On the Hagedorn Behaviour of PP-wave Strings and N=4 SYM Theory at   Finite R-Charge Density
  We discuss the high temperature behaviour of IIB strings in the maximally symmetric plane wave background, and show that there is a Hagedorn temperature. We discuss the map between strings in the pp-wave background and the dual superconformal field theory in the thermal domain. The Hagedorn bound describes a curve in the R-charge chemical potential versus temperature phase diagram of the dual Yang-Mills theory and the theory manifestly exists on both sides. Using a recent observation of Brower, Lowe, and Tan, we update our earlier calculation to reflect that the pp-wave string exists on both sides of the Hagedorn bound as well. 
Brian R. Greene, Koenraad Schalm, and Gary Shiu