Thermodynamics of the near-extremal NS5-brane

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.