Quantum near-horizon geometry of a black 0-brane
We investigate a bunch of D0-branes to reveal its 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 an unique solution which includes the effect of the quantum gravity. Thermodynamic property of the quantum near horizon geometry of the black 0-brane is also studied by using Wald's 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-branes system at the level of quantum gravity.