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We study the black hole - black string phase transitions of gravitationaltheories compactified on a circle using the holographic duality conjecture. Thegauge theory duals of these theories are maximally supersymmetric and stronglycoupled 1 + 1 dimensional SU(N) Yang-Mills theories compactified on a circle,in the large $N$ limit. We perform the strongly coupled finite temperaturegauge theory calculations on a lattice, using the recently developed exactlattice supersymmetry methods based on topological twisting and orbifolding.The spatial Polyakov line serves as relevant order parameter of the confinement- deconfinement phase transitions in the gauge theory duals.

Gauge theory duals of black hole - black string transitions of gravitational theories on a circle