Thermodynamics of Superstring on Near-extremal NS5 and Effective Hagedorn Behavior

TL;DR

This paper analyzes the thermodynamics of superstring theory on near-extremal NS5-branes, revealing effective Hagedorn behavior at temperatures below the traditional Hagedorn limit and exploring the effects of orbifolding on thermal modes.

Contribution

It provides an exact computation of the superstring partition function in a near-extremal NS5 background, decomposing contributions and identifying Hagedorn-like behavior below the Hagedorn temperature.

Findings

Massless excitations with thermal winding indicate effective Hagedorn behavior.

Localized thermal winding modes become tachyonic in orbifolded backgrounds.

Partition function decomposition distinguishes asymptotic and localized contributions.

Abstract

We study the thermodynamical torus partition function of superstring on the near-extremal black NS5-brane background. The exact partition function has been computed with the helps of our previous works:[arXiv:1012.5721 [hep-th]], [arXiv:1109.3365 [hep-th]], and naturally decomposed into two parts. The first part is contributed from strings freely propagating in the asymptotic region, which are identified as the superstring gas at the Hawking temperature on the linear-dilaton background. The second part includes the contribution localized around the `tip of cigar', which characterizes the non-extremality. Remarkably, the latter part includes massless excitations with non-vanishing thermal winding, which signifies that the Hagedorn-like behavior effectively appears, even though the Hawking temperature is much lower than the Hagedorn temperature. We also explore the high-temperature backgrounds defined by the orbifolding along the Euclidean time direction. In those cases, the thermal winding modes localized around the tip are found to be tachyonic, reflecting the singularities of Euclidean backgrounds caused by orbifolding.