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

TL;DR

This paper investigates the phase structure of N=4 super Yang-Mills theory at finite temperature, proposing a large N phase transition at a finite coupling, supported by analysis of free energy expansions and holographic arguments.

Contribution

It provides evidence for a large N phase transition in N=4 super Yang-Mills theory at finite temperature, highlighting the non-smooth extrapolation between weak and strong coupling regimes.

Findings

Existence of a large N phase transition at finite temperature.

Incompatibility of smooth coupling extrapolation.

Absence of world-sheet instantons in Euclidean AdS black hole background.

Abstract

The AdS/CFT correspondence provides valuable constraints on the possible exact form of various physical quantities in the ${\cal N}=4$ 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.