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REVIEW 4 major objections 5 minor 32 references

This paper constructs a time-like Janus solution and argues it is a holographic toy model of a global quantum quench, matching CFT one-point functions and late-time entanglement entropy despite a broken null energy condition.

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2026-08-05 12:06 UTC pith:6THZQSMG

load-bearing objection Clean new time-like Janus solution, but the claimed global-quench agreement rests on an EE comparison that is really vacuum entropy and an unresolved O(γ²) stress tensor. the 4 major comments →

arxiv 2509.01925 v1 pith:6THZQSMG submitted 2025-09-02 hep-th

Time-like Janus Solution -- holographic global quantum quench --

Kenta Suzuki This is my paper
classification hep-th
keywords time-like Janus solutionholographic global quantum quenchconformal perturbation theoryholographic entanglement entropynull energy conditionEinstein-dilaton gravityinterface conformal field theoryscalar perturbation stability
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 builds an exact, smooth solution of three-dimensional Einstein–dilaton gravity that asymptotically looks like anti-de Sitter space but is foliated by two-dimensional de Sitter slices, with a dilaton that changes in time. To keep the geometry nonsingular the deformation parameter must be taken purely imaginary, and the price is that the null energy condition is violated. The author's proposal is that the dual field theory is a two-dimensional conformal field theory with a sudden, spatially uniform perturbation at t = 0 — a global quantum quench — realized as conformal perturbation theory with a time-dependent imaginary source. The bulk one-point function of the operator dual to the dilaton comes out as ⟨O⟩ = −iγ/(2t²), the stress tensor vanishes, and the late-time entanglement entropy equals c/3 log(ℓ/a), all consistent with the proposed CFT picture. The main caveat, stated in Section 8, is that the geometry is covered by two patches that do not join smoothly; all checks are done on one patch under the assumption that a conjectured shock wave at t = ±z does not change the results.

Core claim

The centerpiece is the exact solution (2.15)–(2.17): ds² = dρ² + f(ρ)(−dη² + dx²)/η² with f(ρ) = [−1 + √(1 + 2γ²) cosh(2ρ)]/2 and a complex dilaton. This is a time-like Janus solution: the dilaton interpolates between different constant values in the t > 0 and t < 0 asymptotic regions, so the dual is an interface CFT with the interface extended in space at t = 0. The paper argues the interface is a global quench and identifies the dual action as conformal perturbation theory with source γ[θ(t)φ₊⁽¹⁾ + θ(−t)φ₋⁽¹⁾]O. The evidence is that the bulk one-point function ⟨O⟩ = −iγ/(2t²) for t > 0 is reproduced at first order in perturbation theory, that the holographic stress tensor vanishes, and tha

What carries the argument

The engine is the dS₂-sliced Janus ansatz, ds² = dρ² + f(ρ)ds²_dS₂ with a dilaton depending only on ρ. A Janus solution is a domain-wall geometry in AdS whose dilaton interpolates between two constant values; here the interpolation is in time rather than space. The ansatz reduces Einstein–dilaton to the ODE system (2.6)–(2.8), whose solutions split into a space-like branch and the time-like branch. The key move is the analytic continuation of the deformation parameter γ → iγ, which removes the naked singularity that would otherwise appear in the time-like solution at the cost of a complex dilaton and negative null energy. On the boundary side, the carrying object is conformal perturbation th

Load-bearing premise

The results in Sections 3–5 are computed entirely on one patch of the two-patch geometry; Section 8 says the patches do not connect smoothly, so the central claims depend on the conjectured shock wave at t = ±z not changing one-point functions, extremal surfaces, or perturbation modes.

What would settle it

A concrete calculation would be to derive the shock-wave geometry at t = ±z and compute the HRT surface for an interval with t₀ < ℓ/2; the paper's quench interpretation requires this to reproduce the CFT's early-time linear entropy growth, so a different result, or the absence of a nonsingular shock completion, would refute the central claim.

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If this is right

  • A global quantum quench in a two-dimensional CFT acquires a concrete geometric dual: a time-dependent dilaton profile localized at t = 0, nonsingular on its patch.
  • The matching forces C_OOO = 0 and likely C_TOO = 0, giving explicit predictions for the OPE data of any dual CFT.
  • For late times the holographic entanglement entropy saturates to the static interval value c/3 log(ℓ/a), so the late-time state behaves like the vacuum on a finite interval; the early-time linear growth is not yet derived from the bulk.
  • The same construction extends to finite temperature, yielding a time-dependent black hole whose one-point function has the factor (2π/β)²/sinh²(2πt/β), and to higher dimensions where the one-point function scales as t^(−d).
  • The violation of the null energy condition does not by itself destabilize the geometry: a massless scalar perturbation is stable on this background.

Where Pith is reading between the lines

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

  • Extension: the early-time linear-growth regime of entanglement entropy is the natural testing ground: if a shock-wave completion at t = ±z is written down, the HRT surface for t₀ < ℓ/2 should reproduce S_A ∝ t₀; if it does not, the quench picture needs revision.
  • Extension: because the source is imaginary, the dual CFT is complex-coupled or effectively non-unitary; a precise statement about which real observables are protected would clarify how literally the quench interpretation should be taken.
  • Extension: the vanishing C_OOO and C_TOO constraints could be checked directly in any candidate dual CFT: a nonzero value at O(γ²) would break the bulk-boundary match.
  • Extension: the same imaginary-continuation construction suggests a general recipe for singularity-free time-like Janus backgrounds in d ≥ 3, and the numerical metric functions in Section 7 can be used to test whether the simple 1/t^d one-point form persists at finite γ.

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

4 major / 5 minor

Summary. This paper constructs an exact time-like Janus solution in AdS3 with a complex dilaton, obtained by analytically continuing the Janus deformation parameter to a pure imaginary value. The geometry (2.15)-(2.17) is smooth, asymptotically AdS3, and violates the null energy condition. The paper proposes that the dual boundary theory is a 2D CFT deformed by a global-quench-type source (3.14), and computes holographic one-point functions of the scalar operator and the stress-energy tensor, holographic entanglement entropy, and stability against scalar perturbations. It also generalizes the solution to finite temperature and higher dimensions. The central claims are that the bulk observables agree with conformal perturbation theory and support a global-quench interpretation.

Significance. The exact solution and the O(γ) scalar one-point function are clean and internally consistent; the Appendix B conformal perturbation theory integrals are detailed and useful. If the missing shock-wave glue and the unresolved C_TOO issue were addressed, the construction could serve as a tractable toy model of holographic global quench. As it stands, however, the quantitative evidence for the quench picture is not established: the entanglement entropy result is the vacuum entropy rather than the late-time quench entropy, and the proposed CFT gives a nonzero O(γ²) stress tensor unless an unconstrained OPE coefficient vanishes. The strength of the paper is the explicit solution and the one-point function structure, not the holographic checks.

major comments (4)
  1. [Section 4, Eq. (4.7) and footnote 2] The paper claims that the bulk holographic entanglement entropy (4.7), S_A = (c/3) log(ℓ/a), is consistent with the CFT quench computation [27] quoted in footnote 2 as S_A = cπℓ/(12a). These are not the same limit: (4.9) is the high-temperature extensive result (β_eff = 4a) valid for ℓ ≫ β_eff, whereas (4.7) is the vacuum zero-temperature result. The footnote's statement that (4.7) 'simply corresponds to the zero temperature limit' does not reconcile the two, because the zero-temperature limit of the thermal formula is (c/3) log(ℓ/a), not (4.9). Moreover, the HRT surface used for (4.7) lies entirely in the blue patch at large ρ and never crosses the conjectured shock at t=z, so it sees only a small deformation of AdS3 and contains no information about the quench. The claimed agreement with the CFT quench computation is therefore unsupported.
  2. [Section 8 and Section 4] The global geometry is defined on two patches that meet with a finite metric but discontinuous derivative at t=±z. Section 8 explicitly states that the metric 'does not connect smoothly' and relegates the glue to a conjectured shock wave. All bulk calculations in Sections 3-4 assume that the probes (geodesics, HRT surfaces) stay inside one patch. For the entanglement entropy, the t0 ≫ ℓ regime enforces this assumption, but then the surface never probes the quench region; for t0 < ℓ/2 the extremal surface crosses the patch boundary and the computation is not defined without a constructed shock. Thus the central observable used to support the global-quench interpretation is not actually computed in the full geometry.
  3. [Section 3, Appendix B, Eqs. (B.20)-(B.21)] The proposed dual CFT (3.14) predicts a nonzero O(γ²) stress tensor, ⟨Ttt⟩ = ⟨Tyy⟩ = -3π² C_TOO (ϕ_+^(1))² γ²/(4 t²), unless C_TOO = 0. The bulk computation (3.13) gives ⟨Tμν⟩ = 0. The manuscript states that consistency 'might imply' C_TOO = 0 but leaves this question open. This is an unresolved contradiction between the claimed dual and the bulk solution at the same order as the proposed CFT, and it undermines the abstract's statement that the results are 'consistent with the proposed CFT picture.'
  4. [Section 3, Eqs. (3.14)-(3.16)] The matching of ⟨O⟩ between bulk and CFT fixes only the functional form, not the numerical coefficient. The source strength ϕ_±^(1) in (3.14) is read off from the near-boundary behavior of the bulk dilaton (3.1)-(3.2), and the normalization a of the two-point function (3.16) is left unrestricted. The CFT expression (3.15) therefore agrees with the bulk (3.5) for any a, up to an overall coefficient. The paper acknowledges this in passing, but the abstract's word 'confirm' overstates the content of the check; the comparison is structural rather than a quantitative prediction.
minor comments (5)
  1. [Section 2, Eq. (2.13)] The line 'R = (ϕ)^2 − 6' contains a typo; it should read R = ϕ′^2 − 6.
  2. [Section 2.1] Typo: 'ansazt' should be 'ansatz'.
  3. [Section 4, footnote 2] 'for later timet0 > ℓ/2' is missing a space. More importantly, the footnote's statement that (4.7) is the zero-temperature limit of (4.9) should be corrected, as these are different limits of the thermal formula.
  4. [Section 3, Eq. (3.9)] The shift ρ -> ρ - 1/4 log(1+2γ²) is introduced to achieve Gaussian normal coordinates, but the derivation is not given. A short explanation would improve readability.
  5. [End of Section 2] The sentence 'This solution is not just a simple Wick rotation from the Euclidean version of the usual space-like Janus solution' is cryptic; a brief reference to the branch structure in Appendix A would help the reader understand the distinction.

Circularity Check

0 steps flagged

No significant circularity: the exact bulk solution is derived independently, and the CFT comparisons are explicitly consistency checks with undetermined normalizations or acknowledged limits.

full rationale

The time-like Janus solution (2.15)-(2.17) is obtained by directly solving the Einstein and Klein-Gordon equations; no load-bearing step reduces to a self-citation. The CFT one-point-function comparison in Sec. 3 is a standard source/response consistency check: the source in (3.14) is read off from the near-boundary value of the bulk dilaton (3.1)-(3.2), and the bulk ⟨O⟩ is the corresponding subleading coefficient. The paper explicitly states that the CFT result agrees 'up to the overall numerical coefficient', leaving the normalization a of the unperturbed two-point function free. Thus no fitted parameter is renamed as a prediction; the check fixes functional structure, not numbers, and the paper does not claim more. The stress-tensor check is incomplete at O(γ²), but the text explicitly says the integrals have not yet yielded vanishing results and leaves the question to future work. The entanglement entropy in Sec. 4 is the standard vacuum AdS3 interval entropy (4.7); footnote 2 explicitly states that the cited CFT quench result (4.9) is the high-temperature limit and that (4.7) 'simply corresponds to the zero temperature limit.' Therefore the claim of agreement with the quench computation is overstated, but it is an explicit limitation rather than a circular reduction. Sections 5-7 present self-contained stability, finite-temperature, and general-dimension analyses. The self-citations [13,14] in the introduction are not load-bearing for the main construction. Overall: no load-bearing circularity.

Axiom & Free-Parameter Ledger

2 free parameters · 6 axioms · 1 invented entities

The constructed solution introduces one free parameter (γ), and the CFT check leaves one normalization (a) unfixed. The interpretive layer rests on domain assumptions: the AdS/CFT dictionary, the legitimacy of a complex NEC-violating saddle, the proposed conformal perturbation theory, the conjectured constraints on CFT data (C_OOO = 0, C_TOO = 0), the chosen Dirichlet boundary condition in the stability analysis, and single-patch probe physics. No genuinely new entity is introduced except a conjectured shock wave with no independent evidence.

free parameters (2)
  • γ (time-like Janus deformation parameter) = free real parameter, γ > 0; obtained from γ̂ = iγ
    Integration constant of the dilaton Klein-Gordon equation (2.9). Continued to imaginary values to remove the naked singularity of the naive time-like Janus solution. It sets the strength of the quench source in (3.14) and appears in every one-point function and in the stability and EE analysis.
  • a (OPE normalization of the unperturbed CFT) = undetermined
    Coefficient of the two-point function ⟨O O⟩ in (3.16). The CFT result for ⟨O⟩ matches the bulk result only up to this coefficient ('agrees with the bulk computation up to the overall numerical coefficient'); the paper does not fix a from an independent CFT, so the match is structural.
axioms (6)
  • domain assumption The standard AdS3/CFT2 dictionary: holographic stress tensor (3.7), Brown-Henneaux central charge c = 3/(2G_N) (4.8), and the HRT prescription for entanglement entropy (Section 4, Appendix C)
    Invoked to convert bulk quantities into CFT data; standard but load-bearing for the interpretation.
  • ad hoc to paper The dual of the time-like Janus is the conformal perturbation theory (3.14) with imaginary source iγ(θ(t)ϕ_+^(1) + θ(-t)ϕ_-^(1))O
    Proposed in Section 3, not derived. The source is read off from the bulk dilaton's asymptotic values, and the matching CFT is not independently identified beyond perturbation theory.
  • ad hoc to paper The CFT data satisfy C_OOO = 0 and, for stress-tensor consistency, C_TOO = 0
    C_OOO = 0 is deduced in (3.18) from the absence of an O(γ²) term in the bulk ⟨O⟩; C_TOO = 0 is conjectured in Section 3 and Appendix B because otherwise ⟨T_μν⟩ does not vanish at O(γ²).
  • domain assumption The complexified, NEC-violating saddle (γ̂ = iγ, complex dilaton (2.17)) is a legitimate solution to use for the holographic correspondence
    The action (2.1) is real, so the complex dilaton is a complex saddle, not a real Lorentzian solution. The paper adopts this without a contour or saddle-point justification, following the pseudo-entropy practice of [16].
  • ad hoc to paper Scalar perturbations obey the conformal Dirichlet boundary condition selecting G(η) = √η J_ν(kη) rather than the Bunch-Davies vacuum
    Section 5. The alternative Hankel choice is discarded as divergent; the chosen condition is argued from AdS naturalness but determines the stability conclusion.
  • domain assumption Probes stay inside a single dS2-slice patch (ρ > 0 with t > 0), and the t = ±z boundary can be treated as a conjectured shock wave
    Sections 2.1 and 8. The two patches do not connect smoothly; all computations are single-patch, and early-time extremal surfaces would cross the boundary where the geometry is not defined without the conjectured shock wave.
invented entities (1)
  • Shock wave at t = ±z (conjectured) no independent evidence
    purpose: Gluing the two patches of the time-like Janus solution and explaining early-time linear entanglement growth
    Proposed only in Section 8 ('This type of discontinuity might be understood as a shock wave propagating at the speed of light'). No metric, stress tensor, or quantitative prediction for it is given, so it has no falsifiable handle outside the paper.

pith-pipeline@v1.4.0-alltime-deepseek-medium · 25048 in / 31604 out tokens · 320644 ms · 2026-08-05T12:06:11.828667+00:00 · methodology

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Cite this review

Pith. "Pith review of Time-like Janus Solution -- holographic global quantum quench --." pith.science (2026). https://pith.science/paper/6THZQSMG

@misc{pith2026250901925,
  author       = {Pith},
  title        = {Pith review of: Time-like Janus Solution -- holographic global quantum quench --},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6THZQSMG}},
  note         = {Machine review of arXiv:2509.01925}
}
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read the original abstract

We construct a time-like Janus solution, which is mediated by a time-dependent dilaton field in asymptotic AdS spacetime. This solution breaks the null energy condition, but we argue that it is nevertheless useful as a toy model of holographic global quantum quench. The dual CFT is given by conformal perturbation theory, where the primary scalar operator that is dual to the bulk dilaton field is coupled with a global-quench-type time-dependent source. We compute one-point functions of the scalar operator and the stress-energy tensor, and confirm that the results are consistent with the proposed CFT picture. We also evaluate the holographic entanglement entropy for late time after the global quench, and show that the result agrees with the CFT computation. The stability of the time-like Janus solution against a scalar perturbation is also discussed.

Figures

Figures reproduced from arXiv: 2509.01925 by Kenta Suzuki.

Figure 1
Figure 1. Figure 1: A schematic picture of AdS2 slicing and dS2 slicing of AdS3 spacetime. where η > 0 and ρ > 0, which lead to ds2 3 = dρ2 + sinh2 ρ  −dη2 + dx2 η 2  . (1.5) This metric covers the upper triangle of the left panel in figure 2. For the t < −z region, we need to use coordinate transformations t = −η coth ρ , z = − η sinh ρ , (1.6) with ρ < 0, which again lead to the metric (1.5), but it now covers the lower t… view at source ↗
Figure 2
Figure 2. Figure 2: The coordinates (ρ, η) cover the blue region in the left panel, and the coordinates (ˆρ, ηˆ) covers the pink region in the right panel. 2.1 Solution for the other patch Before discussing an application for the AdS/CFT correspondence, let us also consider the other patch. As we mentioned, the solution presented above only covers the blue patch depicted in the left panel in figure 2. In this patch, η is a ti… view at source ↗
Figure 3
Figure 3. Figure 3: (Left) a schematic picture of the dual ICFT. The interface is located at [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: A sketch of the potential V (f). The dilaton solution is given by (2.14) but now ρ is regarded a function of t and r as ρ = ρ(t, r). This relation can be fixed as follows. AdS3 spacetime can be embedded in four-dimensional hypersurface satisfying −X 2 0 + X 2 1 + X 2 2 − X 2 3 = −1 . (6.6) The AdS3 metric (6.3) is obtained by parametrization X0 = coth µ , X1 = x η sinh µ , X2 = −1 + x 2 − η 2 2η sinh µ , X… view at source ↗
Figure 5
Figure 5. Figure 5: Numerical solutions for f(u) in d = 3 (left) and d = 4 (right). From this asymptotic behavior and (2.16), we can identify p 1 + 2γ 2 4 e 2ρ ≈ 1 sinh2 (µ∗ − µ) , (6.20) where ≈ means that this is an asymptotic relation. Therefore, the asymptotic behavior of the dilaton (3.3) can be now written as ϕ(ρ) = ϕ+ − 2iγ p 1 + 2γ 2 e −2ρ + · · · = ϕ+ − iγ 2 (µ∗ − µ) 2 + · · · = ϕ+ − iγ 2  2π β 2 1 sinh2 ( 2πt β ) … view at source ↗

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Reference graph

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