Remarks on Thermal Strings outside Black Holes

TL;DR

This paper examines the semiclassical behavior of (super) strings near black hole horizons, revealing entropy divergences, phase transitions, and the impact of supersymmetry on horizon regularity.

Contribution

It provides a detailed analysis of string thermodynamics in black hole backgrounds using semiclassical approximations and explores the effects of supersymmetry on horizon behavior.

Findings

Entropy diverges logarithmically with horizon thickness in 2D.

A local Hagedorn transition occurs in higher dimensions.

Supersymmetry enhances string regularity at the horizon.

Abstract

We discuss the semiclassical approximation to the level density of (super) strings propagating in non-compact coset manifolds $G/H$. We show that the WKB ansatz agrees with heuristic red-shift arguments with respect to the ``exact" sigma model metric, up to some deviations from minimal coupling, parametrized by the dilaton. This approximation is used to study thermal ensembles of free strings in black holes, with the ``brick wall" regularization of `t Hooft. In two dimensions the entropy diverges logarithmically with the horizon thickness, and a local Hagedorn transition occurs in higher dimensional models. We also observe that supersymmetry improves the regularity of strings at the horizon.