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

We review and extend earlier work that uses the AdS/CFT correspondence to relate the black-hole–black-string transition of gravitational theories on a circle to a phase transition in maximally supersymmetric (1 + 1)-dimensional SU(N) gauge theories at large N, again compactified on a circle. We perform gravity calculations to determine a likely phase diagram for the strongly coupled gauge theory. We then directly study the phase structure of the same gauge theory, now at weak 't Hooft coupling. In the interesting temperature regime for the phase transition, the (1 + 1)-dimensional theory reduces to a (0 + 1)-dimensional bosonic theory, which we solve using Monte Carlo methods. We find strong evidence that the weakly coupled gauge theory also exhibits a black hole–black string-like phase transition in the large N limit. We demonstrate that a simple Landau–Ginzburg-like model describes the behaviour near the phase transition remarkably well. The weak coupling transition appears to be close to the cusp between a first-order and a second-order transition.