The Hagedorn temperature of AdS5/CFT4 via integrability

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.

6 pages; v3: references and further clarification added, matches journal version

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• Continuum limit of fishnet graphs and AdS sigma model
• Quantum Spectral Curve for the eta-deformed AdS_5xS^5 superstring
• The Hagedorn temperature of AdS5/CFT4 at finite coupling via the Quantum Spectral Curve
• A review of the AdS/CFT Quantum Spectral Curve
• Nonrelativistic near-BPS corners of $\mathcal{N}=4$ super-Yang-Mills with $SU(1,1)$ symmetry
• Probing the holographic model of $\mathcal{N}=4$ SYM rotating quark-gluon plasma
• Solving the Hagedorn temperature of AdS5/CFT4 via the Quantum Spectral Curve: Chemical potentials and deformations
• Duality Relations for Overlaps of Integrable Boundary States in AdS/dCFT
• Introduction to Integrability and One-point Functions in $\mathcal{N}=4$ SYM and its Defect Cousin
• Semiclassical Quantization of the Superstring and Hagedorn Temperature
• From Hagedorn to Lee-Yang: Partition functions of $\mathcal{N}=4$ SYM theory at finite $N$
• Tidal excitation as mixing in thermal CFT
• Confinement and Graded Partition Functions for $\mathcal{N}=4$ SYM
• On analytical perturbative solution of ABJM quantum spectral curve
• Flow of Hagedorn singularities and phase transitions in large $N$ gauge theories
• Finite N corrections to white hot string bits
• Holographic Hagedorn Temperature: Strong Coupling, Flavor and $\theta$-angle Effects
• The Static Heavy Quark-Antiquark Potential within String Theory in Arbitrary Stationary Backgrounds