Gandote, Sonagnon Eunice Edwige2023-11-232023-11-232022https://hdl.handle.net/10539/37127A thesis submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy to the Faculty of Science, University of the Witwatersrand, 2022This thesis considers two distinct problems. First we discuss scrambling and equilibration in N = 4 super Yang-Mills theory using operators that have a very large dimension, of order N2 . A basis for these operators, is provided by the so-called Gauss graph operators. The operators are labelled by a pair of Young diagrams and a graph. We characterize the typical graph and the dynamics associated to it. We show that the resulting dynamics is that of a fast scrambler. Our system equilibrates in a time scale given by t ∼ p λ where p is an order N number equal to the number of nodes in the graph and λ is the ’t Hooft coupling. Finally we use bilocal holography to explore the duality between the free O(N) vector model and higher spin gravity. We demonstrate a mapping between the CFT and the higher spin gravity that is determined by the symmetry of the problem. We then turn to a study of the geometry of this mapping. Using a specific code subspace, we demonstrate that bilocal holography reproduces the entanglement wedge reconstruction. We also make contact with ideas that have been influential in the holographic computation of entanglement entropy.enGauge Gravity DualitiesGroup Representation Theoryscrambling and equilibrationThesis