The Hagedorn Transition and the Matrix Model for Strings

TL;DR

This paper investigates the behavior of strings above the Hagedorn temperature using the Matrix formalism, revealing a phase transition where the string description breaks down and a gluon-dominated phase emerges.

Contribution

It demonstrates that the Hagedorn temperature marks a breakdown of the continuum string picture and describes a phase transition akin to deconfinement in large-N Yang Mills theories.

Findings

The Hagedorn temperature is not a limiting temperature but a phase transition point.

Above this temperature, the favored phase has no string world sheet and consists of massless gluons.

The transition resembles the deconfinement transition in large-N gauge theories.

Abstract

We use the Matrix formalism to investigate what happens to strings above the Hagedorn temperaure. We show that it is not a limiting temperature but a temperature at which the continuum string picture breaks down. We study a collection of $N$ D-0-branes arranged to form a string having $N$ units of light cone momentum. We find that at high temperatures the favoured phase is one where the string world sheet has disappeared and the low energy degrees of freedom consists of $N^2$ massless particles (``gluons''). The nature of the transition is very similar to the deconfinement transition in large-N Yang Mills theories.