Hagedorn transition for strings on pp-waves and tori with chemical potentials

It has been conjectured that string theory in a pp-wave background is dual to a sector of N=4 supersymmetric Yang-Mills theory. We study the Hagedorn transition for free strings in this background. We find that the free energy at the transition point is finite suggesting a confinement/deconfinement transition in the gauge theory. In the limit of vanishing mass parameter the free energy matches that of free strings on an 8-torus with momentum/winding chemical potential. The entropy in the microcanonical ensemble with fixed energy and fixed momentum/winding is computed in each case.