A note on the universality of the Hagedorn behavior of pp-wave strings

Following on from recent studies of string theory on a one-parameter family of integrable deformations of AdS5 x S5 proposed by Lunin and Maldacena, we carry out a systematic analysis of the high temperature properties of type IIB strings on the associated pp-wave geometries. In particular, through the computation of the thermal partition function and free energy we find that not only does the theory exhibit a Hagedorn transition in both the (J, 0, 0) and (J, J, J) class of pp-waves, but that the Hagedorn temperature is insensitive to the deformation suggesting an interesting universality in the high temperature behaviour of the pp-wave string theory. We comment also on the implications of this universality on the confinement/deconfinement transition in the dual N = 1 Leigh-Strassler deformation of N = 4 Yang-Mills theory