Thermodynamics of the Near-Extremal NS5-brane

TL;DR

This paper explores the thermodynamics of near-extremal NS5-branes by mapping their phases to Kaluza-Klein black holes and finds a new stable phase with a limiting temperature above the Hagedorn temperature.

Contribution

It introduces a new stable phase of near-extremal NS5-branes localized on a transverse circle, differing from the traditional smeared phase, and analyzes their thermodynamic properties.

Findings

The localized phase is thermodynamically dominant in the canonical ensemble.

A new limiting temperature exists, above the Hagedorn temperature.

Different behaviors are observed in canonical and microcanonical ensembles.

Abstract

We consider the thermodynamics of the near-extremal NS5-brane in type IIA string theory. The central tool we use is to map phases of six-dimensional Kaluza-Klein black holes to phases of near-extremal M5-branes with a transverse circle in eleven-dimensional supergravity. By S-duality these phases correspond to phases of the near-extremal type IIA NS5-brane. One of our main results is that in the canonical ensemble the usual near-extremal NS5-brane background, dual to a uniformly smeared near-extremal M5-brane, is subdominant to a new background of near-extremal M5-branes localized on the transverse circle. This new stable phase has a limiting temperature, which lies above the Hagedorn temperature of the usual NS5-brane phase. We discuss the limiting temperature and compare the different behavior of the NS5-brane in the canonical and microcanonical ensembles. We also briefly comment on the thermodynamics of near-extremal Dp-branes on a transverse circle.