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

Abstract

We describe how to calculate the Hagedorn temperature of mathcal{N} = 4 SYM theory and type IIB superstring theory on AdS5 × S5 via the Quantum Spectral Curve (QSC) — providing further details on our previous letters [1] and [2]. We solve the QSC equations perturbatively at weak ‘t Hooft coupling λ 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-β and γi deformation) agrees with the one in mathcal{N} = 4 SYM theory at any value of λ.