Evidence for Large N Phase Transition in N=4 Super Yang-Mills Theory at Finite Temperature

Abstract

The AdS/CFT correspondence provides valuable constraints on the possible exact form of various physical quantities in the $\mathcal{N}=4$ super Yang-Mills theory in the large N limit. We examine the free energy as the expansions in a small as well as in a large 't Hooft parameter $\lambda$. We argue that it is impossible to smoothly extrapolate from the weak coupling regime to the strong coupling regime, thus there must exist a large N phase transition in $\lambda$ at a finite temperature. We also argue that there is no world-sheet instanton in the background of the Euclidean anti-de Sitter black hole.

12 pages, harvmac; v2: corrections to some formulas, one reference added

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