Holography and the Sachdev-Ye-Kitaev model

Abstract

In this thesis we will review and discuss the Sachdev-Ye-Kitaev (SYK) model, its generalizations and related bulk models. We discuss the two and four point functions, the effective action and the Schwarzian. Also results regarding the choice of ensemble are presented. The generalizations that we (shortly) discuss are the supersymmetric extension and the tensor models. The second part of the thesis consists of a discussion of a related bulk model, called the Almheiri-Polchinski model. We review its action, symmetries and the (black hole) solutions. In particular we generalize the solutions in the literature and show how these compare. The thesis is concluded by discussing the most important open questions in the holography of the SYK model.