# The Hagedorn temperature of AdS5/CFT4 via integrability

## TL;DR

This paper develops a framework using integrability to compute the Hagedorn temperature of AdS5/CFT4, providing results at weak coupling and discussing potential finite coupling solutions.

## Contribution

It derives thermodynamic Bethe ansatz equations for the Hagedorn temperature in planar N=4 super Yang-Mills theory at any coupling, including new two-loop results.

## Key findings

- Confirmed known weak coupling results at tree-level and one-loop.
- Derived the two-loop Hagedorn temperature.
- Discussed approaches for finite coupling solutions.

## Abstract

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.