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According to the gauge/gravity duality conjecture, the thermodynamics ofgauge theory describing D-branes corresponds to that of black branes insuperstring theory. We test this conjecture directly in the case of D0-branesby applying Monte Carlo methods to the corresponding gauge theory, which takesthe form of the BFSS matrix quantum mechanics. In particular, we take thecontinuum limit by extrapolating the UV cutoff to infinity. First we performsimulations at large N so that string loop corrections can be neglected on thegravity side. Our results for the internal energy exhibit the temperaturedependence consistent with the prediction including the \alpha ' corrections.Next we perform simulations at small N but at lower temperature so that the\alpha ' corrections can be neglected on the gravity side. Our results areconsistent with the prediction including the leading string loop correction,which suggests that the conjecture holds even at finite N.

Numerical tests of the gauge/gravity duality conjecture for D0-branes at finite temperature and finite N