MSc defense by Ioannis Kalogerakis

Black holes are archetypical examples of the conflicts between general relativity and quantum mechanics. Although well understood on a classical level, their quantum nature is less clear. Nevertheless, the holographic principle provides a map that connects these two areas. The first part of the thesis contains a review of our current understanding of the dynamics of black holes in the context of the AdS/CFT correspondence, which is the best realization of holography up to date. Their quantum properties are studied, with a particular focus on chaos. In the subsequent sections, an overview is given of a class of holographic quantum mechanical toy models, such as the Sachdev-Ye-Kitaev model, that have appeared in the literature over the past few years and are able to replicate characteristic features of black holes, such as a continuous spectrum and chaos. Special focus lies on a particular class of Feynman graphs, called melons, that lead to a solvable form of Schwinger-Dyson equations. The final sections contain original research in the context of Spin Matrix Theory. Inspired by large N tensor models, we generalize the theory to the SU(q) sector, in order to study its thermodynamics in the large q limit. In its standard scaling form, the theory is at large q dominated by so-called snail diagrams. As a consequence, it behaves similarly to ordinary vector models. Using a refined scaling technique, we demonstrate the existence of a melonic regime and we give sample solutions of the resulting Schwinger-Dyson equations.