Strings in RR Plane Wave Background at Finite Temperature

TL;DR

This paper computes the thermal partition function for type IIB superstrings in a plane wave background, revealing a higher Hagedorn temperature than flat space and suggesting a possible phase transition at finite temperature.

Contribution

It provides the first calculation of the thermal partition function in a plane wave background with R-R flux, showing how the Hagedorn temperature depends on the background and coupling.

Findings

Hagedorn temperature is higher than in flat space.

Hagedorn temperature tends to infinity at weak coupling.

Free energy remains finite near the Hagedorn temperature.

Abstract

We calculate the thermal partition function in the canonical ensemble for type IIB superstrings in the plane wave background with constant null R-R 5-form. The Hagedorn temperature is found to be higher than the corresponding value for strings in flat space. In the limit corresponding to the weakly coupled field theory we find that the Hagedorn temperature is pushed to infinity. The key property of strings in the plane wave background under investigation on which our result relies is that the effective mass of the bosonic and fermionic coordinates in the light-cone gauge is proportional to the momentum $p^+$. The free energy is finite as the Hagedorn temperature is approached from below, suggesting a possible phase transition.