Entanglement Dynamics in 2D CFT with Boundary: Entropic origin of JT gravity and Schwarzian QM

Abstract

We study the dynamics of the geometric entanglement entropy of a 2D CFT in the presence of a boundary. We show that this dynamics is governed by local equations of motion, that take the same form as 2D Jackiw-Teitelboim gravity coupled to the CFT. If we assume that the boundary has a small thickness $\epsilon$ and constant boundary entropy, we derive that its location satisfies the equations of motion of Schwarzian quantum mechanics with coupling constant $C=c\epsilon /12\pi$. We rederive this result via energy-momentum conservation.

arXiv comment6 pages, 2 figures

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• Reparametrization modes, shadow operators, and quantum chaos in higher-dimensional CFTs
• Quantum Quenches and Thermalization in SYK models
• Towards Black Hole Evaporation in Jackiw-Teitelboim Gravity
• From Quantum Groups to Liouville and Dilaton Quantum Gravity
• Entanglement Entropy of Two Coupled SYK Models and Eternal Traversable Wormhole
• Jackiw-Teitelboim Gravity in the Second Order Formalism
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• Operational islands and black hole dissipation in JT gravity
• Chaotic Correlation Functions with Complex Fermions
• Entanglement in conformal field theory and holography
• Scanning space-time with patterns of entanglement