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.
Highlights
Introduction.—According to the AdS/CFT correspondence [1], N 1⁄4 4 super Yang-Mills (SYM) theory on R × S3 is dual to type IIB string theory on AdS5 × S5
In the planar limit of N 1⁄4 4 SYM theory on R × S3, the origin of the Hagedorn temperature TH is the confinement of the color degrees of freedom due to the theory being on a three-sphere
The Hagedorn temperature is the lowest temperature for which the planar partition function ZðTÞ diverges
Summary
The integrable model is solved on a cylinder of finite circumference L, which accounts for wrapping contributions to the scaling dimension due to the finite length of the spin chain. We find a direct relation between the continuum limit of the free energy of the spin chain associated with planar N 1⁄4 4 SYM theory and the Hagedorn temperature. Using the integrability of the model, we derive thermodynamic Bethe ansatz (TBA) equations that determine the Hagedorn temperature at any value of the ’t Hooft coupling. The Hagedorn temperature from the free energy of the spin chain: In the planar limit, the scaling dimensions of multitrace operators are completely determined by the scaling dimensions of their singletrace factors.
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