Lectures on entanglement entropy in field theory and holography

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.

arXiv comment66 pages

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• Entanglement entropy from entanglement contour: higher dimensions
• On de Sitter future-past extremal surfaces and the "entanglement wedge"
• Machine Learning Statistical Gravity from Multi-Region Entanglement Entropy
• The refined quantum extremal surface prescription from the asymptotic equipartition property
• Non-equilibrium dynamics in Holography
• Symmetry-resolved entanglement entropy in Wess-Zumino-Witten models
• A Spacetime Calculation of the Calabrese-Cardy Entanglement Entropy
• Hamilton-Jacobi formulation of holographic Entanglement Entropy
• Entanglement Entropy in Closed String Theory
• A new look at the entanglement entropy of a single interval in a 2d CFT
• Holographic entanglement negativity for a single subsystem in conformal field theories with a conserved charge
• Developments in non-relativistic field theory and complexity
• Scrambling and the black hole atmosphere