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

Abstract

AbstractWe describe how to calculate the Hagedorn temperature of$$ \mathcal{N} $$N= 4 SYM theory and type IIB superstring theory onAdS5×S5via 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 couplingλup 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$$ \mathcal{N} $$N= 4 SYM theory (real-βandγideformation) agrees with the one in$$ \mathcal{N} $$N= 4 SYM theory at any value ofλ.