Strings in the Ramond-Ramond plane wave background at finite temperature

We calculate the thermal partition function in the canonical ensemble for type IIB superstrings in the plane wave background with a constant null RR five-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.