A note on the extensivity of the holographic entanglement entropy

Carlos A. Fuertes; Jose L.F. Barbon

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A note on the extensivity of the holographic entanglement entropy

Jose L.F. Barbon, Carlos A. Fuertes

High Energy Physics - Theory · Submitted 14 Jan 2008

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim In this note, we show that the holographic ansatz predicts the persistence of the extensivity down to vanishing temperature, for the particular case of conformal field theories in 2+1 dimensions with a magnetic field and/or electric charge condensates.

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We consider situations where the renormalized geometric entropy, as defined by the AdS/CFT ansatz of Ryu and Takayanagi, shows extensive behavior in the volume of the entangled region. In general, any holographic geometry that is `capped' in the infrared region is a candidate for extensivity provided the growth of minimal surfaces saturates at the capping region, and the induced metric at the `cap' is non-degenerate. Extensivity is well-known to occur for highly thermalized states. In this note, we show that the holographic ansatz predicts the persistence of the extensivity down to vanishing temperature, for the particular case of conformal field theories in 2+1 dimensions with a magnetic field and/or electric charge condensates.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We consider situations where the renormalized geometric entropy, as defined by the AdS/CFT ansatz of Ryu and Takayanagi, shows extensive behavior in the volume of the entangled region.	background 0.64	0.33	0.06	asserted 0.55
s1	In general, any holographic geometry that is `capped' in the infrared region is a candidate for extensivity provided the growth of minimal surfaces saturates at the capping region, and the induced metric at the `cap' is non-degenerate.	background 0.52	0.23	0.08	asserted 0.52
s2	Extensivity is well-known to occur for highly thermalized states.	background 1.00	0.04	0.03	asserted 1.00
s3	In this note, we show that the holographic ansatz predicts the persistence of the extensivity down to vanishing temperature, for the particular case of conformal field theories in 2+1 dimensions with a magnetic field and/or electric charge condensates.	result 0.82	0.92	0.92	asserted 1.00

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Original abstract

We consider situations where the renormalized geometric entropy, as defined by the AdS/CFT ansatz of Ryu and Takayanagi, shows extensive behavior in the volume of the entangled region. In general, any holographic geometry that is `capped' in the infrared region is a candidate for extensivity provided the growth of minimal surfaces saturates at the capping region, and the induced metric at the `cap' is non-degenerate. Extensivity is well-known to occur for highly thermalized states. In this note, we show that the holographic ansatz predicts the persistence of the extensivity down to vanishing temperature, for the particular case of conformal field theories in 2+1 dimensions with a magnetic field and/or electric charge condensates.

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References

Forward citations

Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

A Holographic Derivation of the Weak Gravity Conjecture
hep-th 2018-12 conditional novelty 6.0 of 10

Exactly stable extremal black branes in AdS would produce a volume-law entanglement entropy that contradicts a proven area-law theorem, so a superextremal particle must exist.
Volume Law for the Entanglement Entropy in Non-local QFTs
hep-th 2013-11 conditional novelty 5.0 of 10

Free scalar theories with kinetic term exp(A(-∂²)^{w/2}) have ground-state entanglement entropy S ≈ (w/2) A L for interval length L below the non-locality scale A, a volume law, crossing over to a constant of order A²...
Holographic evolution of the mutual information
hep-th 2011-10 conditional novelty 5.0 of 10

In Vaidya black-hole formation backgrounds the holographic mutual information between two boundary regions is non-monotonic in time, vanishes identically in a region of configuration space, and is monogamous whenever ...
Entanglement Entropy from a Holographic Viewpoint
gr-qc 2012-04 conditional novelty 2.0 of 10

A survey of the Ryu-Takayanagi proposal that entanglement entropy in a conformal field theory equals the area of a minimal surface in its dual anti-de Sitter gravity, with applications to black holes and boundary CFT.
Entanglement entropy of black holes
hep-th 2011-04 accept novelty 2.0 of 10

A systematic review showing that the conical-singularity method computes black hole entanglement entropy whose UV divergences renormalize Newton's constant and quadratic curvature couplings, while non-minimally couple...

Show 1 more citing papers

Holographic Entanglement Entropy: An Overview
hep-th 2009-05 conditional novelty 1.0 of 10

A 2009 review argues that entanglement entropy in a conformal field theory is computed by the area of a minimal surface in its dual anti-de Sitter spacetime, and surveys the evidence and applications.

How the literature uses it

13 arXiv papers cite this in 18 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 12 sentences without a confident label

Cites it as background 5 papers

These UV-finite terms are quite interesting and the subject of some recent attention (cf. [ref] ) but will not be the main subject of this paper.

Holographic entanglement entropy probes (non)locality · Introduction · 0.96
Vacuum entanglement entropy in noncommutative field theories has been studied both holographically [ref] and directly [ref] .

Entanglement entropy on a fuzzy sphere with a UV cutoff · Introduction · 0.99
In previously studied examples of extensive behaviour of entanglement entropy (for example, in thermal states) this extensive behaviour was due to the minimal surface `wrapping' a surface in the IR region of the dual, such as a black hole horizon (see for example [ref] ).

Holographic entanglement entropy in nonlocal theories · Introduction · 0.87

What it cites · 20 sentences without a confident label

Compares with 1 paper

We discuss in some detail the conditions that ensure this behavior, and comment on the relation to the confinement property, making contact with the results of [ref] .

Entanglement as a Probe of Confinement · Introduction · 0.85

Cites as background 4 papers

In this note, we begin with a review of the holographic proposal of [ref] , emphasizing the natural emergence of the non-extensive `area law' for the geometric entropy in models with conformal ultraviolet fixed points.

Holographic Derivation of Entanglement Entropy from AdS/CFT · Introduction · 0.85
A very interesting proposal for a holographic [ref] computation of geometric (entanglement) entropy [ref] in conformal field theories was put forward in [ref] (see [ref] for subsequent work).

Black hole entropy as entanglement entropy: a holographic derivation · Introduction · 0.98
A very interesting proposal for a holographic [ref] computation of geometric (entanglement) entropy [ref] in conformal field theories was put forward in [ref] (see [ref] for subsequent work).

Entropy and Area · Introduction · 0.98

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