Holographic entanglement entropy is cutoff-covariant

Jonathan Sorce

REVIEW 1 major objections 5 minor 1 cited by

Holographic entanglement entropy is cutoff-covariant

T0 review · 1 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read This paper proves that any two extremal surfaces in an asymptotically AdS spacetime anchored to the same boundary region have identical area divergences under every smooth radial cutoff, and that their finite area difference is…

desk verdict A rigorous proof that the HRT area-difference cutoff is independent, grounded in an explicit smoothness assumption; the physics was assumed, the proofs are new and worth having. read the letter →

arxiv 1908.02297 v2 pith:7TLP6W3W submitted 2019-08-06 hep-th gr-qc

Jonathan Sorce This is my paper · ORCID

classification hep-thgr-qc

keywords holographicentanglemententropyextremalsurfacesAdS/CFTcorrespondencecutoffindependenceconformalinfinityFefferman-Grahamexpansionvacuumsubtractionmutualinformation

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper establishes that radial-cutoff regulation of holographic entanglement entropy is covariant: in an asymptotically AdS spacetime, any two extremal surfaces that approach the same boundary region have identical area divergences for every choice of defining function $z$, and the finite difference between their areas is independent of which defining function is chosen. This makes the "globally minimal surface" rule pick out the same Hubeny-Rangamani-Takayanagi surface in every radial coordinate, so the entanglement wedge of a boundary region is determined by the region itself and not by a choice of regulator. It also guarantees that divergence-cancelling CFT quantities such as mutual information are well-defined under the holographic dictionary. The proof solves the covariant binormal divergence equation order by order in $z$, showing the surface's binormal is fixed by boundary data up to order $z^{d-3}$ and its coordinate position up to order $z^{d-2}$. The paper additionally identifies when vacuum subtraction between different spacetimes is valid: spacetimes obeying the relaxed Fefferman-Graham falloff $R_{ab}=-(d-1)g_{ab}+o(z^{d-5})$ have universal, state-independent divergences.

What carries the argument

The machinery is the covariant characterization of extremality by the vanishing divergence of the unit binormal. A codimension-2 surface $\Sigma$ has a unique unit binormal $N_{ab}$ normalized by $N_{ab}N^{ab}=-2$; $\Sigma$ is extremal iff $\nabla_a N^{ab}|_\Sigma=0$, independent of how $N_{ab}$ is extended off the surface. Writing this equation in coordinates adapted to a defining function $z$, with rescaled binormal $\tilde N^{\mu\nu}=N^{\mu\nu}/z^2$, produces component equations (3.9)--(3.10) that are solved inductively near $z=0$. Lemma 2 supplies the inductive step: the binormal through order $z^n$ fixes the surface's coordinate position through $z^{n+1}$, and that position fixes the tangential binormal at $z^{n+1}$; the induction runs until order $z^{d-3}$, where the coefficient $(d-2-n)$ vanishes. This yields universal divergent structure, and the cutoff-independence of finite differences follows by comparing the area between two cutoff surfaces, where only the divergent terms matter. The equivalence between direct and transported cutoff prescriptions uses the same divergence control plus Stokes' theorem on an extremal foliation, assuming Conjecture 3.

What would settle it

Find an asymptotically AdS spacetime with two candidate extremal surfaces for the same boundary region, regulate their areas with two different defining functions $z$ and $e^{\omega}z$, and check whether the $z_c^0$ term of their area difference is identical; a single case where it changes would falsify the paper's central claim.

Watch

Extended reading notes

Core claim

The central claim is that the finite difference in area between any two extremal surfaces homologous to the same boundary region is cutoff-independent. More precisely, in any asymptotically (locally) AdS spacetime and for any defining function $z$, two extremal surfaces sharing the same boundary anchor have the same divergent area terms under the cutoff $z=z_c$, and the $z_c^0$ term in their area difference does not change when $z$ is replaced by another defining function $e^{\omega}z$. Consequently the "globally minimal surface" among several extremal candidates is well-defined: unless two candidates are exactly degenerate, exactly one candidate has a negative finite area difference with every other candidate, and that ordering is independent of the regulator. The same argument shows that cutting off the boundary-anchored surface directly and instead anchoring an extremal surface to the transported cutoff region give the same finite area differences, subject to Conjecture 3 on the existence of an extremal foliation. Under the relaxed Fefferman-Graham falloff, area divergences are universal across spacetimes, so vacuum-subtracted entanglement entropy is well-defined; spacetimes with slower matter falloff evade this and can have state-dependent divergences.

Load-bearing premise

The proof assumes every boundary-anchored extremal surface is smooth in a neighborhood of the AdS boundary, so that its binormal and coordinate position admit Taylor expansions in the defining function all the way to $z=0$; a caustic, cusp, or other nonsmooth feature would put the universal-divergence and cutoff-independence arguments outside their stated domain.

Editorial extensions

If this is right

The choice of radial coordinate cannot change which extremal surface is globally minimal, so a boundary region's HRT surface and entanglement wedge are determined by the region alone.
Mutual information and conditional mutual information, computed as divergence-cancelling sums of surface areas, are finite and cutoff-independent in every asymptotically AdS spacetime.
Vacuum subtraction is legitimate exactly for spacetimes satisfying the relaxed Fefferman-Graham falloff; in slower-falloff spacetimes the divergences are state-dependent and the vacuum-subtracted entropy remains infinite.
Directly cutting off a boundary-anchored surface and finding a new extremal surface anchored to the transported cutoff region give the same finite area differences, provided Conjecture 3 holds.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Editorial extension: the same order-by-order binormal expansion predicts a practical numerical test: compute HRT surface area differences for a nontrivial boundary region using two independent defining functions; the $z_c^0$ term should agree to all orders, and any disagreement would localize a broken assumption.
Editorial extension: the local, covariant proof should apply to other boundary-anchored extremal objects, such as subleading extremal saddles or entwinement probes, because the divergence control does not require global minimality.
Editorial extension: Conjecture 3, not the main theorem, is the pressure point for the direct-versus-transported equivalence; in dimensions $d\ge 5$ the area difference between the two prescriptions can diverge for a single surface, so a counterexample to the conjecture would make the corollary fail even though the main theorem stands.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Dear colleague,

You should know about this paper because it settles a question most of us had stopped asking: whether the radial cutoff prescription for HRT surface areas is actually coordinate-independent. Sorce proves that two extremal surfaces homologous to the same boundary region have identical area divergences in any defining-function cutoff, and the finite difference between them is cutoff-invariant. That means the 'globally minimal surface' rule is well-posed, and divergence-cancelling quantities like mutual information are well-defined. The literature routinely assumed these facts; the proofs were not there.

What is new is the machinery. The covariant analysis of extremal surfaces in Appendix B, including the k-normal-form divergence condition and four equivalent characterizations of extremality, is a genuinely useful toolkit. Two of those characterizations are presented as original. The generalized Fefferman-Graham theorem in Appendix A, allowing arbitrary matter falloff, is also a clean extension. The paper is honest about what it assumes: smoothness of the extremal surfaces near the boundary, local integrability of the normal bundle, and Conjecture 3 for the equivalence of two cutoff recipes. The central claims do not rely on Conjecture 3.

The stress-test concern lands, but only partly. The induction in Section 3.1 requires the surface to admit a Taylor expansion in the defining function all the way to the boundary. If an extremal surface develops a caustic or cusp near the boundary, the proof does not apply. The paper states this assumption explicitly in Section 1 but does not prove that HRT surfaces always satisfy it. So the main theorem is conditional on a regularity premise. That is a genuine scope limitation, but it is explicit and it matches assumptions used broadly in the literature. The reader's CONDITIONAL verdict is right; this is not a hidden flaw, just a clearly marked boundary of the result.

The secondary equivalence between 'direct' and 'transported' cutoffs depends on Conjecture 3, which is labeled as a conjecture and used only for that corollary. If you care about the main result, you can ignore it.

Overall: this is a solid, careful paper that deserves a serious referee. The physics was assumed, but the rigorous cleanup is exactly what the holographic entanglement literature needs. I would cite it in my own work on cutoff dependence, and I would bring it to a reading group that cares about the foundations of HRT. Send it to peer review; the referee should check the induction and the Appendix B identities, and should probe the smoothness assumption. Not a desk reject.

Referee Report

1 major / 5 minor

Summary. This paper gives a careful treatment of radial cutoffs for holographic entanglement entropy in asymptotically AdS spacetimes. The author introduces a notion of cutoff based on arbitrary defining functions and proves, under stated smoothness and normal-bundle integrability assumptions, that any two extremal surfaces anchored to the same boundary region have identical area divergences and that the finite difference of their regulated areas is independent of the choice of defining function. The main consequences are that the "globally minimal surface" prescription for the HRT surface is regulator-independent and that divergence-cancelling combinations such as mutual information are well defined. The paper also analyzes vacuum subtraction under a relaxed Fefferman-Graham falloff and, subject to Conjecture 3, argues that direct and transported cutoff prescriptions give the same finite area differences. Appendices provide a generalized Fefferman-Graham expansion and a covariant toolkit for extremal surfaces based on the divergence of the unit binormal.

Significance. If the central result holds, it fills a real gap in the holographic literature: the cutoff-independence of HRT areas is frequently assumed but, to my knowledge, has not been proved at this level of detail. The paper's main technical contribution, the order-by-order solution of the binormal divergence equation in Section 3.1, is original and carefully executed, and the covariant formalism in Appendix B is clean and likely to be useful beyond this application. The paper is also transparent about its scope: the smoothness assumption, the local integrability of the normal bundle, and Conjecture 3 are all stated explicitly. The weakness is that the central theorem is conditional on a regularity premise that is not proved or cited, while the title and abstract advertise the unconditional statement. This is a scope issue rather than a circularity or internal-inconsistency issue; the paper does not assume the result it proves.

major comments (1)

[Section 1 and Section 3.1 (Lemma 2, Eqs. (3.13)–(3.16))] The central theorem is conditional on the smoothness assumption stated in Section 1, but the title and abstract assert cutoff covariance without that qualifier. The induction proving universality of the binormal up to order z^{d-3} requires f1, f2, and ~N^{\mu\nu} to admit Taylor expansions in the defining function z; Lemma 2 uses this expansion at every order, and the same regularity is needed for the area integrals in Section 3.2. The paper neither proves nor cites a regularity theorem ensuring that extremal surfaces anchored on a smooth boundary region are smooth in a neighborhood of the AdS boundary. Please either prove or cite such a regularity result, or reformulate the main theorem and the abstract as applying to smooth extremal surfaces and explicitly state that non-smooth surfaces are outside the scope of the proof. This is the main obstacle to an unconditional version of the claimed result.

minor comments (5)

[Section 3.2, text after Eq. (3.38)] There is a typo: the coordinate range should be x3, ..., x_{d-1}, not x_{d1}.
[Section 3.1, Eq. (3.28) and surrounding text] The notation N_{\mu\nu} = z^2 N_{\mu\nu} reuses the symbol N for the smooth down-index binormal; this is confusing because N already denotes the physical binormal. Please use a different symbol, e.g. \tilde N_{\mu\nu}, for the rescaled down-index object.
[Section 3.2, Conjecture 3 and Eqs. (3.40)–(3.42)] The equivalence of the direct and transported cutoff prescriptions depends on unproved Conjecture 3 and is not a theorem. The sentence "we conclude that these two prescriptions give equivalent answers" should be preceded by an explicit conditional clause, e.g. "Assuming Conjecture 3, we conclude...", so that the conjecture-dependence of this corollary is not lost on the reader.
[Section 3.2, discussion of the cutoff change] The argument that the change in the finite piece under a change of defining function is determined by divergent terms is correct, but it would be clearer to point out explicitly that the coefficient of the z^{-1} term in the integrand of Eq. (3.38) is universal by the results of Section 3.1, and that this coefficient is the only source of a finite change in the finite piece. Adding one sentence would make the logic of the cutoff-independence proof easier to follow.
[Section 1, footnote 12] The proof is formulated locally in coordinates where x1 and x2 are non-tangent to the extremal surface, and the paper states that the argument can be patched over an open cover of the entangling surface. Since this patching is invoked but suppressed, a brief remark in the main text describing how the local results combine would strengthen the rigor of the presentation.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the cutoff-covariance theorem is derived from the covariant extremality condition and explicit asymptotic expansions, with no fitted parameters or load-bearing self-citations.

full rationale

The paper's central claim is that homologous extremal surfaces have identical area divergences and cutoff-independent finite area differences. This is derived rather than assumed: Section 3.1 starts from the covariant extremality condition ∇_a N^{ab}|_Σ=0, rewrites it in coordinates adapted to an arbitrary defining function, and solves Eq. (3.16) order-by-order using Lemma 2, whose proof uses only the geometry of the normal bundle and the explicit expression (3.26) for the binormal in terms of surface gradients. Boundary data, namely the position of the entangling surface ∂Σ, is the input, while universality of the binormal and of the divergent area terms is the output. The transition from identical divergences to cutoff independence in Section 3.2 computes the area between two regulating surfaces under z=e^ω z' and invokes the already-proved universality of divergent terms; it does not presuppose the invariance of the finite difference. The 'globally minimal surface' and mutual-information claims are corollaries of that proven invariance. The direct-versus-transported cutoff equivalence is explicitly made conditional on Conjecture 3, which is presented as a conjecture rather than imported as an established theorem. Assumptions such as smoothness of the surface and local integrability of the normal bundle are stated transparently as regularity premises; Appendix B explains how the latter can be relaxed. External citations, including Fefferman-Graham, Graham-Lee, and Marolf-Wall, are standard mathematical or context-setting references, none of which is a self-citation of the author or a substitute for the derivation. No quantity is fitted, no known result is renamed, and no load-bearing step reduces by construction to its own input.

Assumptions & free parameters 0 free parameters · 6 assumptions · 0 invented entities

No free parameters are fitted to data. The derivations rest on standard AdS asymptotics, the HRT dictionary, and explicit regularity and existence assumptions. Conjecture 3 is an unproved assumption used only for the secondary corollary.

assumptions (6)

domain assumption The HRT prescription S(A) = ext Area(Σ)/(4G_N) over homologous extremal surfaces correctly computes CFT entanglement entropy.
The paper regulates quantities defined by this formula; it does not derive the formula.
domain assumption Boundary-anchored extremal surfaces are smooth near the AdS boundary and their normal bundles are locally integrable.
Section 1: 'We will also assume throughout...' This is needed for the order-by-order expansion of the binormal. The integrability part is stated to be relaxable in Appendix B.
domain assumption Existence of extremal surfaces homologous to the relevant boundary regions is assumed; the paper defers this to cited literature.
Section 1 explicitly says the question of existence is not addressed and cites Refs. [10-14]. Without existence, the selection rule is empty.
ad hoc to paper Conjecture 3 holds: a smooth foliation of extremal surfaces interpolates between each boundary-anchored surface and its cutoff-anchored counterpart.
Section 3.2 formulates this as an unproved conjecture and assumes it; used only for the equivalence of the two cutoff prescriptions, not for the two main abstract claims.
domain assumption Theorem 4 applies only to spacetimes satisfying the relaxed Fefferman-Graham falloff Rab = -(d-1)gab + o(z^{d-5}), with a fixed conformal boundary representative and its unique special defining function.
Section 3.3; the vacuum subtraction theorem is conditional on this falloff.
standard math The bulk metric admits a conformal infinity with defining functions and the asymptotic form (2.7)/(3.8).
Standard asymptotically AdS and Fefferman-Graham background, used throughout Section 3.1.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Holographic entanglement entropy is cutoff-covariant." pith.science (2026). https://pith.science/paper/7TLP6W3W

@misc{pith2026190802297,
  author       = {Pith},
  title        = {Pith review of: Holographic entanglement entropy is cutoff-covariant},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7TLP6W3W}},
  note         = {Machine review of arXiv:1908.02297}
}

read the original abstract

In the AdS/CFT correspondence, it is often convenient to regulate infinite quantities in asymptotically anti-de Sitter spacetimes by introducing a sharp cutoff in a radial coordinate. This procedure is a priori coordinate-dependent, and may not be well-motivated in full, covariant general relativity; however, the fact that physically meaningful quantities such as the entanglement entropy can be obtained by such a regulation procedure suggests some underlying covariance. In this paper, we provide a careful treatment of the radial cutoff procedure for computing holographic entanglement entropy in asymptotically anti-de Sitter spacetimes. We prove two results that are frequently assumed in the literature, but that have not been carefully addressed: (i) that the choice of a "globally minimal surface" among several extremal candidates is independent of the choice of regulator, and (ii) that finite CFT quantities such as the mutual information which involve "divergence-cancelling" sums of holographic entanglement entropies are well-defined. Our results imply that the "globally minimal surface" prescription for computing holographic entanglement entropy is well-posed from the perspective of general relativity, and thus support the belief that this is the correct prescription for identifying the entanglement wedge of a boundary subregion in AdS/CFT. We also comment on the geometric source of state-dependent divergences in the holographic entanglement entropy, and identify precisely the regime of validity of the "vacuum subtraction" protocol for regulating infinite entanglement entropies in arbitrary states by comparing them to the entanglement entropies of identical regions in the vacuum. Our proofs make use of novel techniques for the covariant analysis of extremal surfaces, which are explained in detail and may find use more broadly in the study of holographic entanglement entropy.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

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

Holography in the linearized quantum gravity regime and modular crossed product
hep-th 2026-07 conditional novelty 6.0 of 10

At linearized order, the vacuum-subtracted HRT entropy of a boundary region is the entropy of a coherent graviton state in the modular crossed-product algebra of the dual CFT, assuming a wedge-reconstructing holographic map.

Reference graph

Works this paper leans on

32 extracted references · 7 canonical work pages · cited by 1 Pith paper

[1]

Ryu and T

S. Ryu and T. Takayanagi, Aspects of holographic entanglement entropy , JHEP 2006 (2006) 045 [ hep-th/0605073]

arXiv 2006
[2]

V. E. Hubeny, M. Rangamani and T. Takayanagi, A covariant holographic entanglement entropy proposal, JHEP 2007 (2007) 062 [ 0705.0016]

arXiv 2007
[3]

Lewkowycz and J

A. Lewkowycz and J. Maldacena, Generalized gravitational entropy , JHEP 2013 (2013) 90 [1304.4926]

arXiv 2013
[4]

X. Dong, A. Lewkowycz and M. Rangamani, Deriving covariant holographic entanglement , JHEP 2016 (2016) 28 [ 1607.07506]

arXiv 2016
[5]

X. Dong, D. Harlow and A. C. Wall, Reconstruction of bulk operators within the entanglement wedge in gauge-gravity duality , Phys. Rev. Lett. 117 (2016) 021601 [ 1601.05416]

arXiv 2016
[6]

Cotler, P

J. Cotler, P. Hayden, G. Penington, G. Salton, B. Swingle and M. Walter, Entanglement wedge reconstruction via universal recovery channels , 1704.05839

arXiv
[7]

G. T. Horowitz and R. C. Myers, The AdS/CFT correspondence and a new positive energy conjecture for general relativity , Phys. Rev. D 59 (2006) 026005 [ hep-th/9808079]

arXiv 2006
[8]

Marolf and A

D. Marolf and A. C. Wall, State-dependent divergences in the entanglement entropy , JHEP 2016 (2016) 109 [ 1607.01246]

arXiv 2016

Show all 32 references

[9]

R. M. Wald, General Relativity. University of Chicago Press, 1984

1984
[10]

Anderson, Complete minimal varieties in hyperbolic space , Invent

M. Anderson, Complete minimal varieties in hyperbolic space , Invent. Math 69 (1982) 477

1982
[11]

Anderson, Complete minimal hypersurfaces in hyperbolic n-manifolds, Comment

M. Anderson, Complete minimal hypersurfaces in hyperbolic n-manifolds, Comment. Math. Helv. 58 (264) 1983

1983
[12]

Tonegawa, Existence and regularity of constant mean curvature hypersurfa ces in hyperbolic space, Math

Y. Tonegawa, Existence and regularity of constant mean curvature hypersurfa ces in hyperbolic space, Math. Z. 221 (1996) 591. – 40 –

1996
[13]

A. C. Wall, Maximin surfaces, and the strong subadditivity of the covaria nt holographic entanglement entropy , Class. Quant. Grav. 31 (2014) 225007 [ 1211.3494]

2014 arXiv
[14]

Marolf, A

D. Marolf, A. C. Wall and Z. Wang, Restricted Maximin surfaces and HRT in generic black hole spacetimes, JHEP 2019 (2019) 127 [ 1901.03879]

2019 arXiv
[15]

Feﬀerman and C

C. Feﬀerman and C. R. Graham, Conformal invariants , in Élie Cartan et les mathématiques d’aujourd’hui, (Lyon), pp. 95–116, (1984)

1984
[16]

C. R. Graham and J. M. Lee, Einstein metrics with prescribed conformal inﬁnity on the ball , Adv. in Math. 87 (1991) 186

1991
[17]

C. R. Graham and E. Witten, Conformal anomaly of submanifold observables in AdS/CFT correspondence, Nucl. Phys. B 546 (1999) 52 [ hep-th/9901021]

1999 arXiv
[18]

Feﬀerman and C

C. Feﬀerman and C. R. Graham, The ambient metric , 0710.0919

arXiv
[19]

Headrick, V

M. Headrick, V. E. Hubeny, A. Lawrence and M. Rangamani, Causality & holographic entanglement entropy , JHEP 2014 (2014) 162 [ 1408.6300]

2014 arXiv
[20]

D. D. Blanco, H. Casini, L.-Y. Hung and R. C. Myers, Relative entropy and holography , JHEP 2013 (2013) 60 [ 1305.3182]

2013 arXiv
[21]

J. M. Maldacena, Wilson loops in large N ﬁeld theories , Phys. Rev. Lett. 80 (1998) 4859 [hep-th/9803002]

1998 arXiv
[22]

Balasubramanian, B

V. Balasubramanian, B. D. Chowdhury, B. Czech and J. de B oer, Entwinement and the emergence of spacetime, JHEP 2015 (2015) 48 [ 1406.5859]

2015 arXiv
[23]

Bousso, Z

R. Bousso, Z. Fisher, S. Leichenauer and A. C. Wall, Quantum focusing conjecture , Phys. Rev. D 93 (2016) 064044 [ 1506.02669]

2016 arXiv
[24]

Bousso, Z

R. Bousso, Z. Fisher, J. Koeller, S. Leichenauer and A. C . Wall, Proof of the quantum null energy condition, Phys. Rev. D 93 (2016) 024017 [ 1509.02542]

2016 arXiv
[25]

Koeller and S

J. Koeller and S. Leichenauer, Holographic proof of the quantum null energy condition , Phys. Rev. D 94 (2016) 024026 [ 1512.06109]

2016 arXiv
[26]

Akers, J

C. Akers, J. Koeller, S. Leichenauer and A. Levine, Geometric constraints from subregion duality beyond the classical regime , 1610.08968

arXiv
[27]

Balakrishnan, T

S. Balakrishnan, T. Faulkner, Z. U. Khandker and H. Wang , A general proof of the quantum null energy condition , 1706.09432

arXiv
[28]

Akers, V

C. Akers, V. Chandrasekaran, S. Leichenauer, A. Levine and A. S. Moghaddam, The quantum null energy condition, entanglement wedge nesting , and quantum focusing , 1706.04183

arXiv
[29]

Ceyhan and T

F. Ceyhan and T. Faulkner, Recovering the QNEC from the ANEC , 1812.04683

arXiv
[30]

Ishibashi and R

A. Ishibashi and R. M. Wald, Dynamics in non-globally-hyperbolic static spacetimes III: Anti-de Sitter spacetime , Class. Quant. Grav 21 (2004) 2981 [ hep-th/0402184]

2004 arXiv
[31]

A. J. Speranza, Geometrical tools for embedding ﬁelds, submanifolds, and fo liations, 1904.08012

1904 arXiv
[32]

Bakhmatov, N

I. Bakhmatov, N. Deger, J. Gutowski, E. Ó Colgáin and H. Y avartanoo, Calibrated entanglement entropy , JHEP 2017 (2017) 117 [ 1705.08319]. – 41 –

2017 arXiv

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

Ryu and T

S. Ryu and T. Takayanagi, Aspects of holographic entanglement entropy , JHEP 2006 (2006) 045 [ hep-th/0605073]

arXiv 2006

[2] [2]

V. E. Hubeny, M. Rangamani and T. Takayanagi, A covariant holographic entanglement entropy proposal, JHEP 2007 (2007) 062 [ 0705.0016]

arXiv 2007

[3] [3]

Lewkowycz and J

A. Lewkowycz and J. Maldacena, Generalized gravitational entropy , JHEP 2013 (2013) 90 [1304.4926]

arXiv 2013

[4] [4]

X. Dong, A. Lewkowycz and M. Rangamani, Deriving covariant holographic entanglement , JHEP 2016 (2016) 28 [ 1607.07506]

arXiv 2016

[5] [5]

X. Dong, D. Harlow and A. C. Wall, Reconstruction of bulk operators within the entanglement wedge in gauge-gravity duality , Phys. Rev. Lett. 117 (2016) 021601 [ 1601.05416]

arXiv 2016

[6] [6]

Cotler, P

J. Cotler, P. Hayden, G. Penington, G. Salton, B. Swingle and M. Walter, Entanglement wedge reconstruction via universal recovery channels , 1704.05839

arXiv

[7] [7]

G. T. Horowitz and R. C. Myers, The AdS/CFT correspondence and a new positive energy conjecture for general relativity , Phys. Rev. D 59 (2006) 026005 [ hep-th/9808079]

arXiv 2006

[8] [8]

Marolf and A

D. Marolf and A. C. Wall, State-dependent divergences in the entanglement entropy , JHEP 2016 (2016) 109 [ 1607.01246]

arXiv 2016