Hagedorn Temperature of AdS_{5}/CFT_{4} via Integrability
Troels Harmark1, Matthias Wilhelm1
1Niels Bohr Institute, Copenhagen University, Blegdamsvej 17, 2100 Copenhagen Ø, Denmark.
Abstract:
We establish a framework for calculating the Hagedorn temperature of AdS_{5}/CFT_{4} 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.
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