Hagedorn vs. Hawking-Page transition in string theory

TL;DR

This paper investigates the confinement/deconfinement phase transition in N=4 SU(N) SYM theory using supergravity duals, revealing new insights into the thermodynamics and its relation to string Hagedorn transitions.

Contribution

It introduces a supergravity model with a chemical potential to analyze the phase transition and derives new expressions for black hole mass and free energy.

Findings

New supergravity expressions for black hole mass and free energy

Connection established between phase transition and string Hagedorn transition

Insights into thermodynamics of N=4 SYM on R x S^3 with chemical potential

Abstract

We study the supergravity dual to the confinement/deconfinement phase transition for the N=4 SU(N) SYM on R x S^3 with a chemical potential conjugate to a U(1)\subset SO(6)_R charge. The appropriate supergravity system is a single charge black hole in D=5 N=8 gauged supergravity. Application of the gauge/string theory holographic renormalization approach leads to new expressions for the black hole ADM mass and its generalized free energy. We comment on the relation of this phase transition to the Hagedorn transition for strings in the maximally supersymmetric plane wave background with null RR five form field strength.