Entanglement and defect entropies in gauge/gravity duality

Abstract

In this thesis we investigate and use geometrical prescriptions for the calculation of entanglement entropy in field theories that have a gravity dual according to gauge/gravity duality. The main results of this work will arise from the application of our findings to the study of entanglement and defect entropies in a holographic model of the Kondo effect. Gauge/gravity duality is an important tool for the study of strongly coupled systems. We give a short review over the related idea of the holographic principle and the realisation of the AdS/CFT correspondence in string theory. We also introduce the concept of entanglement entropy and review the methods of holographically calculating it. We then apply recent prescriptions for calculating holographic entanglement entropy in gravitational theories with higher curvature terms to specific example spacetimes, such as stationary black holes, and obtain analytical solutions for extremal surfaces defining entanglement entropy that wrap around the black holes. We argue that these surfaces are unphysical by discussing how they violate certain well motivated causality constraints. We then investigate the geometrical properties of certain models of dualities between AdS spaces and boundary CFTs, with a special interest in a recently proposed holographic model of the Kondo effect. Understanding the impact of energy conditions on the allowed bulk geometries will be one of the main results of this thesis. We then apply the knowledge gained from these studies to the specific Kondo model, and numerically calculate entanglement and impurity entropies. These quantities can be interpreted in terms of the RG flow that the Kondo model undergoes. It will also be discussed in detail to which extend the holographic model reproduces field theory expectations, and how it can be improved. Furthermore, we investigate recent proposals of defining holographic measures of complexity. This is a quantity in quantum information theory. We end with an outlook on possible future research directions.