2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/55705We argue that the large N strong/weak phase transition is a generic phenomenon in a finite temperature supersymmetric Yang-Mills theory of maximal supersymmetry. ${\cal N}=4$, D=4 SYM is the canonical example, where we also argue that the large N Hawking-Page phase transition disappears for a sufficiently small coupling. The Hawking-Page transition temperature is lowered by the first $\ap$ correction. Physically, the strong/weak phase transition is identified with the correspondence point of Horowitz and Polchinski. We also try to construct toy models to demonstrate the large N phase transitions, with limited success.15 pages, harvmac. Minor errors corrected, argument in sect. 3 improvedHigh Energy Physics - Theorytext