Renormalized entanglement entropy and curvature invariants

Abstract

Renormalized entanglement entropy can be defined using the replica trick for any choice of renormalization scheme; renormalized entanglement entropy in holographic settings is expressed in terms of renormalized areas of extremal surfaces. In this paper we show how holographic renormalized entanglement entropy can be expressed in terms of the Euler invariant of the surface and renormalized curvature invariants. For a spherical entangling region in an odd-dimensional CFT, the renormalized entanglement entropy is proportional to the Euler invariant of the holographic entangling surface, with the coefficient of proportionality capturing the (renormalized) F quantity. Variations of the entanglement entropy can be expressed elegantly in terms of renormalized curvature invariants, facilitating general proofs of the first law of entanglement.

arXiv comment32 pages

References in corpus (22)

• Holographic Derivation of Entanglement Entropy from AdS/CFT
• A Covariant Holographic Entanglement Entropy Proposal
• Entanglement entropy and conformal field theory
• Towards a derivation of holographic entanglement entropy
• Information in Black Hole Radiation
• Replica Wormholes and the Entropy of Hawking Radiation
• The Page curve of Hawking radiation from semiclassical geometry
• Entanglement entropy in free quantum field theory
• Towards the F-Theorem: N=2 Field Theories on the Three-Sphere
• Entanglement and correlation functions following a local quench: a conformal field theory approach
• Conformal Anomaly Of Submanifold Observables In AdS/CFT Correspondence
• Renormalized entanglement entropy
• Counterterms, Kounterterms, and the variational problem in AdS gravity
• Holographic entanglement entropy in AdS4/BCFT3 and the Willmore functional
• Renormalized Volume
• Einstein-AdS action, renormalized volume/area and holographic Renyi entropies
• A Bound on Holographic Entanglement Entropy from Inverse Mean Curvature Flow
• Topological terms, AdS_2n gravity and renormalized Entanglement Entropy of holographic CFTs
• Renormalization of Entanglement Entropy from topological terms
• Shape dependence of renormalized holographic entanglement entropy
• Renormalized AdS gravity and holographic entanglement entropy of even-dimensional CFTs
• Non-conformal entanglement entropy

Cited by in corpus (6)

• Renormalized holographic entanglement entropy for Quadratic Curvature Gravity
• Non-Gaussianity of Entanglement Entropy and Correlations of Composite Operators
• Entanglement entropy in scalar field theory and ${\mathbb{Z}}_M$ gauge theory on Feynman diagrams
• CFT correlators from shape deformations in Cubic Curvature Gravity
• Generalised proofs of the first law of entanglement entropy
• Disks globally maximize the entanglement entropy in $2+1$ dimensions