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Renormalized entanglement entropy and curvature invariants

Renormalized entanglement entropy and curvature invariants
Renormalized entanglement entropy and curvature invariants
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.
1029-8479
Taylor, Marika
5515acab-1bed-4607-855a-9e04252aec22
Too, Linus Ho Yi
b76dcfbd-4d76-406d-858c-a38fe181e09a
Taylor, Marika
5515acab-1bed-4607-855a-9e04252aec22
Too, Linus Ho Yi
b76dcfbd-4d76-406d-858c-a38fe181e09a

Taylor, Marika and Too, Linus Ho Yi (2020) Renormalized entanglement entropy and curvature invariants. Journal of High Energy Physics. (In Press)

Record type: Article

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.

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2004.09568 - Author's Original
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Accepted/In Press date: 28 October 2020

Identifiers

Local EPrints ID: 444949
URI: http://eprints.soton.ac.uk/id/eprint/444949
ISSN: 1029-8479
PURE UUID: 93efcb6f-1764-4b10-a547-ca107a7b9e69
ORCID for Marika Taylor: ORCID iD orcid.org/0000-0001-9956-601X

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Date deposited: 12 Nov 2020 17:33
Last modified: 18 Feb 2021 17:18

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