Gauge gravity dualities from group representation theory

Abstract

This 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.