Holographic entanglement entropy for disconnected regions

Mukund Rangamani; Veronika E. Hubeny

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Holographic entanglement entropy for disconnected regions

Veronika E. Hubeny, Mukund Rangamani

High Energy Physics - Theory · Submitted 26 Nov 2007

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

The authors' main claim We present a simple derivation of the entanglement entropy for a region made up of a union of disjoint intervals in 1+1 dimensional quantum field theories using holographic techniques.

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We present a simple derivation of the entanglement entropy for a region made up of a union of disjoint intervals in 1+1 dimensional quantum field theories using holographic techniques. This generalizes the results for 1+1 dimensional conformal field theories derived previously by exploiting the uniformization map. We further comment on the generalization of our result to higher dimensional field theories.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We present a simple derivation of the entanglement entropy for a region made up of a union of disjoint intervals in 1+1 dimensional quantum field theories using holographic techniques.	contribution 0.99	0.96	0.67	asserted 1.00
s1	This generalizes the results for 1+1 dimensional conformal field theories derived previously by exploiting the uniformization map.	background 0.53	0.17	0.11	asserted 1.00
s2	We further comment on the generalization of our result to higher dimensional field theories.	future work 0.83	0.54	0.05	unclear 0.86

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Original abstract

We present a simple derivation of the entanglement entropy for a region made up of a union of disjoint intervals in 1+1 dimensional quantum field theories using holographic techniques. This generalizes the results for 1+1 dimensional conformal field theories derived previously by exploiting the uniformization map. We further comment on the generalization of our result to higher dimensional field theories.

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References

Forward citations

Cited by 11 Pith papers

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

Quantum Complexity Dynamics for Disjoint Subsystems
hep-th 2026-08 accept novelty 7.0 of 10

A noncontiguous subsystem can have exponentially higher complexity than its larger complement at finite temperature, and fragmenting a subsystem into m pieces shortens its thermalization time by a factor of m.
Entanglement Renyi entropies in holographic theories
hep-th 2010-06 accept novelty 7.0 of 10

Fursaev's derivation of the Ryu-Takayanagi formula is shown to use non-saddle-point geometries; corrected Renyi entropy calculations in two-dimensional holographic theories reproduce the Ryu-Takayanagi predictions, in...
Entanglement entropy of two disjoint intervals in conformal field theory
hep-th 2009-05 conditional novelty 7.0 of 10

The paper derives an exact formula for the Renyi entanglement entropy of two disjoint intervals in a free compactified boson, expressed via Riemann-Siegel theta functions, valid for all integer replica indices n.
Remarks on the entanglement entropy for disconnected regions
hep-th 2008-12 conditional novelty 7.0 of 10

Extensive mutual information has a unique local form, and among the theories checked only the two-dimensional massless Dirac fermion realizes it exactly.
Mutual information after a local quench in conformal field theory
hep-th 2013-11 conditional novelty 6.0 of 10

After a local quench in a 2d CFT, two-interval mutual information is separation-independent at leading order, while the falling-mass holographic model of the same quench yields mutual information that decays logarithm...

Show 6 more citing papers

Time Evolution of Entanglement Entropy from Black Hole Interiors
hep-th 2013-03 accept novelty 6.0 of 10

Entanglement entropy in a holographic CFT grows linearly in time at a rate set by the maximum of a geometric quantity in the black hole interior, and the 2d bulk and boundary computations match exactly.
Comments on quantum gravity and entanglement
hep-th 2009-07 conditional novelty 6.0 of 10

Connected spacetime emerges from quantum entanglement: dial the entanglement between two regions toward zero and the geometry between them pinches off into two disconnected pieces.
On the Time Evolution of Holographic n-partite Information
hep-th 2014-06 conditional novelty 5.0 of 10

For n parallel strips with small separation, the holographic n-partite information reduces to a three-entropy combination and is argued, numerically and structurally, to be positive for even n and negative for odd n t...
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 and conformal field theory
cond-mat.stat-mech 2009-05 accept novelty 2.0 of 10

Conformal field theory fixes the universal scaling of entanglement entropy in one-dimensional critical systems, with the central charge setting the logarithmic coefficient.
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

27 arXiv papers cite this in 35 sentences

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Papers citing it · 25 sentences without a confident label

Contests it 1 paper

However in [ref] the linear combination that gives the entanglement entropy undergoes a phase transition thus the derivation is flawed.], i.e. [equation] Where the coefficients are constants that are independent from the choice of the partition.

Entanglement contour and modular flow from subset entanglement entropies · The partial entanglement entropy proposal · contest 0.92

Cites it as background 9 papers

For example, there have been studies in the ground state [ref] , in thermal (black hole) states [ref] and in some time-dependent situations corresponding to global quenches [ref] .

Mutual information after a local quench in conformal field theory · Introduction · 0.95
In the context of the holographic correspondence, the case of disjoint regions has been addressed in [ref] .

Holographic entanglement entropy: near horizon geometry and disconnected regions · Introduction · 0.88
Recently there have been discussions of different generalizations of the Eq. [ref] in application to the entanglement entropy for disconnected regions [ref] that still respect the strong sub-additivity condition.

Minimal surfaces and entanglement entropy in anti-de Sitter space · Entanglement entropy and minimal surfaces · 0.83

What it cites · 31 sentences without a confident label

Contests 1 paper

We have noted in disconnectd that while [ref] propose a far simpler expression for the entanglement entropy of a region bounded by two curves (namely cases (a) and (c) of twoDregions), involving only the three naturally defined minimal surfaces, this doesn't seem to reduce to the requisite result for the infinite strip case.

AdS/CFT and Strong Subadditivity of Entanglement Entropy · Discussion · contest 0.80

Uses the method or tool of 3 papers

By the holographic prescription of [ref] we have

Holographic Derivation of Entanglement Entropy from AdS/CFT · Disconnected regions in $1+1$ dimensional field theories · 0.97
By the holographic prescription of [ref] we have

Aspects of Holographic Entanglement Entropy · Disconnected regions in $1+1$ dimensional field theories · 0.97
The covariant holographic prescription [ref] for computing this is to consider the problem of finding a co-dimension two extremal surface $_$ in the bulk geometry $$ (dual to the state in question), which ends on the boundary of the chosen region $$ at the spacetime boundary $$. $S_$ is then given by the area of $_$ in Planck units , $S_= Area $_$ 4 G_N$.

A Covariant Holographic Entanglement Entropy Proposal · Introduction · 0.88

Compares with 1 paper

We obtain the answer predicted by the field theory analysis of [ref] for CFTs, but now only using geometrical arguments.

Entanglement Entropy and Quantum Field Theory · Introduction · 0.95

Cites as background 7 papers

The technology to compute entanglement entropy is best developed in the case of 1+1 dimensional CFTs [ref] (, [ref] for earlier work and [ref] for generalizations to integrable non-conformal systems).

Form factors of branch-point twist fields in quantum integrable models and entanglement entropy · Introduction · 0.92
The technology to compute entanglement entropy is best developed in the case of 1+1 dimensional CFTs [ref] (, [ref] for earlier work and [ref] for generalizations to integrable non-conformal systems).

Entanglement Entropy and Quantum Field Theory · Introduction · 0.92
The technology to compute entanglement entropy is best developed in the case of 1+1 dimensional CFTs [ref] (, [ref] for earlier work and [ref] for generalizations to integrable non-conformal systems).

Geometric and Renormalized Entropy in Conformal Field Theory · Introduction · 0.92

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