Hot String Soup

TL;DR

This paper explores the behavior of long fundamental strings above the Hagedorn temperature, deriving equilibrium distributions and analyzing the effects of open strings on the long string phase.

Contribution

It provides an explicit solution to the Boltzmann equation for weakly interacting long strings and clarifies the conditions under which the long string phase is suppressed.

Findings

Average number of long strings grows logarithmically with energy

Equilibrium distributions are explicitly solvable

Open strings suppress the long string phase

Abstract

Above the Hagedorn energy density closed fundamental strings form a long string phase. The dynamics of weakly interacting long strings is described by a simple Boltzmann equation which can be solved explicitly for equilibrium distributions. The average total number of long strings grows logarithmically with total energy in the microcanonical ensemble. This is consistent with calculations of the free single string density of states provided the thermodynamic limit is carefully defined. If the theory contains open strings the long string phase is suppressed.