Five-Brane Thermodynamics from the Matrix Model

TL;DR

This paper studies the thermodynamics of five-branes in the matrix model of M-theory, identifying a phase transition as the Hagedorn transition, and contrasting it with membrane backgrounds.

Contribution

It demonstrates the existence of a Gross-Witten phase transition at finite temperature corresponding to the Hagedorn transition in the five-brane background.

Findings

Identifies a critical temperature with a phase transition in the matrix model.

Shows the phase transition corresponds to deconfinement and Hagedorn behavior.

Contrasts the five-brane background with the membrane background, which lacks Hagedorn behavior.

Abstract

A certain sector of the matrix model for M-theory on a plane wave background has recently been shown to produce the transverse five-brane. We consider this theory at finite temperature. We find that, at a critical temperature it has a Gross-Witten phase transition which corresponds to deconfinement of the matrix model gauge theory. We interpret the phase transition as the Hagedorn transition of M-theory and of type II string theory in the five-brane background. We also show that there is no Hagedorn behaviour in the transverse membrane background case.