Quantum near-horizon geometry of a black 0-brane

We investigate a bunch of D0-branes to reveal their quantum nature from the gravity side. In the classical limit, it is well described by a non-extremal black 0-brane in type IIA supergravity. The solution is uplifted to the eleven dimensions and expressed by a non-extremal M-wave solution. After reviewing the effective action for the M-theory, we explicitly solve the equations of motion for the near-horizon geometry of the M-wave. As a result, we derive a unique solution that includes the effect of the quantum gravity. The thermodynamic properties of the quantum near-horizon geometry of the black 0-brane are also studied by using Wald's entropy formula. Combining our result with that of the Monte Carlo simulation of the dual thermal gauge theory, we find strong evidence for the gauge/gravity duality in the D0-brane system at the level of quantum gravity