Entanglement Entropy of a Scalar Field in Anti-de Sitter Space

Dimitrios Katsinis; Georgios Pastras; Ioannis Papadimitriou; Konstantinos Boutivas; Nikolaos Tetradis

REVIEW 1 major objections 4 minor 2 cited by

Entanglement Entropy of a Scalar Field in Anti-de Sitter Space

T0 review · 1 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read The paper derives numerically the ultraviolet-divergent entanglement entropy of a free scalar in AdS4 and claims universal logarithmic coefficients -1/90, -1/6, and -1/3.

desk verdict A credible Srednicki-style computation of UV-divergent entanglement entropy in AdS4; the log coefficients are likely right, but the fit precision is overstated and the radius-convention drift needs clarification. read the letter →

arxiv 2505.15980 v1 pith:6KAFFKZ7 submitted 2025-05-21 hep-th gr-qcquant-ph

Konstantinos Boutivas , Dimitrios Katsinis , Ioannis Papadimitriou , Georgios Pastras , Nikolaos Tetradis This is my paper · ORCID

classification hep-thgr-qcquant-ph

keywords entanglemententropyanti-deSitterspacescalarfieldconformalanomalyUVdivergencesarealawPoschl-Tellerpotentialde

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

This paper calculates, numerically, the entanglement entropy of a free massive scalar field in (3+1)-dimensional anti-de Sitter space, for spherical entangling surfaces centered at the origin. It claims that the ultraviolet-divergent part has a specific structure: the area-law term scales as $sin^{2}$(w_R/a)/$epsilon^{2}$, and the logarithmic divergence is controlled by three universal coefficients that depend on mass, curvature, and the conformal anomaly. The reported values are d2=-1/90, d3=-1/6, and d4=-1/3, which match existing flat-space and de Sitter results and the conformal-anomaly expectation. If correct, this establishes that the scheme-independent logarithmic part of the entanglement entropy is fully determined by mass, curvature, and anomaly data, and it sharpens the de Sitter/anti-de Sitter analytic-continuation relation.

What carries the argument

The central objects are the angular-momentum sector decomposition of the scalar field in hyper-spherical harmonics and the resulting one-dimensional Schrodinger problems with trigonometric Poschl-Teller potentials, parameterized by nu = ell + d/2 - 1 and kappa = $\sqrt$($mu^{2}$ $a^{2}$ + $d^{2}$/4). Discretizing the tortoise coordinate w on a chain of harmonic oscillators with Dirichlet endpoint conditions yields a coupling matrix; the ground-state wavefunction gives the entanglement entropy through the correlation-function method. The UV-divergent coefficients are extracted by extrapolating first in angular momentum ell and then in the lattice size N, which acts as the UV cutoff a/epsilon. The Poschl-Teller form is what connects the calculation to the known flat-space and de Sitter results, and the restriction kappa >= 1/2 ensures the discretization endpoint conditions impose Dirichlet boundary conditions.

What would settle it

Recompute the logarithmic coefficient using a genuinely different UV regulator, such as discretizing the radial coordinate r with constant lattice spacing instead of the tortoise coordinate w, or compute the same coefficient analytically through a heat-kernel or conformal-anomaly calculation; if the ln(a/epsilon) coefficient deviates from d3 = -1/6 and d4 = -1/3, or if the finite-N remainder R(n,N) fails to decay as assumed when N is increased substantially, the universality claim fails.

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Extended reading notes

Core claim

The paper claims that for a free scalar field in AdS4 in global coordinates, with a spherical entangling surface at tortoise coordinate w_R, the UV-divergent entanglement entropy is S_AdS = d1/$epsilon^{2}$ $sin^{2}$(w_R/a) + (d2 + (d3 $mu^{2}$ $a^{2}$ + d4) $tan^{2}$(w_R/a)) ln(a/epsilon) + finite, with d1 approximately 0.29543145, d2 = -1/90, d3 = -1/6, and d4 = -1/3, for the mass window kappa >= 1/2. The leading term is regulator-dependent in an extreme way: discretizing the tortoise coordinate w rather than the radial coordinate r multiplies the area contribution by 1/$cos^{2}$(w_R/a), so the proper-area form is recovered only after accounting for the regulator. The logarithmic coefficients are claimed to be regulator-independent and to reproduce three known results: the flat-space A-type conformal anomaly coefficient -1/90, the flat-space massive-field shift -$mu^{2}$/6, and the conformal-coupling cancellation that fixes -1/3, with the de Sitter coefficient +1/3 related by analytic continuation.

Load-bearing premise

The result rests on the assumption that the finite-N numerical data are exactly described by the expansion S_infinity = ($a^{2}$/$epsilon^{2}$) S^(2) + S_l^(0) ln(a/epsilon) + S^(0) + R, with S_l^(0) = a_l + b_l $tan^{2}$(w_R/a) and b_l = d3 $mu^{2}$ $a^{2}$ + d4; if the true continuum limit contains subleading terms that mimic these functional forms at the N values used, the fitted coefficients d2, d3, and d4 would be biased.

Editorial extensions

If this is right

For entangling radii much smaller than the AdS length, the entropy reduces to the flat-space sphere result: d1 matches the area-law coefficient and d2 = -1/90 reproduces the A-type conformal anomaly.
The mass dependence of the logarithmic divergence in AdS is the same as in flat space, with d3 = -1/6, so a massive scalar acquires the same mu^2 correction to the log term as in Minkowski space.
For a conformally coupled scalar with mu^2 a^2 = -2, the d3 and d4 contributions cancel, leaving only d2 = -1/90, which enforces the conformal-anomaly prediction in a curved background.
The de Sitter coefficient c4 = 1/3 and the AdS coefficient d4 = -1/3 are opposite in sign, exactly as required by the analytic continuation H^2 to -1/a^2, giving a quantitative dS/AdS dictionary for entanglement entropy.
The leading 1/epsilon^2 term is regulator-dependent: discretizing w instead of r changes its coefficient by 1/cos^2(w_R/a), so only the logarithmic coefficients are universal in this calculation.

Reading between the lines

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

A natural next target is the finite part S^(0)(n, mu^2 a^2), which the paper could not determine; with a structural ansatz, the same numerical machinery might extract curvature- and mass-dependent finite terms that probe the F-type anomaly or the dS/AdS relation.
Because the endpoint conditions used in the discretization do not select a unique self-adjoint extension in the window 0 <= kappa < 1/2, the entanglement entropy in that mass window may depend on the choice of boundary condition, turning entanglement entropy into a probe of boundary-condition dependence.
Applying the same method to de Sitter space in static rather than planar coordinates would test whether the global-AdS and static-dS results are direct analytic continuations, confirming that c4 = 1/3 and d4 = -1/3 are the same universal quantity seen from two foliations.
The regulator dependence of the leading term suggests that comparisons of area-law coefficients across curved spacetimes require fixing a common discretization convention; only the logarithmic terms can be compared unambiguously without such a convention.

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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

Bottom line: this is a solid numerical paper that almost certainly gets the right answer, but the precision claims outrun the evidence. The genuinely new piece is the AdS4 global-coordinate version of Srednicki's harmonic-chain calculation for a massive scalar, with a mass-dependent logarithmic coefficient d3 = -1/6 and the conformal-anomaly coefficient d4 = -1/3. That result is not in the prior literature, and the dS-to-AdS analytic continuation plus the flat-space and Hertzberg-Wilczek checks make it very plausible.

What the paper does well: the treatment of boundary conditions is careful and sophisticated. The discussion of self-adjoint extensions, the BF bound, and the restriction to κ≥1/2 is exactly the kind of analysis this problem needs. The numerical work uses 128-bit precision, and the eigenfunction comparison in Fig. 2 is reassuring. The cross-checks—flat-space limit for small radius, conformal anomaly for d4, dS comparison—are the right checks and they all line up.

The soft spots are real but not fatal. First, there are no error bars, residuals, or stability tests anywhere. Claiming 0.1% accuracy on d2, d3, d4 with no stated uncertainty is not supportable. Second, and more specifically, the radius convention is ambiguous. Equation (2.47) defines w_R/a = (π/2)(n+1/2)/(N+1), but the data selection n=(k+1)j with N=49+50k gives w_R/a = πj/100 + π/[200(k+1)], so the physical radius drifts by O(1/N) across the N values used in the extrapolation. If that drift is not accounted for, it injects a 1/ϵ term into S∞ that is absent from the ansatz (3.6)-(3.7), and that can bias the log coefficient. The paper needs to state the exact convention, show the drift is either absent or included in the fit, and demonstrate that the log coefficient is stable under that choice. Third, the completeness of the ansatz (3.6)-(3.7) is assumed; there is no control of the remainder or discussion of why no 1/ϵ term appears. The d1 area term is regulator-dependent and the 1/cos^2 argument is heuristic, though the paper is honest about that.

Who is this for? People computing entanglement entropy in curved space, especially those doing Srednicki-style numerics. It is not a holography paper; the connection to Ryu-Takayanagi is explicitly out of scope. The result deserves a serious referee, and I would send it to JHEP, but only after a revision that adds error analysis, clarifies the radius convention, and ideally releases the code and data. As it stands, it is a conditional accept, not a clean accept.

Referee Report

1 major / 4 minor

Summary. The paper computes the entanglement entropy of a free, minimally coupled scalar field in (3+1)-dimensional anti-de Sitter space in global coordinates, using the discretization method of Srednicki. For spherical entangling surfaces centered at the origin, the authors numerically extract the coefficients of the UV-divergent terms and propose the expression S_AdS = d1/epsilon^2 sin^2(w_R/a) + (d2 + d3 mu^2 a^2 + d4) tan^2(w_R/a) ln(a/epsilon) + finite, with d1 approximately 0.29543145, d2 = -1/90, d3 = -1/6, and d4 = -1/3 (Eqs. (3.9), (3.13), and (4.1)). The paper argues that the logarithmic coefficients are universal, consistent with the conformal-anomaly result and with flat-space massive and massless results, and that the dS/AdS analytic continuation relates the coefficient d4 in AdS to the corresponding coefficient c4 in de Sitter space.

Significance. If the numerical results are correct, the paper provides a concrete, non-holographic computation of the universal logarithmic entanglement-entropy coefficients for a scalar field in AdS4, confirming the conformal-anomaly connection in a curved background and complementing the earlier de Sitter analysis by the same group. The technical reduction of the problem to a set of one-dimensional Pöschl-Teller sectors is a useful framework that could be extended to other entangling surfaces and boundary conditions. However, the central coefficients are obtained through a chain of fits without reported uncertainties or residuals, and the mapping from the discrete subsystem to the continuum entangling radius is ambiguous; these issues currently limit the strength of the claimed 0.1% accuracy.

major comments (1)

[Section 3.2, Eqs. (3.8)-(3.9)] The leading coefficient d1 = 0.29543145 is quoted without an uncertainty or a goodness-of-fit measure. The claim that the functional form S^(2) = d1 sin^2(w_R/a) holds for all masses and all w_R is qualitative, as Fig. 4 shows no residuals. Since the paper acknowledges in Section 4 that the relation of this term to the proper area requires a heuristic 1/cos^2(w_R/a) factor, and since the value is compared with the flat-space coefficient only in the limit w_R << a, the reader cannot assess how precisely d1 is determined. Please provide a residual plot and a quantitative comparison with the flat-space coefficient.

minor comments (4)

[Section 2.1, below Eq. (2.10)] The surface term in the displayed action is written with 'a sin 2w/a' as the denominator; please clarify the intended parentheses, presumably a sin(2w/a).
[Section 3.2, Fig. 6 caption] The right panel is labeled with -b_l rather than b_l, so the reader must infer the sign of the fitted intercept; please state the fitted functions explicitly in the caption.
[Section 4, conformal coupling paragraph] The sentence 'the conformal theory would arise through a coupling R phi^2/6 of the field to gravity, which results in an effective mass term mu^2 = -2/a^2' is confusing, because with R = -12/a^2 and xi = 1/6 the effective mass is mu^2_eff = mu^2 + 2/a^2, so the parameter mu^2 = -2/a^2 corresponds to a vanishing effective mass; please rephrase for clarity.
[Section 3.1, paragraph on data selection] The statement that the entangling surfaces 'have the same physical radius for all N' is inconsistent with Eq. (2.47), as detailed in major comment 1; the text should be corrected to remove this inconsistency regardless of the convention ultimately adopted.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central coefficients are numerical fits checked against independent external results, not predictions forced by the same inputs.

full rationale

Walking the derivation chain: the paper discretizes the AdS scalar Hamiltonian, computes each angular-momentum sector contribution S_ell via (2.44), sums over ell using the extrapolation (3.4), expands S_infinity according to (3.6), and fits S^(2) and S_l^(0) to the functional forms (3.8), (3.10)-(3.12). The quoted coefficients d1, d2, d3, and d4 are outputs of those numerical fits ('obtained by a numerical fit', 'determined with an accuracy of 0.1%'), not quantities predicted from a separately fitted subset of the same data. No step exhibits an equation reducing an output to an input by construction. The Section 4 argument that 'fixes' d4 = -1/3 is a consistency check: given the fitted d2 = -1/90 and d3 = -1/6, requiring the conformal mass mu^2 a^2 = -2 to reproduce the A-type conformal-anomaly coefficient -1/90 forces d4 = -1/3. The paper explicitly says this value 'is in agreement with our result,' so it is an independent constraint checked against the fit, not the origin of the fitted value. The self-citations [9,10,27,28] are methodological (ell_max extrapolation strategy, correlation-function equivalence, and dS comparison) and are not load-bearing for the central AdS claim; the external benchmarks [4-7,30] are independent of the paper's fitted values. The ansatz (3.6)-(3.7) and the radius-label convention (2.47) with the n=(k+1)j selection are potential numerical-accuracy concerns, but they are modeling assumptions rather than circular reductions. Therefore the paper shows no significant circularity.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central claim rests on four fitted numerical coefficients. The axioms are mostly domain assumptions about the regulator and the vacuum, plus standard prior results used for comparison. No new entities are introduced.

free parameters (4)

d1 = 0.29543145
Coefficient of the leading 1/epsilon^2 term, fit as S^(2) = d1 sin^2(w_R/a); regulator dependent.
d2 = -1/90
Constant part of the logarithmic coefficient, fit as a_l(mu^2 a^2) = constant; matches flat-space coefficient.
d3 = -1/6
Mass coefficient of the logarithmic term, fit as the slope of b_l versus mu^2 a^2, reported as -1/6.0004.
d4 = -1/3
Curvature coefficient of the logarithmic term, fit as the intercept -1/3.0003; also expected from conformal anomaly cancellation.

assumptions (5)

domain assumption The ground state of the free scalar in AdS4 with Dirichlet boundary conditions is the physical vacuum for kappa >= 1/2.
The calculation restricts to kappa >= 1/2 to avoid fixing self-adjoint extensions; Sections 2.1 and 2.2.
domain assumption Uniform discretization of the tortoise coordinate w with endpoint conditions (2.39) is a valid regulator whose continuum limit gives the field-theory entanglement entropy.
Section 2.2, eqs. (2.36)-(2.42). The paper shows eigenfunction agreement, but the regulator's effect on divergences is scheme dependent.
ad hoc to paper The large-N and large-ell extrapolation ansatze (3.4)-(3.7) capture the continuum and infinite-sum limits.
Section 3.1. The fit forms are assumed, not derived.
domain assumption The relation w_R/a = pi/2 (n + 1/2)/(N + 1) locates the entangling surface in the continuum.
Section 2.3, eq. (2.47).
standard math The conformal anomaly results of Solodukhin and the flat-space massive result of Hertzberg and Wilczek are correct prior inputs.
Used in Section 4 to interpret d2, d3, and d4; cited refs [4] and [30].

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Pith. "Pith review of Entanglement Entropy of a Scalar Field in Anti-de Sitter Space." pith.science (2026). https://pith.science/paper/6KAFFKZ7

@misc{pith2026250515980,
  author       = {Pith},
  title        = {Pith review of: Entanglement Entropy of a Scalar Field in Anti-de Sitter Space},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6KAFFKZ7}},
  note         = {Machine review of arXiv:2505.15980}
}

read the original abstract

We study the entanglement entropy of a free massive scalar field at its ground state in (3+1)-dimensional AdS space in global coordinates. We consider spherical entangling surfaces centered at the origin of AdS. We determine the structure of the UV-divergent terms in the entanglement entropy and compute the numerical values of the respective coefficients. We confirm the connection between the coefficient of the logarithmic term and the conformal anomaly.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

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

Boundary Conditions and Entanglement in Anti-de Sitter Space
hep-th 2026-08 conditional novelty 6.0 of 10

For a conformally coupled scalar in AdS4, the UV-divergent entanglement entropy is independent of boundary conditions, while the UV-finite part acquires a boundary-condition dependent R^2/a^2 correction with coefficie...
Entanglement on a Sphere
hep-th 2025-07 conditional novelty 6.0 of 10

The entanglement entropy of a scalar field on the R×S^3 Einstein universe has an infrared contribution from the zero mode with coefficient c_IR = 1/6, distinct from the de Sitter value 1/3.

Reference graph

Works this paper leans on

30 extracted references · 3 canonical work pages · cited by 2 Pith papers

[1]

Sorkin,1983 paper on entanglement entropy: ”On the Entropy of the Vacuum outside a Horizon”, in10th International Conference on General Relativity and Gravitation, vol

R.D. Sorkin,1983 paper on entanglement entropy: ”On the Entropy of the Vacuum outside a Horizon”, in10th International Conference on General Relativity and Gravitation, vol. 2, pp. 734–736, 1984 [1402.3589]

arXiv 1983
[2]

Bombelli, R.K

L. Bombelli, R.K. Koul, J. Lee and R.D. Sorkin,A Quantum Source of Entropy for Black Holes,Phys. Rev. D34(1986) 373

1986
[3]

Srednicki,Entropy and area,Phys

M. Srednicki,Entropy and area,Phys. Rev. Lett.71(1993) 666 [hep-th/9303048]

arXiv 1993
[4]

Solodukhin,Entanglement entropy, conformal invariance and extrinsic geometry,Phys

S.N. Solodukhin,Entanglement entropy, conformal invariance and extrinsic geometry,Phys. Lett. B665(2008) 305 [0802.3117]

arXiv 2008
[5]

Casini and M

H. Casini and M. Huerta,Entanglement entropy for the n-sphere,Phys. Lett. B694(2011) 167 [1007.1813]

arXiv 2011
[6]

Casini and M

H. Casini and M. Huerta,Entanglement entropy in free quantum field theory,J. Phys. A42 (2009) 504007 [0905.2562]

arXiv 2009
[7]

Lohmayer, H

R. Lohmayer, H. Neuberger, A. Schwimmer and S. Theisen,Numerical determination of entanglement entropy for a sphere,Phys. Lett. B685(2010) 222 [0911.4283]

arXiv 2010
[8]

Maldacena and G.L

J. Maldacena and G.L. Pimentel,Entanglement entropy in de Sitter space,JHEP02(2013) 038 [1210.7244]

arXiv 2013

Show all 30 references

[9]

Boutivas, D

K. Boutivas, D. Katsinis, G. Pastras and N. Tetradis,Entanglement Entropy as a Probe Beyond the Horizon,2407.07824

arXiv
[10]

Boutivas, D

K. Boutivas, D. Katsinis, G. Pastras and N. Tetradis,Numerical calculation of entanglement entropy in de Sitter space,Phys. Rev. D111(2025) 065010 [2407.07811]

2025 arXiv
[11]

Page,Average entropy of a subsystem,Phys

D.N. Page,Average entropy of a subsystem,Phys. Rev. Lett.71(1993) 1291 [gr-qc/9305007]

1993 arXiv
[12]

Ryu and T

S. Ryu and T. Takayanagi,Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett.96(2006) 181602 [hep-th/0603001]

2006 arXiv
[13]

Ryu and T

S. Ryu and T. Takayanagi,Aspects of Holographic Entanglement Entropy,JHEP08(2006) 045 [hep-th/0605073]

2006 arXiv
[14]

Sugishita,Entanglement entropy for free scalar fields in AdS,JHEP09(2016) 128 [1608.00305]

S. Sugishita,Entanglement entropy for free scalar fields in AdS,JHEP09(2016) 128 [1608.00305]. – 21 –

2016 arXiv
[15]

Breitenlohner and D.Z

P. Breitenlohner and D.Z. Freedman,Positive Energy in anti-De Sitter Backgrounds and Gauged Extended Supergravity,Phys. Lett. B115(1982) 197

1982
[16]

Breitenlohner and D.Z

P. Breitenlohner and D.Z. Freedman,Stability in Gauged Extended Supergravity,Annals Phys.144(1982) 249

1982
[17]

de Haro, S.N

S. de Haro, S.N. Solodukhin and K. Skenderis,Holographic reconstruction of space-time and renormalization in the AdS / CFT correspondence,Commun. Math. Phys.217(2001) 595 [hep-th/0002230]

2001 arXiv
[18]

Skenderis,Lecture notes on holographic renormalization,Class

K. Skenderis,Lecture notes on holographic renormalization,Class. Quant. Grav.19(2002) 5849 [hep-th/0209067]

2002 arXiv
[19]

Papadimitriou and K

I. Papadimitriou and K. Skenderis,AdS / CFT correspondence and geometry,IRMA Lect. Math. Theor. Phys.8(2005) 73 [hep-th/0404176]

2005 arXiv
[20]

Papadimitriou,Lectures on Holographic Renormalization,Springer Proc

I. Papadimitriou,Lectures on Holographic Renormalization,Springer Proc. Phys.176(2016) 131

2016
[21]

Klebanov and E

I.R. Klebanov and E. Witten,AdS / CFT correspondence and symmetry breaking,Nucl. Phys. B556(1999) 89 [hep-th/9905104]

1999 arXiv
[22]

Papadimitriou,Multi-Trace Deformations in AdS/CFT: Exploring the Vacuum Structure of the Deformed CFT,JHEP05(2007) 075 [hep-th/0703152]

I. Papadimitriou,Multi-Trace Deformations in AdS/CFT: Exploring the Vacuum Structure of the Deformed CFT,JHEP05(2007) 075 [hep-th/0703152]

2007 arXiv
[23]

Ishibashi and R.M

A. Ishibashi and R.M. Wald,Dynamics in nonglobally hyperbolic static space-times. 3. Anti-de Sitter space-time,Class. Quant. Grav.21(2004) 2981 [hep-th/0402184]

2004 arXiv
[24]

Barroso and J.P.M

V.S. Barroso and J.P.M. Pitelli,Boundary conditions and vacuum fluctuations inAdS4,Gen. Rel. Grav.52(2020) 29 [1904.10920]

2020 arXiv
[25]

Gitman, I.V

D.M. Gitman, I.V. Tyutin and B.L. Voronov,Self-adjoint Extensions in Quantum Mechanics, vol. 62 ofProgress in Mathematical Physics, Birkhäuser Boston, MA, 1 ed. (2012), 10.1007/978-0-8176-4662-2

2012 doi
[26]

Peschel,Calculation of reduced density matrices from correlation functions,J

I. Peschel,Calculation of reduced density matrices from correlation functions,J. Phys. A36 (2003) L205 [cond-mat/0212631]

2003 arXiv
[27]

Katsinis and G

D. Katsinis and G. Pastras,Entanglement in (1+1)-dimensional free scalar field theory: Tiptoeing between continuum and discrete formulations,Phys. Rev. D110(2024) 085015 [2406.11031]

2024 arXiv
[28]

Katsinis, G

D. Katsinis, G. Pastras and N. Tetradis,Entanglement of harmonic systems in squeezed states,JHEP10(2023) 039 [2304.04241]

2023 arXiv
[29]

Abate and G

N. Abate and G. Torroba,Irreversibility of quantum field theory in de Sitter: the C, F and A theorems,2411.08961

arXiv
[30]

Hertzberg and F

M.P. Hertzberg and F. Wilczek,Some Calculable Contributions to Entanglement Entropy, Phys. Rev. Lett.106(2011) 050404 [1007.0993]. – 22 –

2011 arXiv

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [1]

Sorkin,1983 paper on entanglement entropy: ”On the Entropy of the Vacuum outside a Horizon”, in10th International Conference on General Relativity and Gravitation, vol

R.D. Sorkin,1983 paper on entanglement entropy: ”On the Entropy of the Vacuum outside a Horizon”, in10th International Conference on General Relativity and Gravitation, vol. 2, pp. 734–736, 1984 [1402.3589]

arXiv 1983

[2] [2]

Bombelli, R.K

L. Bombelli, R.K. Koul, J. Lee and R.D. Sorkin,A Quantum Source of Entropy for Black Holes,Phys. Rev. D34(1986) 373

1986

[3] [3]

Srednicki,Entropy and area,Phys

M. Srednicki,Entropy and area,Phys. Rev. Lett.71(1993) 666 [hep-th/9303048]

arXiv 1993

[4] [4]

Solodukhin,Entanglement entropy, conformal invariance and extrinsic geometry,Phys

S.N. Solodukhin,Entanglement entropy, conformal invariance and extrinsic geometry,Phys. Lett. B665(2008) 305 [0802.3117]

arXiv 2008

[5] [5]

Casini and M

H. Casini and M. Huerta,Entanglement entropy for the n-sphere,Phys. Lett. B694(2011) 167 [1007.1813]

arXiv 2011

[6] [6]

Casini and M

H. Casini and M. Huerta,Entanglement entropy in free quantum field theory,J. Phys. A42 (2009) 504007 [0905.2562]

arXiv 2009

[7] [7]

Lohmayer, H

R. Lohmayer, H. Neuberger, A. Schwimmer and S. Theisen,Numerical determination of entanglement entropy for a sphere,Phys. Lett. B685(2010) 222 [0911.4283]

arXiv 2010

[8] [8]

Maldacena and G.L

J. Maldacena and G.L. Pimentel,Entanglement entropy in de Sitter space,JHEP02(2013) 038 [1210.7244]

arXiv 2013