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

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