The Hagedorn Transition, Deconfinement and N=4 SYM Theory

TL;DR

This paper investigates the thermodynamics of N=4 Super Yang-Mills theory, revealing a deconfinement transition and Hagedorn behavior, and connects these phenomena to string theory and black holes via AdS/CFT correspondence.

Contribution

It demonstrates the existence of a deconfinement transition and Hagedorn behavior in N=4 SYM theory at zero coupling and explores their relation through holography.

Findings

Deconfinement transition observed at large N and zero coupling.

Hagedorn behavior appears below the transition, indicating phase approach.

Hagedorn and deconfinement temperatures are found to be identical.

Abstract

N=4 Super Yang-Mills theory supplies us with a non-Abelian 4D gauge theory with a meaningful perturbation expansion, both in the UV and in the IR. We calculate the free energy on a 3-sphere and observe a deconfinement transition for large N at zero coupling. The same thermodynamic behaviour is found for a wide class of toy models, possibly also including the case of non-zero coupling. Below the transition we also find Hagedorn behaviour, which is identified with fluctuations signalling the approach to the deconfined phase. The Hagedorn and the deconfinement temperatures are identical. Application of the AdS/CFT correspondence gives a connection between string Hagedorn behaviour and black holes.