| Summary: | Abstract We describe how to calculate the Hagedorn temperature of N $$ \mathcal{N} $$ = 4 SYM theory and type IIB superstring theory on AdS 5 × S 5 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 N $$ \mathcal{N} $$ = 4 SYM theory (real-β and γ i deformation) agrees with the one in N $$ \mathcal{N} $$ = 4 SYM theory at any value of λ.
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