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

TL;DR

This paper uses the Quantum Spectral Curve formalism to calculate the Hagedorn temperature of AdS5/CFT4 across all coupling regimes, confirming previous weak coupling results and providing new insights at strong coupling.

Contribution

It introduces a method to compute the Hagedorn temperature at finite coupling using the Quantum Spectral Curve, including perturbative and numerical solutions, and extends understanding to strong coupling.

Findings

Confirmed weak coupling Hagedorn temperature results.

Computed the three-loop Hagedorn temperature.

Interpolated the temperature between weak and strong coupling regimes.

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.