On the Hagedorn Behaviour of PP-wave Strings and N=4 SYM Theory at Finite R-Charge Density

TL;DR

This paper investigates the high-temperature behavior of IIB strings in a maximally symmetric plane wave background, revealing a Hagedorn temperature and exploring its implications for the dual N=4 SYM theory at finite R-charge density.

Contribution

It demonstrates the existence of a Hagedorn temperature for strings in the pp-wave background and maps this to the phase diagram of the dual gauge theory, updating previous results with recent insights.

Findings

Identification of a Hagedorn temperature in the pp-wave string background

Mapping of the Hagedorn bound to the R-charge versus temperature phase diagram

Confirmation that the string theory exists on both sides of the Hagedorn bound

Abstract

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.