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

TL;DR

This paper investigates the Hagedorn transition of free strings in a pp-wave background, revealing a finite free energy at the transition point and connections to confinement/deconfinement phenomena in the dual gauge theory.

Contribution

It provides a detailed analysis of the Hagedorn transition in pp-wave backgrounds and relates it to gauge theory phase transitions, including the effects of chemical potentials.

Findings

Finite free energy at the transition suggests a confinement/deconfinement transition.

Matching free energy with strings on an 8-torus in the massless limit.

Computed entropy in microcanonical ensemble for fixed energy and momentum/winding.

Abstract

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.