity side.