The Hagedorn temperature of AdS5/CFT4 via integrability

Understand

We establish a framework for calculating the Hagedorn temperature of AdS5/CFT4 via integrability.

• Concretely, we derive the thermodynamic Bethe ansatz equations that yield the Hagedorn temperature of planar N=4 super Yang-Mills theory at any value of the 't Hooft coupling.
• We solve these equations perturbatively at weak coupling via the associated Y-system, confirming the known results at tree-level and one-loop order as well as deriving the previously unknown two-loop Hagedorn temperature.
• Finally, we comment on solving the equations at finite coupling.