Msc defense by Katherina Hauer

The Hagedorn temperature at any coupling

The AdS_5/CFT_4 correspondence has the property of integrability, which leads to the formalism of Quantum Spectral Curves
(QSC). Itis a system of finite-difference equations and can be used to determine the Hagedorn temperature for weak and strong coupling.

Based on the method introduced by Maldacena in 1998, we solve the QSC numerically in thestrong coupling limit at the Hagedorn temperature. We then attemptto find an analytic description of the constituent functions P andQ of the QSC formalism in the strong coupling limit.

The focus of the study lies on the analysis of those functions concerning their dependence of the spectral parameter and the coupling. In order to find an analytic expression we fit the numeric solutions. We apply different ansätze for those functions and compare them regarding numeric stability and their behaviour in the limit $g\to \infty$.