The String Density of States from The Convolution Theorem

TL;DR

This paper investigates the thermodynamics of a bosonic string gas, revealing a phase transition at the Hagedorn temperature characterized by a transition to a state dominated by a very large string, without negative specific heat regions.

Contribution

It introduces a novel analysis of the string density of states using the convolution theorem, elucidating the phase transition and thermal properties of string gases in the microcanonical ensemble.

Findings

No negative specific heat region in the infinite volume limit.

Existence of a phase transition at the Hagedorn temperature.

Presence of a dominant 'fat' string in the high-energy phase.

Abstract

We study the microcanonical density of states and the thermal properties of a bosonic string gas starting from a calculation of the Helmholtz free energy in the S-representation. By adding more and more strings to the single string system, we induce that, for infinite volume, there is no negative specific heat region but a transition at a finite value of the energy per string from the low energy regime to a region of infinite specific heat at the Hagedorn temperature. Forcing the description of this phase in terms of strings gives a picture in which there is a very fat string in a sea of low energetic ones. We argue that the necessary changing of this description should not change the fact that perturbatively $T_H$ is a maximum temperature of the system.