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We review and extend earlier work that uses the AdS/CFT correspondence torelate the black hole-black string transition of gravitational theories on acircle to a phase transition in maximally supersymmetric 1+1-dimensional SU(N)gauge theories at large N, again compactified on a circle. We perform gravitycalculations to determine a likely phase diagram for the strongly coupled gaugetheory. We then directly study the phase structure of the same gauge theory,now at weak 't Hooft coupling. In the interesting temperature regime for thephase transition, we may reduce the 1+1-dimensional theory to a 0+1-dimensionalbosonic theory, which we solve using Monte Carlo methods. We find strongevidence that the weakly coupled gauge theory also exhibits a black hole-blackstring like phase transition in the large N limit. We demonstrate that a simpleLandau-Ginzburg like model describes the behaviour near the phase transitionremarkably well. The weak coupling transition appears to be close to the cuspbetween a first order and a second order transition.Comment: 21 pages, revtex, 11 figures. v2: small corrections, added references  and a new appendix on the relation of our work to previous discussions of the  same theor

Black-hole–black-string phase transitions in thermal (1 + 1)-dimensional supersymmetric Yang–Mills theory on a circle