Near-Hagedorn Thermodynamics and Random Walks - Extensions and Examples

TL;DR

This paper explores various string theory backgrounds to understand near-Hagedorn thermodynamics, focusing on the random walk model, Hagedorn temperature, and boundary conditions across different spacetime configurations.

Contribution

It extends previous work by analyzing explicit examples and modifications of the random walk picture in diverse backgrounds, clarifying the thermodynamic behavior near the Hagedorn temperature.

Findings

Determined Hagedorn temperature in toroidally compactified backgrounds

Analyzed boundary conditions for the thermal scalar in orbifold models

Explored the link between quantum numbers and thermodynamics

Abstract

In this paper, we discuss several explicit examples of the results obtained in JHEP 1402 (2014) 127. We elaborate on the random walk picture in these spacetimes and how it is modified. Firstly we discuss the linear dilaton background. Then we analyze a previously studied toroidally compactified background where we determine the Hagedorn temperature and study the random walk picture. We continue with flat space orbifold models where we discuss boundary conditions for the thermal scalar. Finally, we study the general link between the quantum numbers in the fundamental domain and the strip and their role in thermodynamics.