Thermal Partition Functions for S-branes

TL;DR

This paper computes the thermal partition functions of open strings on S-brane backgrounds, revealing an unavoidable Hagedorn divergence at all temperatures, which relates to open string pair production and closed string emissions.

Contribution

It introduces a method to calculate thermal partition functions for S-branes and demonstrates the persistent divergence across all temperatures, including zero.

Findings

Hagedorn divergence appears at all temperatures

Divergence persists even at zero temperature

Space-like linear dilaton backgrounds may mitigate divergence

Abstract

We calculate the thermal partition functions of open strings on the S-brane backgrounds (the bouncing or rolling tachyon backgrounds) both in the bosonic and superstring cases. According to hep-th/0302146, we consider the discretized temperatures compatible with the pure imaginary periodicity of tachyon profiles. The ``effective Hagedorn divergence'' is shown to appear no matter how low temperature is chosen (including zero-temperature). This feature is likely to be consistent with the large rate of open string pair production discussed in hep-th/0209090 and also emission of closed string massive modes hep-th/0303139. We also discuss the possibility to remove the divergence by considering the space-like linear dilaton backgrounds as in hep-th/0306132.