The Hagedorn temperature of AdS5/CFT4 at finite coupling via the Quantum Spectral Curve

Abstract

Building on the recently established connection between the Hagedorn temperature and integrability [Phys.Rev.Lett. 120 (2018) no.7, 071605], we show how the Quantum Spectral Curve formalism can be used to calculate the Hagedorn temperature of AdS5/CFT4 for any value of the 't Hooft coupling. We solve this finite system of finite-difference equations perturbatively at weak coupling and numerically at finite coupling. We confirm previous results at weak coupling and obtain the previously unknown three-loop Hagedorn temperature. Our finite-coupling results interpolate between weak and strong coupling and allow us to extract the first perturbative order at strong coupling. Our results indicate that the Hagedorn temperature for large 't Hooft coupling approaches that of type IIB string theory in ten-dimensional Minkowski space.

7 pages; v2: clarifications added, typos corrected

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• Nonrelativistic near-BPS corners of $\mathcal{N}=4$ super-Yang-Mills with $SU(1,1)$ symmetry
• Higher Order Corrections to the Hagedorn Temperature at Strong Coupling
• 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
• Hagedorn temperature in holography: world-sheet and effective approaches
• The fate of the Konishi multiplet in the β-deformed Quantum Spectral Curve
• On analytical perturbative solution of ABJM quantum spectral curve
• Confinement and Graded Partition Functions for $\mathcal{N}=4$ SYM
• ABJM quantum spectral curve at twist 1: algorithmic perturbative solution
• Flow of Hagedorn singularities and phase transitions in large $N$ gauge theories
• Vacuum configuration of winding superstrings from non-standard semiclassical quantization
• Finite N corrections to white hot string bits
• Holographic Hagedorn Temperature: Strong Coupling, Flavor and $\theta$-angle Effects