Solving the Hagedorn temperature of AdS5/CFT4 via the Quantum Spectral Curve: Chemical potentials and deformations

TL;DR

This paper computes the Hagedorn temperature of $ ext{AdS}_5/ ext{CFT}_4$ using the Quantum Spectral Curve, extending methods to include chemical potentials and deformations, with results valid at weak and finite coupling.

Contribution

It introduces a method to calculate the Hagedorn temperature via the QSC, including chemical potentials and deformations, and provides perturbative and numerical results up to seven-loop order.

Findings

Perturbative results expressed with harmonic polylogarithms.

Hagedorn temperature computed at finite coupling.

Deformations of $ ext{N}=4$ SYM do not alter the Hagedorn temperature.

Abstract

We describe how to calculate the Hagedorn temperature of $\mathcal{N}=4$ SYM theory and type IIB superstring theory on $AdS_5\times S^5$ via the Quantum Spectral Curve (QSC) -- providing further details on our previous letters 1706.03074 and 1803.04416. We solve the QSC equations perturbatively at weak 't Hooft coupling $\lambda$ up to seven-loop order and numerically at finite coupling, finding that the perturbative results can be expressed in terms of single-valued harmonic polylogarithms. Moreover, we generalize the QSC to describe the Hagedorn temperature in the presence of chemical potentials. Finally, we show that the Hagedorn temperature in certain deformations of $\mathcal{N}=4$ SYM theory (real-$\beta$ and $\gamma_i$ deformation) agrees with the one in $\mathcal{N}=4$ SYM theory at any value of $\lambda$.