HIGH TEMPERATURE EXPANSION OF STRING FREE ENERGY IN HYPERBOLIC SPACE

TL;DR

This paper analyzes the high temperature behavior of open bosonic string free energy in hyperbolic space, deriving the leading term near the Hagedorn temperature and exploring connections to black hole entropy.

Contribution

It provides the first high temperature expansion of string free energy in hyperbolic space and discusses infrared regularization and black hole entropy corrections.

Findings

Leading high temperature term near Hagedorn instability derived

Infrared regularization issues identified

Connections to quantum black hole entropy outlined

Abstract

The high temperature behaviour of the open bosonic string free energy in the space $S^1 \otimes H^N$ with vanishingly small curvature is investigated. The leading term of the high temperature expansion of the one-loop free energy, near the Hagedorn instability, is obtained. The problem of infrared regularization of thermodynamical quantities is pointed out. For minimally coupling quantum fields related to the normal modes of strings, the results are similar to the ones valid for Rindler space. In the lower mass string states regime a connection with the quantum corrections to the black hole entropy is outlined.