Large-N strong weak coupling phase transition and the correspondence principle

We argue that the large-N strong/weak phase transition is a generic phenomenon in a finite temperature supersymmetric Yang-Mills theory of maximal supersymmetry. 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 alpha' 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. (C) 1999 Published by Elsevier Science B.V. All rights reserved.