We present the first Monte Carlo results for supersymmetric matrix quantum mechanics with sixteen supercharges at finite temperature. The recently proposed non-lattice simulation enables us to include the effects of fermionic matrices in a transparent and reliable manner. The internal energy nicely interpolates the weak coupling behavior obtained by the high temperature expansion, and the strong coupling behavior predicted from the dual black hole geometry. The Polyakov line takes large values even at low temperature suggesting the absence of a phase transition in sharp contrast to the bosonic case. These results provide highly non-trivial evidences for the gauge/gravity duality.

We perform a direct test of the gauge-gravity duality associated with the system of N D0-branes in type IIA superstring theory at finite temperature. Based on the fact that higher derivative corrections to the type IIA supergravity action start at the order of alpha;{'3}, we derive the internal energy in expansion around infinite 't Hooft coupling up to the subleading term with one unknown coefficient. The power of the subleading term is shown to be nicely reproduced by the Monte Carlo data obtained nonperturbatively on the gauge theory side at finite but large effective (dimensionless) 't Hooft coupling constant. This suggests, in particular, that the open strings attached to the D0-branes provide the microscopic origin of the black hole thermodynamics of the dual geometry including alpha;{'} corrections. The coefficient of the subleading term extracted from the fit to the Monte Carlo data provides a prediction for the gravity side.

We study matrix quantum mechanics at finite temperature by Monte Carlo simulation. The model is obtained by dimensionally reducing 10d U(N ) pure Yang-Mills theory to 1d. Following Aharony et al., one can view the same model as describing the high temperature regime of (1+1)d U(N ) super Yang-Mills theory on a circle. In this interpretation an analog of the deconfinement transition was conjectured to be a continuation of the black-hole/black-string transition in the dual gravity theory. Our detailed analysis in the critical regime up to N = 32 suggests the existence of the non-uniform phase, in which the eigenvalue distribution of the holonomy matrix is non-uniform but gapless. The transition to the gapped phase is of second order. The internal energy is constant (giving the ground state energy) in the uniform phase, and rises quadratically in the non-uniform phase, which implies that the transition between these two phases is of third order.

Lattice simulation of supersymmetric gauge theories is not straightforward. In some cases the lack of manifest supersymmetry just necessitates cumbersome fine-tuning, but in the worse cases the chiral and/or Majorana nature of fermions makes it difficult to even formulate an appropriate lattice theory. We propose to circumvent all these problems inherent in the lattice approach by adopting a non-lattice approach in the case of one-dimensional supersymmetric gauge theories, which are important in the string/M theory context.