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Modave Summer School in Mathematical Physics

Entanglement Entropy in Field Theory and Gravity

Nabil Iqbal

Published Mar 16, 2016• 2 citations
Publisher

Abstract

This is an introductory set of lectures given by the author at the Modave Summer School 2015 on the various incarnations of entanglement entropy. Topics covered include an overview of the basic properties of entanglement entropy, its structure in quantum field theory, its computation in two-dimensional conformal field theory, a simple application to c -theorems in two dimensions, and the Ryu-Takayanagi formula and its extensions in holography

DOI
10.22323/1.271.0002

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This is an introductory set of lectures given by the author at the Modave Summer School 2015 on the various incarnations of entanglement entropy. Topics covered include an overview of the basic properties of entanglement entropy, its structure in quantum field theory, its computation in two-dimensional conformal field theory, a simple application to c -theorems in two dimensions, and the Ryu-Takayanagi formula and its extensions in holography
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.
These lecture notes 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 that physics is realized geometrically by the Ryu-Takayanagi formula. 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.
These lecture notes 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 that physics is realized geometrically by the Ryu-Takayanagi formula. 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.
These lecture notes provide a comprehensive introduction to 2d conformal field theory, covering foundational topics such as free fields, minimal models, Zamolodchikov's ccc-theorem, Wess-Zumino-Witten models, modular invariant partition functions, and the connections to entanglement entropy. The material presented is based on lectures at the Southeast University Summer School and the course at Fudan University.
In these notes we give a pedagogical account of the replica trick derivation of CFT entanglement and its holographic counterpart, i.e. the Lewkowycz Maldacena derivation of the Ryu-Takayanagi formula. The application to an ‘island set-up’ for the calculation of black hole radiation entropy is briefly discussed. Further topics focused on are the relation to thermal entropy, thermofield double constructions and statements about the emergence of gravity from entanglement through reinterpretations of gravitational first laws.