  We study the gauge/gravity duality for supersymmetric SU(N) Yang-Mills theory
in 1+0 dimension with sixteen supercharges using lattice simulations. The
conjectured duality states that the gravity side is described by N D0-branes in
type IIA superstring at large N, and the thermal gauge theory reproduces the
black hole thermodynamics at low temperature. In this paper, we explain the
Sugino lattice action used in the simulations in detail, and examine the
supersymmetric Ward-Takahashi identity to confirm the restoration of
supersymmetry in the continuum limit. We also estimate the internal energy of
the black hole from the lattice results for N=14,32, and find that it smoothly
approaches the prediction of the gravity side as the temperature decreases.
