## Abstract

We describe how to calculate the Hagedorn temperature of N = 4 SYM theory and type IIB superstring theory on AdS(5) x 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 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 N = 4 SYM theory (real-beta and gamma(i) deformation) agrees with the one in N = 4 SYM theory at any value of lambda.

Original language | English |
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Article number | 136 |

Journal | Journal of High Energy Physics |

Volume | 2022 |

Issue number | 7 |

Number of pages | 53 |

ISSN | 1029-8479 |

DOIs | |

Publication status | Published - 21 Jul 2022 |

## Keywords

- 1/N Expansion
- AdS-CFT Correspondence
- Confinement
- Integrable Field Theories
- YANG-MILLS THEORY
- MULTIPLE POLYLOGARITHMS
- N=4
- TRANSITION
- DUALITY