A non-standard off-shell quantization of the worldsheet metric yields a self-consistent vacuum configuration and Hagedorn temperatures for confining holographic theories, reproducing known next-to-leading order and providing new partial next-to-next-to-leading order predictions.
Solving the Hagedorn temperature of AdS5/CFT4 via the Quantum Spectral Curve: Chemical potentials and deformations
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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 $\lambda$.
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Vacuum configuration of winding superstrings from non-standard semiclassical quantization
A non-standard off-shell quantization of the worldsheet metric yields a self-consistent vacuum configuration and Hagedorn temperatures for confining holographic theories, reproducing known next-to-leading order and providing new partial next-to-next-to-leading order predictions.