Pith. sign in

REVIEW 3 major objections 4 minor 4 cited by

Universality of pseudoentropy for deformed spheres in dS/CFT

T0 review · 3 major / 4 minor · reviewed 2026-08-03 · deepseek-v4-flash

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

Pith's one-line read For slightly deformed spherical entangling surfaces in dS/CFT, the universal part of pseudoentropy is governed by the analytically continued stress-tensor two-point coefficient, with the sphere as a local extremum.

desk verdict Einstein gravity result for dS pseudoentropy is solid; the higher-curvature generalization is not on-shell and needs rework. read the letter →

arxiv 2512.02164 v2 pith:XA3B2A3J submitted 2025-12-01 hep-th

Giorgos Anastasiou , Ignacio J. Araya , Avijit Das , Javier Moreno This is my paper · ORCID
classification hep-th MSC 81T4083E30 PACS 04.60.-m11.25.Tq
keywords pseudoentropydS/CFTcorrespondenceshapedeformationsphereextremumstress-tensortwo-pointcoefficienthigher-curvaturegravityanalyticcontinuationholographicentanglemententropy
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 asks what happens to holographic pseudoentropy in the de Sitter/conformal field theory correspondence when the entangling region is a small deformation of a sphere. It claims that the universal part of the pseudoentropy changes at second order in the deformation through a term proportional to the coefficient C_T of the two-point stress-energy tensor correlator of the non-unitary dual CFT, obtained by analytic continuation from AdS/CFT. This makes the sphere a local extremum of pseudoentropy. The same structure is shown to hold for quadratic-curvature gravity, which the authors take as evidence for universality across non-unitary holographic CFTs. A sympathetic reader would care because it extends a known AdS entanglement-entropy formula to a cosmological, non-unitary setting and identifies C_T as the governing data for shape dependence in dS.

What carries the argument

The central object is the coefficient C_T of the two-point stress-energy tensor correlator, encoded in the OPE as <T T> ~ C_T / x^{2d}, which in dS/CFT is obtained from its AdS/CFT value by the analytic continuation L_*|AdS -> -i L_*|dS. The argument is carried by the holographic extremal-area prescription: the pseudoentropy is the area (in units of 4G) of a codimension-two extremal surface anchored on the deformed sphere, split into a timelike piece in the Lorentzian dS section and a spacelike piece in the Euclidean section. At linear order in the deformation the embedding equations separate and are solved in terms of associated Legendre and hypergeometric functions; the quadratic correctio

What would settle it

Solve the full variational problem for the quadratic-curvature entropy functional without imposing the vanishing trace of the extrinsic curvature and compare the resulting order-epsilon^2 universal coefficient with the paper's expression; any discrepancy falsifies the higher-curvature universality claim. Alternatively, in an explicit dS/CFT dual (e.g., a known d=3 non-unitary CFT), compute C_T directly from the two-point stress-tensor correlator and check it against the holographic formula.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is that for an entangling surface given by a unit sphere perturbed as T0 = pi/2 + epsilon sum a_lm Y_lm, the universal piece of dS holographic pseudoentropy takes the form S_u = S^(1)_u + epsilon^2 S^(2)_u. The correction S^(2)_u is C_T times a mode sum with weights (l-1)_d, a rising factorial, and a factor pi/2 (odd d) or 1 (even d). This follows from solving the extremal-surface equations on the timelike and spacelike segments of the bulk and finding that parity-dependent terms cancel between them. The coefficient C_T is identified with the analytic continuation of the AdS/CFT stress-tensor two-point coefficient, via L_* restricted to AdS mapping to

Load-bearing premise

The higher-curvature result assumes that the same extremal surface that solves the Einstein gravity problem also extremizes the quadratic-curvature entropy functional, and this is asserted rather than demonstrated; if the true surface differs, the claimed universality for those theories must be revised.

Editorial extensions

If this is right

  • The sphere is a local extremum of universal pseudoentropy in dS/CFT, since the epsilon^2 correction keeps the sign of the unperturbed value.
  • The shape dependence of dS pseudoentropy is fixed by the analytically continued stress-tensor two-point coefficient, extending the AdS/CFT shape-deformation formula for entanglement entropy to non-unitary holographic CFTs.
  • In even dimensions the universal finite part is free of UV-regulator contamination, making it a clean observable tied to timelike entanglement entropy.
  • For quadratic-curvature gravity the same structure survives with C_T rescaled by coupling-dependent coefficients, suggesting universality across higher-curvature theories.
  • The analytic continuation L_*|AdS -> -i L_*|dS maps the AdS C_T to the dS C_T, reinforcing the view that some dS/CFT data is obtainable by continuation from AdS/CFT.

Reading between the lines

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

  • If C_T is the controlling coefficient, it gives a practical way to extract C_T for non-unitary CFTs from dS holography; testing it in explicit dS/CFT models (such as known d=3 constructions) would be a direct check.
  • The paper only establishes a local extremum; following the unitary-CFT story, one might conjecture the sphere is a global extremum in d=3 for the holographic universality class, but that requires additional argument.
  • Because C_T can vanish or become complex in non-unitary theories, the shape-deformation formula cannot hold for all non-unitary CFTs; the paper's own discussion already notes this and restricts to the holographic universality class.
  • The higher-curvature extrapolation relies on an unproven extremal-surface condition; a full variational treatment of the quadratic-curvature functional could either confirm or correct the reported C_T rescaling.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper studies holographic pseudoentropy in dS/CFT for a slightly deformed spherical entangling surface B^{d-1}_ε. In Einstein-dS gravity it claims the universal part admits the expansion S_u = S^(1) + ε² S^(2), with S^(2) given by Eq. (7), controlled by the analytically continued stress-tensor two-point coefficient C_T of Eq. (18); parity-dependent terms from timelike and spacelike parts of the RT surface are said to cancel. The same structure is claimed for quadratic curvature gravity, with C_T modified as in Eq. (21). The authors interpret the result as an extension of Mezei's formula to the non-unitary dS/CFT setting and as evidence that the sphere is a local extremum of pseudoentropy.

Significance. If correct, this is a natural and useful extension of the AdS/CFT shape-dependence formula to the non-unitary dS/CFT setting. The explicit separation into timelike/spacelike segments and the claimed parity cancellations are nontrivial, and the quadratic-curvature generalization is a reasonable test of universality. The manuscript is also honest about limitations, notably the C_T=0 caveat for certain non-unitary CFTs. However, the central Einstein-gravity computation is partly presented by assertion: the key intermediate expressions are not derived, and the higher-curvature extension rests on an unjustified identification of the extremal surface. These issues prevent acceptance in the paper's current form.

major comments (3)
  1. [Holographic pseudoentropy for perturbed spheres, Eqs. (12)–(17)] Eqs. (12)–(13) are the solutions of the linearized shape equations (10)–(11), and Eqs. (14)–(17) are the O(ε²) area contributions. These are the computational core of the main result, yet no derivation is given; in particular the claimed parity cancellations that reduce the sums to Eq. (7) are only asserted. The absence of even a representative intermediate step (for d=3 or d=4) makes the central claim hard to verify. A revised version should include the derivation, at least in a supplementary file or appendix, and ideally an independent numerical or CFT-side cross-check of the final coefficient.
  2. [Higher-curvature gravity, Eqs. (19)–(21)] Eq. (20) is obtained by evaluating Eq. (19) on a surface with K_i=0. But K_i=h^{ab}K^i_{ab} is only the trace; the full λ3 term is quadratic in the extrinsic curvature tensor. The stationarity condition of the full Dong–Camps functional contains δ[K^i_{ab}K_i^{ab}] = 2K_i^{ab}δK_{iab}+..., which does not vanish when only the trace K_i vanishes, since the traceless part of K_i^{ab} is generically nonzero on the deformed area-extremal surface. Thus K_i=0 extremizes the area functional but not the entropy functional (19); substituting it into (19) is off-shell. The linearized shape equations for T_ℓ(τ) and T_E,ℓ(τ_E) acquire λ3-dependent terms, so the coefficient in Eq. (21) is not established. The authors should solve the corrected variational equations at O(ε) and recompute S^(2) for quadratic gravity.
  3. [Eq. (18) and Discussion, C_T identification] The identification of the coefficient in Eq. (7) with the two-point stress-tensor coefficient C_T of the dual non-unitary CFT is not tested by an independent calculation. Eq. (18) is the standard AdS/CFT C_T with the analytic continuation L→−iL inserted; no dS/CFT computation of ⟨T T⟩ is shown. Since one of the main claims is that C_T controls shape dependence of pseudoentropy, an independent check, or at least a direct citation of an explicit dS/CFT two-point function computation, is needed. I also note the Discussion already concedes that non-unitary CFTs with C_T=0 escape the formula, which qualifies the word 'universality' and should be reflected in the abstract.
minor comments (4)
  1. [Eq. (5) and Eq. (4)] The notation T0 is used both as the Euclidean time coordinate in the deformation profile (5) and as a characteristic length of the subregion in Eq. (4). This is confusing; use a separate symbol such as t_E^* for the profile.
  2. [Abstract and Discussion] The statements that the correction 'retains the sign' of the unperturbed result and that the sphere is a local extremum assume C_T is real and positive. Since C_T is allowed to be complex or negative in non-unitary CFTs, the sign statement should be qualified (e.g., by specifying a phase convention or a restricted class of theories).
  3. [Figure 2] Figure 2 is schematic but no deformation parameters or ℓ values are given. It should either be labelled as illustrative or accompanied by the actual values used.
  4. [Page 4, around Eqs. (14)–(17)] The text says 'in both even and odd dimensions, we find: i) real, finite contributions...'. Since the pseudoentropy is generally complex and the prefactors contain (-i)^{d-1}, the word 'real' is misleading; this presumably refers to real coefficients after extracting the overall phases. Please rephrase.

Circularity Check

1 steps flagged · score 4.0 of 10

The O(ε²) coefficient is computed from the extremal area, then Eq. (18) renames that coefficient C_T; the central 'C_T-controlled' claim is therefore partly a relabeling, though the shape dependence and extremum sign are genuinely derived.

  1. self definitional [Eq. (7) and Eq. (18), section 'Holographic pseudoentropy for perturbed spheres']
    "In the latter expressions, we identify the coefficient of the two-point stress-energy tensor for CFTs dual to Einstein-dS gravity as CT = (−i)^{d−1} Γ(d+ 2) / [8π^{(d+2)/2}(d−1)Γ(d/2)] L^{d−1}_⋆/G , (18)"

    The prefactor multiplying the ℓ,m sum in the computed O(ε²) universal pseudoentropy — Eqs. (14)–(17) — is exactly the L^{d−1}_⋆/G combination that Eq. (18) renames C_T. No independent evaluation of the dual non-unitary CFT's ⟨TT⟩ two-point coefficient is performed; the paper itself says 'we conjecture this coefficient to be the C_T'. Thus the claim that S_u^(2) is controlled by C_T is true by definition of C_T: the coefficient was computed from the area functional and then labelled C_T. The nontrivial shape-dependent sum, the cancellations between timelike and spacelike sectors, and the sign of the extremum are independent content, but the advertised C_T-universality statement reduces to a relabeling unless C_T is obtained from the CFT side.

full rationale

The Einstein-dS computation itself is self-contained: the extremal profile equations (10)–(11) are solved with the stated boundary and junction conditions, and the resulting area integrals (14)–(17) are genuine first-principles calculations. Summing them does reproduce the Pochhammer-weighted ℓ,m sum in Eq. (7) without any input from a dual CFT two-point function. That part is not circular. The circularity is confined to the interpretive step: Eq. (18) defines C_T to be precisely the coefficient that already appears in the computed O(ε²) entropy, and Eq. (7) is then presented as a C_T-controlled universality statement. Since the non-unitary CFT's C_T is not independently computed or measured, this is a definition/conjecture rather than a derivation. The same relabeling recurs in Eq. (21) for quadratic-curvature gravity. Separately, the higher-curvature section imposes K_i=0 as the extremal-surface condition on the Dong–Camps functional (19) without extremizing the λ3 K^i_ab K_i^ab term; I treat that as a derivation gap or correctness concern, not as circularity. Overall, because the central shape-dependence and extremum results are derived, but the C_T identification is a constructed label, the circularity score is moderate: 4.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

The main Einstein result introduces no fitted constants: L_* and G are standards inputs and the deformation amplitudes a_ℓm parametrize the boundary profile. The quadratic-gravity part brings in undetermined couplings λ1-λ3. The main conjectural input is the identification of Eq. (18) with the CFT stress-tensor coefficient C_T, supported by analytic continuation rather than an independent non-unitary CFT computation.

free parameters (1)
  • λ1, λ2, λ3 = undetermined
    Quadratic gravity couplings in L_QG = R − 2Λ + λ1R² + λ2R_μνR^μν + λ3R_μνρσR^μνρσ; the higher-curvature result C_T|QG depends on them through a_d and the λ3 term.
assumptions (5)
  • domain assumption dS/CFT correspondence and the RT prescription for pseudoentropy, Eq. (8)
    The whole computation interprets the area of extremal codimension-two surfaces in dS as pseudoentropy; this is the central holographic premise.
  • domain assumption Mixed Lorentzian/Euclidean Hartle-Hawking geometry with junction conditions at τ=τ_E=0
    The extremal surface is glued across the τ=0 hypersurface using T_ℓ(0)=T_{E,ℓ}(0) and ∂_τ T_ℓ(0)=i ∂_{τ_E}T_{E,ℓ}(0); the factor i is essential for the parity cancellations in Eqs. (14)-(17).
  • domain assumption Analytic continuation L_*|AdS → −i L_*|dS transfers CFT data
    Used to identify the coefficient in Eqs. (18) and (21) with C_T; the authors acknowledge that scalar primary two-point coefficients do not continue this way [50], so the assumption is not automatic.
  • domain assumption Dong-Camps entropy functional applies to dS via the replica trick, Eq. (19)
    Extends the entropy functional to quadratic gravity in dS; relies on the cited result [44].
  • ad hoc to paper Extremal surface for S_QG is given by K_i=0
    Asserted before Eq. (20); the full functional contains λ3∫K^i_ab K_i^ab, so this should be derived from the full variational problem rather than assumed.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Universality of pseudoentropy for deformed spheres in dS/CFT." pith.science (2026). https://pith.science/paper/XA3B2A3J

@misc{pith2026251202164,
  author       = {Pith},
  title        = {Pith review of: Universality of pseudoentropy for deformed spheres in dS/CFT},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XA3B2A3J}},
  note         = {Machine review of arXiv:2512.02164}
}
abstract

We determine the universal part of pseudoentropy for small shape deformations of spherical entangling surfaces in the context of de Sitter/conformal field theory (dS/CFT) correspondence. The leading correction at quadratic order in the deformation parameter is controlled by the analytic continuation of the coefficient of the two-point stress-energy tensor correlator in AdS/CFT (i.e., $\left. L_{*} \right|_{\text{AdS}}\rightarrow -i \left. L_{*} \right|_{\text{dS}}$), thereby establishing the sphere as a local extremum. The same structure holds in higher-curvature theories, as we check explicitly for quadratic curvature gravity, suggesting a universal behavior across non-unitary holographic CFTs. Our findings extend the Mezei formula to the dS/CFT setting and indicate that the shape dependence of pseudoentropy in dS holography resembles that of entanglement entropy in AdS space. Thus, we conjecture this coefficient to be the $C_T$ for the non-unitary CFT dual.

Figures

Figures reproduced from arXiv: 2512.02164 by the authors.

Figure 1
Figure 1. In green, the entangling region B d−1 ϵ is the per￾turbation around the unit-ball B d−1 , stereographically projected on S d−1 . global dSd+1 coordinates, the metric ds 2 = gµνdx µdx ν reads ds 2 = L 2 ⋆ [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. (Left) Front view of the RT surface for small perturbations around the ball-shaped entangling region at [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 4 Pith papers

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

  1. Selecting Complex Extremal Surfaces with the Kontsevich--Segal--Witten Criterion

    hep-th 2026-07 conditional novelty 7.0 of 10

    In AdS3, dS3, and AdS4 hyperbolic examples, the Kontsevich-Segal-Witten criterion uniquely selects a three-piece complex contour for timelike extremal surfaces, while timelike strips in AdS4 violate the criterion near...

  2. de Sitter holography from a Lorentzian torus

    hep-th 2026-08 conditional novelty 6.0 of 10

    A new holographic duality is proposed: quantum gravity on a two-time version of de Sitter space is dual to a conformal field theory on a Lorentzian torus, reproducing de Sitter entropy, correlators, and pseudoentropy.

  3. Universal relation between $C_{T}$ and the CFT Weyl anomaly

    hep-th 2026-02 conditional novelty 6.0 of 10

    In any even-dimensional CFT, C_T = [d/(d−1)]·[(d+1)!/(d/2−1)!]·c, where c is the coefficient of the quadratic-in-Weyl term in the trace anomaly.

  4. Renormalized pseudoentropy in dS/CFT

    hep-th 2026-02 conditional novelty 5.0 of 10

    Renormalized holographic pseudoentropy in dS/CFT is constructed from conformal-gravity actions in four and six dimensions, yielding finite sphere values and Mezei-like shape dependence for small deformations.

Reference graph

Works this paper leans on

77 extracted references · 63 linked inside Pith · cited by 4 Pith papers

  1. [1]

    Bombelli, R

    L. Bombelli, R. K. Koul, J. Lee, and R. D. Sorkin, Phys. Rev. D34, 373 (1986)

    1986

  2. [2]

    Srednicki, Phys

    M. Srednicki, Phys. Rev. Lett.71, 666 (1993), arXiv:hep-th/9303048

    arXiv 1993

  3. [3]

    Calabrese and J

    P. Calabrese and J. L. Cardy, J. Stat. Mech.0406, P06002 (2004), arXiv:hep-th/0405152 [hep-th]

    arXiv 2004

  4. [4]

    Ryu and T

    S. Ryu and T. Takayanagi, Phys. Rev. Lett.96, 181602 (2006), arXiv:hep-th/0603001 [hep-th]

    arXiv 2006

  5. [5]

    Van Raamsdonk, Gen

    M. Van Raamsdonk, Gen. Rel. Grav.42, 2323 (2010), arXiv:1005.3035 [hep-th]

    arXiv 2010

  6. [6]

    Lewkowycz and J

    A. Lewkowycz and J. Maldacena, JHEP08, 090, arXiv:1304.4926 [hep-th]

    arXiv

  7. [7]

    Nakata, T

    Y. Nakata, T. Takayanagi, Y. Taki, K. Tamaoka, and Z. Wei, Phys. Rev. D103, 026005 (2021), arXiv:2005.13801 [hep-th]

    arXiv 2021

  8. [8]

    K. Doi, J. Harper, A. Mollabashi, T. Takayanagi, and Y. Taki, Phys. Rev. Lett.130, 031601 (2023), arXiv:2210.09457 [hep-th]

    arXiv 2023

Show all 77 references
  1. [9]

    K. Doi, J. Harper, A. Mollabashi, T. Takayanagi, and Y. Taki, JHEP05, 052, arXiv:2302.11695 [hep-th]

    arXiv

  2. [10]

    Couvreur, J

    R. Couvreur, J. L. Jacobsen, and H. Saleur, Phys. Rev. Lett.119, 040601 (2017), arXiv:1611.08506 [cond-mat.stat-mech]

    2017 arXiv

  3. [11]

    Herviou, N

    L. Herviou, N. Regnault, and J. H. Bardarson, SciPost Phys.7, 069 (2019), arXiv:1908.09852 [cond-mat.mes-hall]

    2019 arXiv

  4. [12]

    Chang, J.-S

    P.-Y. Chang, J.-S. You, X. Wen, and S. Ryu, Phys. Rev. Res.2, 033069 (2020), arXiv:1909.01346 [cond-mat.str-el]

    2020 arXiv

  5. [13]

    C.-M. Jian, B. Bauer, A. Keselman, and A. W. W. Ludwig, Phys. Rev. B106, 134206 (2022), arXiv:2012.04666 [cond- mat.stat-mech]

    2022 arXiv

  6. [14]

    Strominger, JHEP10, 034, arXiv:hep-th/0106113

    A. Strominger, JHEP10, 034, arXiv:hep-th/0106113

    arXiv

  7. [15]

    Witten, inStrings 2001: International Conference(2001) arXiv:hep-th/0106109

    E. Witten, inStrings 2001: International Conference(2001) arXiv:hep-th/0106109

    2001 arXiv

  8. [16]

    The coefficientC T—see Eq

    with the leading correction, at quadratic order inϵ, reading S(2) u =C T π(d+2)/2(d−1) 2d−2Γ(d+ 2)Γ(d/2) X ℓ,m a2 ℓ,m(ℓ−1) d × ( π/2if oddd , 1if evend , (7) where(x) n = Qn k=1(x+k−1)isthePochhammersymbol. The coefficientC T—see Eq. (18) below—characterizes the two-point stre...

  9. [17]

    J. M. Maldacena, JHEP05, 013, arXiv:astro-ph/0210603

    arXiv

  10. [18]

    J. M. Maldacena, Int. J. Theor. Phys.38, 1113 (1999), [Adv. Theor. Math. Phys.2,231(1998)], arXiv:hep-th/9711200 [hep-th]

    1999 arXiv

  11. [19]

    S. S. Gubser, I. R. Klebanov, and A. M. Polyakov, Phys. Lett.B428, 105 (1998), arXiv:hep-th/9802109 [hep-th]

    1998 arXiv

  12. [20]

    Witten, Adv

    E. Witten, Adv. Theor. Math. Phys.2, 253 (1998), arXiv:hep-th/9802150 [hep-th]

    1998 arXiv

  13. [21]

    Anninos, T

    D. Anninos, T. Hartman, and A. Strominger, Class. Quant. Grav.34, 015009 (2017), arXiv:1108.5735 [hep-th]

    2017 arXiv

  14. [22]

    Mollabashi, N

    A. Mollabashi, N. Shiba, T. Takayanagi, K. Tamaoka, and Z. Wei, Phys. Rev. Res.3, 033254 (2021), arXiv:2106.03118 [hep-th]

    2021 arXiv

  15. [23]

    Hikida, T

    Y. Hikida, T. Nishioka, T. Takayanagi, and Y. Taki, JHEP05, 129, arXiv:2203.02852 [hep-th]

    arXiv

  16. [24]

    Ryu and T

    S. Ryu and T. Takayanagi, JHEP08, 045, arXiv:hep-th/0605073 [hep-th]

    arXiv

  17. [25]

    Nishioka, S

    T. Nishioka, S. Ryu, and T. Takayanagi, J. Phys. A42, 504008 (2009), arXiv:0905.0932 [hep-th]

    2009 arXiv

  18. [26]

    Additionally, the recently proposed timelike entanglement entropy, defined for timelike-separated regions in Lorentzian field theories, can also take complex values and is naturally interpreted as a pseudoentropy [8, 9, 60, 63, 66, 70, 71]

  19. [27]

    Sanches and S

    F. Sanches and S. J. Weinberg, Phys. Rev. D94, 084034 (2016), arXiv:1603.05250 [hep-th]

    2016 arXiv

  20. [28]

    Arias, F

    C. Arias, F. Diaz, and P. Sundell, Class. Quant. Grav.37, 015009 (2020), arXiv:1901.04554 [hep-th]

    2020 arXiv

  21. [29]

    Ruan and Y.-k

    S.-M. Ruan and Y.-k. Suzuki, (2025), arXiv:2508.14478 [hep-th]

    2025 arXiv

  22. [30]

    It arises from performing Wick rotation on the Lorentzian timetin the AdS formulation

    The compact Euclidean directiontE ∈[0, π]serves as one of the angular coordinates on the global boundarySd. It arises from performing Wick rotation on the Lorentzian timetin the AdS formulation

  23. [31]

    The mixed nature of the bulk manifold is a consequence of the Hartle-Hawking geometry associated with the ‘no-boundary proposal’ in dS/CFT holography[14, 16]

  24. [32]

    Osborn and A

    H. Osborn and A. C. Petkou, Annals Phys.231, 311 (1994), arXiv:hep-th/9307010 [hep-th]

    1994 arXiv

  25. [33]

    Throughout this Letter we use: i)α,β,γ,δfor indices in the conformal field theory, ii)µ, ν, ρ, σas indices for the dual gravity theory, iii)a,bfor the codimension-two surfaceΣ A andi,jfor normal directions toΣ A

  26. [34]

    Osborn and A

    H. Osborn and A. Stergiou, JHEP06, 079, arXiv:1603.07307 [hep-th]

    arXiv

  27. [35]

    Flohr, Int

    M. Flohr, Int. J. Mod. Phys. A18, 4497 (2003), arXiv:hep-th/0111228

    2003 arXiv

  28. [36]

    Buchel, J

    A. Buchel, J. Escobedo, R. C. Myers, M. F. Paulos, A. Sinha, and M. Smolkin, JHEP03, 111, arXiv:0911.4257 [hep-th]

    arXiv

  29. [37]

    R. C. Myers, M. F. Paulos, and A. Sinha, JHEP08, 035, arXiv:1004.2055 [hep-th]

    arXiv

  30. [38]

    Allais and M

    A. Allais and M. Mezei, Phys. Rev. D91, 046002 (2015), arXiv:1407.7249 [hep-th]

    2015 arXiv

  31. [39]

    Mezei, Phys

    M. Mezei, Phys. Rev.D91, 045038 (2015), arXiv:1411.7011 [hep-th]

    2015 arXiv

  32. [40]

    Notice that the extrinsic curvature along theθdirection vanishes identically,Kθ ab =h µ a hθ b ∇µnθ θ = 0since, for any value ofb,h θ b = 0

  33. [41]

    Inthecaseoftheundeformedsphere, thesecondjunction(regularity)conditionisunnecessary, sincethefinalpseudoentropy is independent of the coefficient that would otherwise remain undetermined by this additional requirement [9]

  34. [42]

    Israel, Nuovo Cim

    W. Israel, Nuovo Cim. B44S10, 1 (1966), [Erratum: Nuovo Cim.B 48, 463 (1967)]

    1966

  35. [43]

    The surface takes on a geometry reminiscent of a shuttlecock, withℓcorresponding to the number of feathers in its skirt

  36. [44]

    Faulkner, R

    T. Faulkner, R. G. Leigh, and O. Parrikar, JHEP04, 088, arXiv:1511.05179 [hep-th]

    arXiv

  37. [45]

    K. K. Nanda, K. Narayan, S. Porey, and G. Yadav, (2025), arXiv:2509.02775 [hep-th]

    2025

  38. [46]

    Dong, JHEP01, 044, arXiv:1310.5713 [hep-th]

    X. Dong, JHEP01, 044, arXiv:1310.5713 [hep-th]

    arXiv

  39. [47]

    Camps, JHEP03, 070, arXiv:1310.6659 [hep-th]

    J. Camps, JHEP03, 070, arXiv:1310.6659 [hep-th]

    arXiv

  40. [48]

    While, for generic entangling surfaces, cubic curvature invariants are affected by the splitting problem [72–74], which introduces ambiguities in the regularization of the conical singularity—and hence in the resulting holographic entropy functional, this issue does not arise ...

  41. [49]

    D. V. Fursaev, A. Patrushev, and S. N. Solodukhin, Phys. Rev.D88, 044054 (2013), arXiv:1306.4000 [hep-th]

    2013 arXiv

  42. [50]

    Anastasiou, M

    G. Anastasiou, M. Bravo, and R. Olea, JHEP09, 093, arXiv:2504.06382 [hep-th]. 7

    arXiv

  43. [51]

    K. Doi, N. Ogawa, K. Shinmyo, Y.-k. Suzuki, and T. Takayanagi, JHEP02, 093, arXiv:2405.14237 [hep-th]

    arXiv

  44. [52]

    Fonda, D

    P. Fonda, D. Seminara, and E. Tonni, JHEP12, 037, arXiv:1510.03664 [hep-th]

    arXiv

  45. [53]

    Anastasiou, J

    G. Anastasiou, J. Moreno, R. Olea, and D. Rivera-Betancour, JHEP09, 173, arXiv:2002.06111 [hep-th]

    2002 arXiv

  46. [54]

    Bueno, H

    P. Bueno, H. Casini, O. L. Andino, and J. Moreno, JHEP10, 179, arXiv:2107.12394 [hep-th]

    arXiv

  47. [55]

    J. S. Dowker, (2010), arXiv:1012.1548 [hep-th]

    2010 arXiv

  48. [56]

    Casini, M

    H. Casini, M. Huerta, and R. C. Myers, JHEP05, 036, arXiv:1102.0440 [hep-th]

    arXiv

  49. [57]

    Bueno, H

    P. Bueno, H. Casini, O. L. Andino, and J. Moreno, Phys. Rev. Lett.131, 171601 (2023), arXiv:2307.05164 [hep-th]

    2023 arXiv

  50. [58]

    Anastasiou, I

    G. Anastasiou, I. J. Araya, A. Argandoña, and R. Olea, JHEP11, 031, arXiv:2208.00093 [hep-th]

    arXiv

  51. [59]

    Bueno and W

    P. Bueno and W. Witczak-Krempa, Phys. Rev. B93, 045131 (2016), arXiv:1511.04077 [cond-mat.str-el]

    2016 arXiv

  52. [60]

    Chen, (2023), arXiv:2302.14303 [hep-th]

    Z. Chen, (2023), arXiv:2302.14303 [hep-th]

    2023 arXiv

  53. [61]

    A. Das, S. Sachdeva, and D. Sarkar, Phys. Rev. D109, 066007 (2024), arXiv:2312.16056 [hep-th]

    2024 arXiv

  54. [62]

    W.-z. Guo, S. He, and Y.-X. Zhang, Phys. Rev. D112, 086020 (2025), arXiv:2402.00268 [hep-th]

    2025

  55. [63]

    Grieninger, K

    S. Grieninger, K. Ikeda, and D. E. Kharzeev, JHEP05, 030, arXiv:2312.08534 [hep-th]

    arXiv

  56. [64]

    M. P. Heller, F. Ori, and A. Serantes, Phys. Rev. Lett.134, 131601 (2025), arXiv:2408.15752 [hep-th]

    2025 arXiv

  57. [65]

    Jiang, P

    X. Jiang, P. Wang, H. Wu, and H. Yang, Phys. Rev. D108, 046004 (2023), arXiv:2302.13872 [hep-th]

    2023 arXiv

  58. [66]

    Li, Z.-Q

    Z. Li, Z.-Q. Xiao, and R.-Q. Yang, JHEP04, 004, arXiv:2211.14883 [hep-th]

    arXiv

  59. [67]

    Narayan and H

    K. Narayan and H. K. Saini, Eur. Phys. J. C84, 499 (2024), arXiv:2303.01307 [hep-th]

    2024 arXiv

  60. [68]

    Anastasiou, I

    G. Anastasiou, I. J. Araya, J. Moreno, and A. Das, to appear

  61. [69]

    Anastasiou, I

    G. Anastasiou, I. J. Araya, and R. Olea, JHEP10, 123, arXiv:2209.02006 [hep-th]

    arXiv

  62. [70]

    Anastasiou, I

    G. Anastasiou, I. J. Araya, P. Bueno, J. Moreno, R. Olea, and A. Vilar Lopez, JHEP01, 081, arXiv:2409.19485 [hep-th]

    arXiv

  63. [71]

    B. Liu, H. Chen, and B. Lian, Phys. Rev. B110, 144306 (2024), arXiv:2210.03134 [cond-mat.stat-mech]

    2024 arXiv

  64. [72]

    Narayan, Phys

    K. Narayan, Phys. Rev. D107, 126004 (2023), arXiv:2210.12963 [hep-th]

    2023 arXiv

  65. [73]

    Miao, JHEP10, 049, arXiv:1503.05538 [hep-th]

    R.-X. Miao, JHEP10, 049, arXiv:1503.05538 [hep-th]

    arXiv

  66. [74]

    Miao and W.-z

    R.-X. Miao and W.-z. Guo, JHEP08, 031, arXiv:1411.5579 [hep-th]

    arXiv

  67. [75]

    Camps and W

    J. Camps and W. R. Kelly, JHEP03, 061, arXiv:1412.4093 [hep-th]

    arXiv

  68. [76]

    Bueno, J

    P. Bueno, J. Camps, and A. V. López, JHEP04, 145, arXiv:2012.14033 [hep-th]

    2012 arXiv

  69. [77]

    Anastasiou, I

    G. Anastasiou, I. J. Araya, J. Moreno, R. Olea, and D. Rivera-Betancour, Phys. Rev. D104, 086003 (2021), arXiv:2102.11242 [hep-th]

    2021 arXiv

Pith tools

Reviewed August 3, 2026 · model on record in the stance chip above.