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

TL;DR

This paper investigates the high temperature behavior of string theory on deformed pp-wave backgrounds, revealing a universal Hagedorn transition temperature unaffected by the deformation, with implications for dual gauge theories.

Contribution

It demonstrates the universality of the Hagedorn temperature in pp-wave string theories under certain deformations, extending understanding of high temperature string behavior.

Findings

Hagedorn transition occurs in both studied pp-wave classes.

Hagedorn temperature remains unchanged despite deformations.

Implications for confinement/deconfinement in dual gauge theories.

Abstract

Following on from recent studies of string theory on a one-parameter family of integrable deformations of $AdS_{5}\times S^{5}$ 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 $\mathcal{N}=1$ Leigh-Strassler deformation of ${\cal N}=4$ Yang-Mills theory.