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A generalization of the AdS/CFT conjecture postulates a duality between IIAstring theory and 16 supercharge Yang-Mills quantum mechanics in the large N 'tHooft limit. At low temperatures string theory describes black holes, whosethermodynamics may hence be studied using the dual quantum mechanics. Thisquantum mechanics is strongly coupled which motivates the use of latticetechniques. We argue that, contrary to expectation, the theory when discretizednaively will nevertheless recover continuum supersymmetry as the latticespacing is sent to zero. We test these ideas by studying the 4 superchargeversion of this Yang-Mills quantum mechanics in the 't Hooft limit. We use botha naive lattice action and a manifestly supersymmetric action. Using MonteCarlo methods we simulate the Euclidean theories, and study the latticecontinuum limit, for both thermal and non-thermal periodic boundary conditions,confirming continuum supersymmetry is recovered for the naive action whenappropriate. We obtain results for the thermal system with N up to 12. Thesefavor the existence of a single deconfined phase for all non-zero temperatures.These results are an encouraging indication that the 16 supercharge theory iswithin reach using similar methods and resources.

Towards lattice simulation of the gauge theory duals to black holes and hot strings