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We study the black hole -black string phase transitions of gravitational theories compactified on a circle using the holographic duality conjecture. The gauge theory duals of these theories are maximally supersymmetric and strongly coupled 1 + 1 dimensional SU (N ) Yang-Mills theories compactified on a circle, in the large N limit. We perform the strongly coupled finite temperature gauge theory calculations on a lattice, using the recently developed exact lattice supersymmetry methods based ondoi:10.1088/1742-6596/462/1/012022 fatcat:dk3ajn23svb5zimnimbsz6apau