Counting Closed String States in a Box

TL;DR

This paper develops a geometrical method to compute the density of states for a string gas in finite volume, revealing thermodynamic properties like maximum temperature and positive specific heat, consistent with R-duality.

Contribution

It introduces a geometrical approach to count string states in a finite volume and explores the thermodynamics, including maximum temperature and pressure, consistent with R-duality.

Findings

Maximum temperature (Hagedorn temperature) in finite volume

Positive specific heat for the string gas

Pressure behavior consistent with R-duality

Abstract

The computation of the microcanonical density of states for a string gas in a finite volume needs a one by one count because of the discrete nature of the spectrum. We present a way to do it using geometrical arguments in phase space. We take advantage of this result in order to obtain the thermodynamical magnitudes of the system. We show that the results for an open universe exactly coincide with the infinite volume limit of the expression obtained for the gas in a box. For any finite volume the Hagedorn temperature is a maximum one, and the specific heat is always positive. We also present a definition of pressure compatible with R-duality seen as an exact symmetry, which allows us to make a study on the physical phase space of the system. Besides a maximum temperature the gas presents an asymptotic pressure.