Pith. sign in

REVIEW 2 major objections 3 minor 39 references

The paper claims that in de Sitter space the first gravitational correction to the observer four-point function has the opposite sign to the black hole result, and that this anti-scrambling sign is a key test of any quantum description of t

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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

T0 review · deepseek-v4-flash

2026-08-03 01:54 UTC pith:B3G45QFO

load-bearing objection The dS2 anti-scrambling OTOC is the real result; the dS3 generalization is conditional on an unproven s-wave truncation, and the Euclidean folds are a sketch. the 2 major comments →

arxiv 2607.14215 v2 pith:B3G45QFO submitted 2026-07-15 hep-th

Anti-scrambling and euclidean folds from observer correlators in de Sitter space

Daniel Harlow , Ying Zhao This is my paper
classification hep-th
keywords anti-scramblingde Sitter spaceobserver correlatorsout-of-time-order correlatorJackiw-Teitelboim gravityEuclidean foldsscrambling timeLyapunov exponent
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper gathers gravitational 'data' about the de Sitter horizon by computing correlation functions on the worldline of an observer. The two-point function looks thermal, but the out-of-time-order four-point function displays anti-scrambling: the first gravitational correction has a positive sign (time advance) rather than the negative sign (time delay) found for black holes. The Lyapunov exponent is 2π/β, saturating the chaos bound, and for perturbations separated by more than two scrambling times the backreaction produces a big crunch singularity. The paper then proposes that such anti-scrambling correlators could arise in an ordinary quantum system whose Hamiltonian is bounded both above and below, through correlation functions folded in Euclidean time.

Core claim

The central discovery is that the observer four-point function in de Sitter space, computed with classical gravity in the eikonal regime, takes the form (4.32)–(4.36): a product of two-point functions times a factor whose first correction is positive — the opposite sign to the black hole result. This sign traces directly to the negative sign of the 2–2 gravitational scattering phase δ ≈ −2p₊p₋/b₀ (4.23), which in turn is a consequence of the anti-scrambling time advance: throwing a shell through the cosmological horizon moves the horizon away from the observer, so probe particles arrive earlier rather than later. The paper also finds a Lyapunov exponent 2π/β saturating the chaos bound (not 4

What carries the argument

The central object is the eikonal 2–2 gravitational scattering phase δ(p₊p₋) between the two shells, whose derivative gives the time advance; its negative sign δ ≈ −2p₊p₋/b₀ (Eq. 4.23) is what turns scrambling into anti-scrambling. This phase enters the four-point function (4.19) via e^{iδ}, and the resulting exact expression (4.32) is a perfect match to the black hole out-of-time-order correlator except for the replacement w → −w. The second piece of machinery is the Euclidean fold: the continuation (6.9) reverses the sign of sin((τ₄₃+τ₂₁)/2) without changing the product of two-point functions, converting a scrambling correlator into the anti-scrambling one.

Load-bearing premise

The anti-scrambling sign rests on assuming the two-shell gravitational collision is dominated by the spherically symmetric (s-wave) sector and that a single eikonal phase δ ≈ −2p₊p₋/b₀ captures the scattering; if inelastic scattering out of the s-wave sector contributes at the same order, the sign can flip. The paper asserts, but does not derive, that restricting to heavy operators χⁿ makes the s-wave sector dominate.

What would settle it

Compute the four-point function including the full set of non-spherically-symmetric (inelastic) scattering channels, for instance using the localized perturbation calculation of section 3.5, at the same order in G. If the first gravitational correction to the OTOC (4.36) becomes negative once inelastic scattering is included, the anti-scrambling claim is false. Alternatively, test the Euclidean fold prescription in a concrete bounded-energy quantum system such as the SYK model: if the analytically continued correlator does not match (4.32) in the semiclassical limit, the proposal fails.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Any fundamental quantum description of the de Sitter static patch must reproduce the anti-scrambling four-point function (4.36), including the positive sign of the first gravitational correction — a sharp, quantitative test.
  • The Lyapunov exponent in de Sitter is 2π/β, saturating the chaos bound, not the 4π/β reported in earlier work.
  • Two-sided observer correlators in de Sitter violate the thermal bound (4.38), showing that ordinary thermal quantum mechanics cannot produce them; a non-standard ingredient such as folded Euclidean time is required.
  • For time separations beyond 2t_scr, gravitational backreaction creates a big crunch singularity in the post-collision region: a thermal-scale perturbation can destroy the universe if thrown in more than two scrambling times before another emission.
  • If the Euclidean fold proposal is correct, de Sitter correlators would be reproduced by a finite (bounded-above-and-below) quantum system, effectively operating at negative temperature.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the anti-scrambling sign is robust, the requirement of a Hamiltonian bounded both above and below for Euclidean folds suggests that a microscopic description of the static patch might be inherently finite-dimensional, much like a spin model; this is a nontrivial constraint on holographic proposals.
  • A direct test of the proposal would be to compute the four-point function in a concrete bounded-energy system, such as a finite-size SYK model or a spin chain, using the fold prescription (6.9) and compare with (4.32); the paper itself flags the SYK model as a test of the analytic continuation.
  • The big-crunch regime at 2t_scr, if robust, offers a sharper prediction than the sign: a microscopic theory must exhibit a divergence or breakdown at that exact time separation, which could discriminate among candidate duals.
  • The negative-temperature interpretation of the de Sitter static patch (entropy decreases when energy increases) is a natural consequence of the anti-scrambling sign and could serve as an organizing principle for future constructions.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 3 minor

Summary. The paper gathers gravitational 'data' on observer correlation functions in de Sitter space, with the goal of constraining any fundamental quantum description of the dS static patch. The authors reduce spherically-symmetric dS3 gravity with dust to JT gravity with positive cosmological constant (Sec. 3.1), construct one- and two-shell solutions, and use them to compute the time advance of a probe (Secs. 3.3-3.4). They then derive the observer two-point function and the out-of-time-order four-point function, Eq. (4.36), whose first gravitational correction has a sign opposite to the black-hole result. This 'anti-scrambling' correction is traced to the negative eikonal phase (4.23). The result is cross-checked in Sec. 5 using a worldline theory, with the four-point correction (5.37) reproducing (4.36) for operators of dimension one. The paper also notes that for time separations beyond 2t_scr the back-reaction destroys the universe (Sec. 3.4). In Sec. 6, the authors propose that anti-scrambling correlators could arise from a quantum system whose Hamiltonian is bounded above and below, using correlators folded in Euclidean time. The proposal is explicitly incomplete: the fold integer n is undetermined, and the analytic continuation is assumed to commute with the semiclassical limit. The dS3 generalization is also not fully established because it relies on s-wave dominance that is asserted rather than derived. The dS2/JT results, by contrast, appear internally coherent and are ba

Significance. If the central claim holds, the paper provides concrete, non-perturbative constraints on any quantum-mechanical description of the de Sitter static patch: a conventional thermal two-point function but an anti-scrambling four-point function, with a violation of the thermal commutator bound in the two-sided continuation (4.38). The dS2/JT derivation is a genuine strength: the sign of the 1/b0 correction follows from the classical time-advance via the phase-shift relation, and the worldline calculation in Sec. 5 independently reproduces the four-point result. The paper is also admirably transparent about its own limitations, explicitly flagging the dS3 inelastic-scattering gap, the undetermined fold integer n, and the Stokes-phenomenon risk. However, the headline claims about 'de Sitter space' and about a quantum realization via Euclidean folds are not yet at the same level of support as the dS2 calculation. The dS3 claim depends on a truncation that is not justified in this manuscript, and the Euclidean-fold idea remains a conjecture rather than a demonstrated realization. Because those two elements are load-bearing for the paper's broadest conclusions, the manuscript requires revisi

major comments (2)
  1. [Sec. 4, closing paragraph; App. B, Eq. (B.9)] The advertised generalization to dS3 is load-bearing for the paper's headline, but it rests on an unproven s-wave truncation. The text concedes that in dS3 'quantum mechanically there can be inelastic scattering out of the s-wave sector' and then restricts to heavy operators chi^n at large n with the assertion that 'the s-wave sector dominates'. No partial-wave expansion or estimate of inelastic matrix elements is provided, and the systematic treatment is explicitly delegated to references [27,29]. Moreover, Sec. 3.5 identifies a concrete non-spherically-symmetric contribution, the recoil effect, which is 'systematically included' in [27,29], not here. Since the abstract and title make a general statement about de Sitter space, and the strong conclusion that every quantum description of the dS static patch must reproduce these correlators depends on the sign of the 1/b0 correction, the d
  2. [Sec. 6, Eqs. (6.9)-(6.12)] The Euclidean-fold proposal is not yet a demonstration that anti-scrambling can be realized in a quantum system with a Hamiltonian bounded both above and below. The fold prescription contains an arbitrary integer n, and the text states: 'At present we do not have a way of selecting a particular value of n' and 'we do not at the moment know how to turn this observation into a general rule'. The prescription is also tied to a specific operator ordering, and the paper acknowledges that the analytic continuation could fail if a Stokes phenomenon disrupts the semiclassical limit. The abstract, however, states that anti-scrambling 'can be realized in a quantum system whose Hamiltonian is bounded from both above and below using correlators that are folded in Euclidean time.' As written, this overstates the status of the proposal. To support the claim, the paper should either provide a concrete
minor comments (3)
  1. [Introduction and Sec. 2] The paper states that previous papers [24-26] found a Lyapunov exponent 4pi/beta, while the present work finds 2pi/beta saturating the chaos bound. This discrepancy is not reconciled. Since the difference might be due to a different time coordinate, to a different physical effect, or to an error in the earlier works, the authors should add an explicit comparison. This is important for readers trying to place the new 'anti-scrambling' claim relative to the existing literature.
  2. [Sec. 5.2, Eq. (5.31)] The two-point function (5.31) is obtained in a renormalization scheme where q=1, chosen so that the renormalized Euclidean time has period 2pi. The constant -Delta^2/(pi b0) in (5.31) looks scheme-dependent. Please state explicitly whether the physical correlator is scheme-independent at this order, and if so, where the scheme dependence cancels.
  3. [Various] Minor typos and formatting: in Sec. 1, 'the operatore τ Hwithτ>0' lacks spaces; in Sec. 6, the figure label contains 'ds Sitter' instead of 'de Sitter'; and the text alternates between 'dS2' and 'dS 2' in a way that should be unified. These do not affect the scientific content.

Circularity Check

0 steps flagged

No significant circularity: the anti-scrambling OTOC sign is derived from the classical time advance and independently cross-checked; the Euclidean-fold section is an explicitly labeled proposal, not a derivation from inputs.

full rationale

The paper's central quantitative claim, the positive (anti-scrambling) sign of the 1/b0 correction in Eq. (4.36), is obtained by a genuine derivation chain: the classical two-shell solution gives the time advance (3.34), the eikonal phase-shift relation (4.20)–(4.23) converts that advance into a scattering phase of negative sign, and the OTOC follows from the phase-shifted mode integral. No parameter is fitted to the four-point function; the sign is forced by the gravitational focusing argument for cosmological horizons. Section 5 independently reproduces the same sign from the worldline boundary action, Eq. (5.35)–(5.37), which would be impossible if the OTOC were simply an input. The self-citations [33,34] are used only for standard JT solution methods and nomenclature and are not load-bearing for the anti-scrambling claim. The Euclidean-fold discussion in Section 6 is reverse-engineered from the dS answer through the w→-w replacement, but the paper explicitly labels it a proposal: 'We do not have a complete proposal for how to do this, but as we now explain one possibility is to use correlation functions that are folded in Euclidean signature.' It also acknowledges unresolved ambiguities (choice of n, possible Stokes phenomena, inability to handle the >2t_scr crunch). Thus the fold section is a constructive suggestion, not a claimed derivation, so it does not make the derivation circular. The dS3 s-wave truncation is an unproven assumption delegated to [27,29], but that is a correctness risk rather than a circularity: the dS2/JT calculation stands independently, and the dS3 generalization is presented as a restriction to heavy operators rather than as a consequence fitted to the desired OTOC.

Axiom & Free-Parameter Ledger

2 free parameters · 7 axioms · 1 invented entities

The central claim rests on standard GR/CFT machinery plus two ad hoc postulates in Sec. 6 (bounded Hamiltonian, commuting semiclassical limit). No data fitting; the free parameters are a scheme choice (q) and an undetermined integer (n).

free parameters (2)
  • fold integer n = undetermined
    Continuation (6.9) depends on an arbitrary integer n; Sec. 6: 'we do not have a way of selecting a particular value of n.' The Euclidean-fold realization of anti-scrambling is not defined without it.
  • renormalization parameter q = 1 (chosen)
    Sec. 5.2: chosen so the Euclidean clock tau_ren has period 2pi; it controls scheme-dependent O(1/b0) terms in the two-point function (5.31)-(5.32).
axioms (7)
  • domain assumption Null energy condition and gravitational focusing (Gao-Wald tall-diagram theorem)
    Invoked in Sec. 2.2 to establish that throwing matter through a dS horizon moves it away from the observer; the sign of the entire anti-scrambling effect follows from this.
  • domain assumption Dimensional-reduction equivalence: 3D Einstein gravity with spherical dust = JT gravity with Lambda>0 (eq. 3.8)
    Sec. 3.1, following [33,34]; all quantitative results live in the 2D JT model, so a failure of the reduction would invalidate the computation.
  • domain assumption Eikonal approximation: four-point function (4.19) dominated by a single 2-2 gravitational scattering phase e^{i delta}
    Sec. 4; standard from [5] but controls the central OTOC computation, including the sign that defines anti-scrambling.
  • domain assumption Time-advance/phase-shift relation (4.20): X_+ - (X_+)' = partial delta / partial p_+
    Sec. 4; the bridge between the classical time advance and the quantum correlator; a failure here would disconnect the geometry from the OTOC.
  • ad hoc to paper Existence of a quantum system with Hamiltonian bounded above and below whose folded Euclidean correlators realize (6.2)
    Sec. 6: 'we will simply need to postulate that we are considering a quantum system whose Hamiltonian is bounded from both below and above'; no concrete model is given.
  • ad hoc to paper The semiclassical limit commutes with the analytic continuation (no Stokes phenomenon)
    Explicitly flagged in Sec. 6 as possibly failing; the authors call for checking this in a concrete model such as SYK.
  • standard math Standard conformal-field-theory machinery (conformal transformation of boundary correlators, Hilbert transform (C.13))
    Appendix C; used to compute wiggly-boundary CFT correlators in the worldline theory of Sec. 5.
invented entities (1)
  • Euclidean folds no independent evidence
    purpose: Prescription that reverses Euclidean time separations across operators, converting a scrambling OTOC into the anti-scrambling one (w -> -w) using a Hamiltonian bounded above and below.
    Introduced in Sec. 6 as an 'empirical observation'; no concrete system realizes it, the integer n is unselected, and it fails for the >2t_scr crunch regime. No falsifiable handle outside the paper.

pith-pipeline@v1.3.0-alltime-deepseek · 50230 in / 25262 out tokens · 249198 ms · 2026-08-03T01:54:50.100135+00:00 · methodology

0 comments
read the original abstract

The de Sitter horizon behaves in a qualitatively different way from a black hole horizon, which poses a challenge to any attempt to develop a fundamental quantum description of de Sitter space. In this paper we gather some ``data'' on this problem using gravitational calculations, seeing that they lead to an ``anti-scrambling'' phenomenon that is contrary to the behavior of standard many-body quantum systems. We organize our discussion in terms of correlation functions computed on the worldline of an observer living in the spacetime, with the two-point function looking like a conventional thermal correlator but the four-point function showing anti-scrambling. We propose that anti-scrambling can be realized in a quantum system whose Hamiltonian is bounded from both above and below using correlators that are folded in Euclidean time.

Review history (2 revisions) →

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

39 extracted references · 32 linked inside Pith

  1. [1]

    J. M. Maldacena,Eternal black holes in anti-de Sitter,JHEP04(2003) 021, [hep-th/0106112]

    Pith/arXiv arXiv 2003

  2. [2]

    D. T. Son and A. O. Starinets,Minkowski space correlators in AdS / CFT correspondence: Recipe and applications,JHEP09(2002) 042, [hep-th/0205051]

    Pith/arXiv arXiv 2002

  3. [3]

    S. H. Shenker and D. Stanford,Black holes and the butterfly effect,JHEP03(2014) 067, [arXiv:1306.0622]

    Pith/arXiv arXiv 2014

  4. [4]

    D. A. Roberts and D. Stanford,Two-dimensional conformal field theory and the butterfly effect,Phys. Rev. Lett.115(2015), no. 13 131603, [arXiv:1412.5123]

    Pith/arXiv arXiv 2015

  5. [5]

    S. H. Shenker and D. Stanford,Stringy effects in scrambling,JHEP05(2015) 132, [arXiv:1412.6087]

    Pith/arXiv arXiv 2015

  6. [6]

    Strominger,The dS / CFT correspondence,JHEP10(2001) 034, [hep-th/0106113]

    A. Strominger,The dS / CFT correspondence,JHEP10(2001) 034, [hep-th/0106113]

    Pith/arXiv arXiv 2001

  7. [7]

    J. M. Maldacena,Non-Gaussian features of primordial fluctuations in single field inflationary models,JHEP05(2003) 013, [astro-ph/0210603]

    Pith/arXiv arXiv 2003

  8. [8]

    Banks, B

    T. Banks, B. Fiol, and A. Morisse,Towards a quantum theory of de Sitter space,JHEP 12(2006) 004, [hep-th/0609062]

    Pith/arXiv arXiv 2006

  9. [9]

    X. Dong, B. Horn, E. Silverstein, and G. Torroba,Micromanaging de Sitter holography, Class. Quant. Grav.27(2010) 245020, [arXiv:1005.5403]

    Pith/arXiv arXiv 2010

  10. [10]

    Anninos, T

    D. Anninos, T. Hartman, and A. Strominger,Higher Spin Realization of the dS/CFT Correspondence,Class. Quant. Grav.34(2017), no. 1 015009, [arXiv:1108.5735]. 14We requireξ(u)=0 whenρ(u)=0. This impliesξ 0 =0. – 42 –

    Pith/arXiv arXiv 2017

  11. [11]

    Coleman, E

    E. Coleman, E. A. Mazenc, V. Shyam, E. Silverstein, R. M. Soni, G. Torroba, and S. Yang,De Sitter microstates from T T+Λ 2 and the Hawking-Page transition,JHEP 07(2022) 140, [arXiv:2110.14670]

    Pith/arXiv arXiv 2022

  12. [12]

    Susskind,De Sitter Space, Double-Scaled SYK, and the Separation of Scales in the Semiclassical Limit,JHAP5(2025), no

    L. Susskind,De Sitter Space, Double-Scaled SYK, and the Separation of Scales in the Semiclassical Limit,JHAP5(2025), no. 1 1–30, [arXiv:2209.09999]

    Pith/arXiv arXiv 2025

  13. [13]

    Narovlansky and H

    V. Narovlansky and H. Verlinde,Double-scaled SYK and de Sitter holography,JHEP 05(2025) 032, [arXiv:2310.16994]

    Pith/arXiv arXiv 2025

  14. [14]

    Tietto and H

    D. Tietto and H. Verlinde,A microscopic model of de Sitter spacetime with an observer,arXiv:2502.03869

    Pith/arXiv arXiv

  15. [15]

    V. F. Mukhanov and G. V. Chibisov,Quantum Fluctuations and a Nonsingular Universe,JETP Lett.33(1981) 532–535

    1981

  16. [16]

    S. W. Hawking,The Development of Irregularities in a Single Bubble Inflationary Universe,Phys. Lett. B115(1982) 295

    1982

  17. [17]

    A. H. Guth and S. Y. Pi,Fluctuations in the New Inflationary Universe,Phys. Rev. Lett.49(1982) 1110–1113

    1982

  18. [18]

    J. M. Bardeen, P. J. Steinhardt, and M. S. Turner,Spontaneous Creation of Almost Scale - Free Density Perturbations in an Inflationary Universe,Phys. Rev. D28(1983) 679

    1983

  19. [19]

    Chandrasekaran, R

    V. Chandrasekaran, R. Longo, G. Penington, and E. Witten,An algebra of observables for de Sitter space,JHEP02(2023) 082, [arXiv:2206.10780]

    Pith/arXiv arXiv 2023

  20. [20]

    Witten,A background-independent algebra in quantum gravity,JHEP03(2024) 077, [arXiv:2308.03663]

    E. Witten,A background-independent algebra in quantum gravity,JHEP03(2024) 077, [arXiv:2308.03663]

    Pith/arXiv arXiv 2024

  21. [21]

    Banks and W

    T. Banks and W. Fischler,Holographic Theory of Accelerated Observers, the S-matrix, and the Emergence of Effective Field Theory,arXiv:1301.5924

    Pith/arXiv arXiv

  22. [22]

    Gao and R

    S. Gao and R. M. Wald,Theorems on gravitational time delay and related issues, Class. Quant. Grav.17(2000) 4999–5008, [gr-qc/0007021]

    Pith/arXiv arXiv 2000

  23. [23]

    Leblond, D

    F. Leblond, D. Marolf, and R. C. Myers,Tall tales from de Sitter space 1: Renormalization group flows,JHEP06(2002) 052, [hep-th/0202094]

    Pith/arXiv arXiv 2002

  24. [24]

    Aalsma and G

    L. Aalsma and G. Shiu,Chaos and complementarity in de Sitter space,JHEP05 (2020) 152, [arXiv:2002.01326]

    Pith/arXiv arXiv 2020

  25. [25]

    D. K. Kolchmeyer and H. Liu,Chaos and the Emergence of the Cosmological Horizon, arXiv:2411.08090

    Pith/arXiv arXiv

  26. [26]

    Narovlansky,Towards a microscopic description of de Sitter dynamics, arXiv:2506.02109

    V. Narovlansky,Towards a microscopic description of de Sitter dynamics, arXiv:2506.02109. – 43 –

    Pith/arXiv arXiv

  27. [27]

    Y. Chen, D. Stanford, H. Tang, and Z. Yang,Negative shocks versus static patch holography,arXiv:2607.14042

    Pith/arXiv arXiv

  28. [28]

    Cui and D

    W. Cui and D. K. Kolchmeyer,A de Sitter Anti-Scrambling Algebra, arXiv:2607.13665

    Pith/arXiv arXiv

  29. [29]

    Milekhin, V

    A. Milekhin, V. Narovlansky, and J. Xu,Out-of-time-ordered Correlators in de Sitter Revisited,arXiv:2607.13137

    Pith/arXiv arXiv

  30. [30]

    S. W. Hawking,Gravitational radiation from colliding black holes,Phys. Rev. Lett.26 (1971) 1344–1346

    1971

  31. [31]

    Batra,Timelike boundaries in de Sitter JT gravity and the Gao-Wald theorem, JHEP01(2025) 044, [arXiv:2407.08913]

    G. Batra,Timelike boundaries in de Sitter JT gravity and the Gao-Wald theorem, JHEP01(2025) 044, [arXiv:2407.08913]

    Pith/arXiv arXiv 2025

  32. [32]

    A. Goel, L. V. Iliesiu, J. Kruthoff, and Z. Yang,Classifying boundary conditions in JT gravity: from energy-branes toα-branes,JHEP04(2021) 069, [arXiv:2010.12592]

    Pith/arXiv arXiv 2021

  33. [33]

    Harlow and J.-q

    D. Harlow and J.-q. Wu,Algebra of diffeomorphism-invariant observables in Jackiw-Teitelboim gravity,JHEP05(2022) 097, [arXiv:2108.04841]

    Pith/arXiv arXiv 2022

  34. [34]

    Alonso-Monsalve, D

    E. Alonso-Monsalve, D. Harlow, and P. Jefferson,Phase space of Jackiw-Teitelboim gravity with positive cosmological constant,JHEP03(2026) 008, [arXiv:2409.12943]

    Pith/arXiv arXiv 2026

  35. [35]

    Barrabes and W

    C. Barrabes and W. Israel,Thin shells in general relativity and cosmology: The Lightlike limit,Phys. Rev. D43(1991) 1129–1142

    1991

  36. [36]

    D. N. Page and W. K. Wootters,EVOLUTION WITHOUT EVOLUTION: DYNAMICS DESCRIBED BY STATIONARY OBSER V ABLES,Phys. Rev. D27 (1983) 2885

    1983

  37. [37]

    Jensen,Chaos in AdS 2 Holography,Phys

    K. Jensen,Chaos in AdS 2 Holography,Phys. Rev. Lett.117(2016), no. 11 111601, [arXiv:1605.06098]

    Pith/arXiv arXiv 2016

  38. [38]

    Maldacena, D

    J. Maldacena, D. Stanford, and Z. Yang,Conformal symmetry and its breaking in two dimensional Nearly Anti-de-Sitter space,PTEP2016(2016), no. 12 12C104, [arXiv:1606.01857]

    Pith/arXiv arXiv 2016

  39. [39]

    Engels¨ oy, T

    J. Engels¨ oy, T. G. Mertens, and H. Verlinde,An investigation of AdS 2 backreaction and holography,JHEP07(2016) 139, [arXiv:1606.03438]. – 44 –

    Pith/arXiv arXiv 2016