Applications of holography and entanglement

Abstract

In this thesis we will investigate a number of topics on the applications of the gauge-gravity duality to topics in condensed matter physics and quantum entanglement. This duality is a conjectured equivalence between type IIB string theory on asymptotically anti-de Sitter backgrounds with certain quantum field theories in one dimension less. Using this conjecture we can model strongly-coupled quantum systems using classical gravity duals which provide novel methods for calculating otherwise computationally inaccessible quantum properties. We will use this for the following applications:

• We study a novel method for introducing broken translational symmetry into a holographic model whilst retaining homogeneity in the field equations. We demonstrate that this leads to a finite DC conductivity and shows features of heavy fermion models in the AC conductivity.

• We explore the nature of real time scalar correlators in holographic models of critical systems that possess a non-relativistic scaling symmetry. Specifically we explore systems with dual Schrödinger or Lifshitz scaling symmetries, and discuss the problems that arise when trying to apply the standard framework of real time holography to these systems.

• We provide an explicit counterexample to the holographic F-theorem, and an analytic argument that shows that this violation is not specific to the model in consideration but is rather a more general property of a class of holographic systems.

• Finally we introduce a holographic renormalization scheme for the entanglement entropy based on the standard framework of holographic renormalization. We connect this to the field theory via the replica trick and use it to calculate a number of explicit examples both analytically and numerically.

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Identifiers

ORCID for Marika Taylor: orcid.org/0000-0001-9956-601X

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