Lectures on entanglement entropy in field theory and holography

TL;DR

This paper introduces entanglement entropy in quantum field theories and holography, emphasizing geometric interpretations and physical properties, with a focus on two-dimensional examples and the Ryu-Takayanagi formula.

Contribution

It provides an accessible overview connecting entanglement entropy in field theories with holographic duals, highlighting geometric realizations and unique features of holographic entanglement.

Findings

Illustrates how the Ryu-Takayanagi formula geometrically encodes entanglement

Highlights special properties of holographic entanglement entropy

Provides foundational understanding for quantum information in field theories

Abstract

These notes, based on lectures given at various schools over the last few years, aim to provide an introduction to entanglement entropies in quantum field theories, including holographic ones. We explore basic properties and simple examples of entanglement entropies, mostly in two dimensions, with an emphasis on physical rather than formal aspects of the subject. In the holographic case, the focus is on how the Ryu-Takayanagi formula geometrically realizes general features of field-theory entanglement, while revealing special properties of holographic theories. In order to make the notes somewhat self-contained for readers whose background is in high-energy theory, a brief introduction to the relevant aspects of quantum information theory is included.