The Hagedorn/Deconfinement Phase Transition in Weakly Coupled Large N Gauge Theories

TL;DR

This paper investigates deconfinement phase transitions in weakly coupled large N SU(N) gauge theories on compact manifolds, revealing the nature of phases and their potential connection to black hole formation in dual string theories.

Contribution

It demonstrates the occurrence of deconfinement transitions in large N gauge theories on compact manifolds and links these transitions to black hole formation in dual string theories.

Findings

Deconfinement transitions occur at temperatures inversely proportional to the manifold's length scale.

Low temperature phase exhibits stringy Hagedorn growth in density of states.

High temperature phase has free energy of order N^2.

Abstract

We demonstrate that weakly coupled, large N, d-dimensional SU(N) gauge theories on a class of compact spatial manifolds (including S^{d-1} \times time) undergo deconfinement phase transitions at temperatures proportional to the inverse length scale of the manifold in question. The low temperature phase has a free energy of order one, and is characterized by a stringy (Hagedorn) growth in its density of states. The high temperature phase has a free energy of order N^2. These phases are separated either by a single first order transition that generically occurs below the Hagedorn temperature or by two continuous phase transitions, the first of which occurs at the Hagedorn temperature. These phase transitions could perhaps be continuously connected to the usual flat space deconfinement transition in the case of confining gauge theories, and to the Hawking-Page nucleation of AdS_5 black holes in the case of the N=4 supersymmetric Yang-Mills theory. We suggest that deconfinement transitions may generally be interpreted in terms of black hole formation in a dual string theory. Our analysis proceeds by first reducing the Yang-Mills partition function to a (0+0)-dimensional integral over a unitary matrix U, which is the holonomy (Wilson loop) of the gauge field around the thermal time circle in Euclidean space; deconfinement transitions are large N transitions in this matrix integral.