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

Gauge/gravity duality and lattice simulations of one dimensional SYM with sixteen supercharges