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 $Ad{S}_5\times S^5$ 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 $\lambda$.

arXiv comment52 pages; v2: added the analytic value for the leading correction at strong coupling (due to J. Maldacena and E. Urbach), as well as numeric values for the sub- and subsubleading correction

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• Higher Order Corrections to the Hagedorn Temperature at Strong Coupling
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• From Hagedorn to Lee-Yang: Partition functions of $\mathcal{N}=4$ SYM theory at finite $N$
• Hagedorn temperature in holography: world-sheet and effective approaches
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• Vacuum configuration of winding superstrings from non-standard semiclassical quantization