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The origin of space-time as seen from matrix model simulations

The AdS/CFT correspondence, or more generally the gauge/gravity duality, is a remarkable conjecture obtained from superstring theory with various D-brane backgrounds. According to this conjecture, a higher-dimensional curved space-time emerges from supersymmetric gauge theory in lower-dimensional flat space-time. In the first part of this article, we review Monte Carlo studies of U(N) supersymmetric gauge theories, which confirmed the gauge/gravity duality for various observables. In particular, Monte Carlo results for thermodynamic quantities enable us to understand the microscopic origin of the black hole entropy associated with the dual geometry. We also discuss results for Wilson loops and correlation functions, which agree nicely with the predictions from the gravity side. In the second part, we review recent developments in a nonperturbative formulation of superstring theory, which may be regarded as a counterpart of the lattice gauge theory in QCD. In particular, we discuss Monte Carlo results for the Lorentzian matrix model, which suggest that (3+1)-dimensional expanding universe emerges dynamically from type IIB superstring theory in (9+1) dimensions if one treats the theory nonperturbatively.