{"id":"2705516c-b8f8-4c48-9745-861354565cb8","arxiv_id":"2509.01925","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"A time-like Janus solution with imaginary deformation parameter is proposed as a holographic toy model of a global quantum quench, with partial consistency checks from CFT one-point functions and late-time entanglement entropy.","lead":"A new time-dependent version of the Janus geometry is constructed in AdS3, with a dilaton that varies in time and a deformation parameter analytically continued to imaginary values to remove a naked singularity. The paper proposes this space-time as a toy model of a holographic global quantum quench and checks the proposal with one-point functions and entanglement entropy.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Section 4's bulk EE (4.7)=c/3 log(ℓ/a) does not match the CFT quench result (4.9)=cπℓ/(12a) cited in footnote 2; the missing extensive term is tied to the unconstructed shock at t=z, so the claimed global-quench agreement is unsupported.","rationale":"The reader's weakest assumption was the two-patch non-smoothness. I agree that this is critical, but I identify the sharper and more concrete failure mode: even within a single patch, the computed observable (4.7) does not equal the CFT quench result (4.9) that the paper itself cites. The extensive thermal entropy expected after a global quench is absent precisely because the extremal surface never crosses the unconstructed shock. This is a direct internal inconsistency between two displayed equations, not a matter of external consensus. The one-point function match at O(γ) is a real structural success and the exact solution is valuable, so the verdict should remain CONDITIONAL as the reader proposed. My read does not change that verdict; it sharpens the condition: the shock wave must be constructed and the HRT surface recomputed, and the O(γ²) stress tensor must be resolved (C_TOO = 0 or a modified bulk computation) before the abstract's claim of agreement can be accepted. I therefore keep the reader's verdict unchanged.","tokens_in":25692,"tokens_out":11409,"duration_ms":139518,"concrete_test":"Construct the global geometry by imposing Israel junction conditions on a null shell at t = z (the boundary ρ = 0 of the two patches), using the jumps in f'(ρ) from (2.16) and (2.24). Then compute the HRT geodesic for an interval of length ℓ at t0 ≫ ℓ in this glued spacetime, including the segment inside the |t| < z patch. If the surface crosses the shell and the resulting S contains a term cπℓ/(12a), the quench interpretation is supported; if S remains c/3 log(ℓ/a) with no O(ℓ/a) term, Eq. (4.7) is not the late-time quench entropy and the Section 4 claim fails. A complementary check is to compute the entanglement entropy directly in the perturbed CFT (3.14) via replica trick, testing whether the complex, imaginary source yields the extensive term or indeed only the vacuum log.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that the time-like Janus solution is dual to a global quantum quench rests on agreement of bulk and CFT observables. The most load-bearing gap is the entanglement entropy. Section 4 computes S_A = (c/3) log(ℓ/a) in Eq. (4.7), under the approximations γ = O(ε), z/t0 = O(ε), t0 ≫ ℓ. Footnote 2 states that the CFT late-time quench result [27] is S_A = cπℓ/(12a), understood as the high-temperature limit with β_eff = 4a. These two expressions are not equal in the regime ℓ/a ≫ 1; (4.7) is the zero-temperature (β → ∞) limit of the thermal entropy formula, i.e., the vacuum entropy before any quench. Thus the paper's claim that the bulk EE agrees with the CFT quench computation is not supported by the text. The cause is structural: the global geometry is defined only on two patches that do not connect smoothly (Section 8), and the unconstructed shock wave at t = ±z is precisely the ingredient that, in standard holographic quenches, produces the extensive thermal entropy. Because the HRT surface used for (4.7) stays entirely in the blue patch at large ρ (t0 ≫ ℓ) and never crosses the conjectured shock, it sees only asymptotically AdS vacuum. The paper's own footnote 2 concedes the mismatch by saying the result 'simply corresponds to the zero temperature limit.' Until the shock is constructed and the extremal surface is recomputed including the glued region, the EE cannot be claimed as evidence for the quench picture. A secondary but related unresolved point is the O(γ²) stress tensor: Appendix B finds ⟨T_yy⟩ = -(3π² C_TOO (ϕ_+^{(1)})² / 4) γ²/t₁² + O(γ³), while the bulk gives (3.13) = 0; consistency requires C_TOO = 0, which is left open. Both items are flagged by the author as future work, but they sit exactly on the central claim.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":26085,"tokens_out":7129,"duration_ms":72283,"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":[{"comment":"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.","section":"Section 4, Eq. (4.7) and footnote 2"},{"comment":"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.","section":"Section 8 and Section 4"},{"comment":"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.'","section":"Section 3, Appendix B, Eqs. (B.20)-(B.21)"},{"comment":"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.","section":"Section 3, Eqs. (3.14)-(3.16)"}],"minor_comments":[{"comment":"The line 'R = (ϕ)^2 − 6' contains a typo; it should read R = ϕ′^2 − 6.","section":"Section 2, Eq. (2.13)"},{"comment":"Typo: 'ansazt' should be 'ansatz'.","section":"Section 2.1"},{"comment":"'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.","section":"Section 4, footnote 2"},{"comment":"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.","section":"Section 3, Eq. (3.9)"},{"comment":"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.","section":"End of Section 2"}],"recommendation":"major_revision","confidential_remarks":"The paper's central quantitative claim of entanglement-entropy agreement is not supported by the computation presented, and the paper's own footnote 2 effectively concedes the mismatch. The O(γ²) stress-tensor issue in Appendix B is also unresolved. These are fixable in principle—for example, by constructing the shock-wave glue and by proving or disproving C_TOO = 0—but they are load-bearing for the global-quench interpretation. The exact solution itself is interesting and the conformal perturbation theory calculations are competently done. I would not object to reconsideration after a major revision that either resolves these gaps or substantially softens the claims."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: Suzuki has a genuinely new exact solution—a time-like Janus background with complex dilaton that avoids the naked singularity of [16] by sending the deformation parameter imaginary, at the cost of NEC violation. The O(γ) conformal perturbation theory one-point function is a real structural check, and the stability analysis is a useful addition. But the paper's central claim that holographic observables match the proposed CFT quench picture is not fully earned. The EE computation in Section 4 gives S = (c/3) log(ℓ/a), which is just the vacuum AdS result; footnote 2 admits the CFT quench result is S = cπℓ/(12a) (high-temperature limit), so the two are not equal in the regime considered. The match is to the zero-temperature limit—i.e., before the quench. The stress tensor at O(γ²) is also nonzero from the CFT side unless C_TOO = 0, which is left open (eqs. B.20–B.21). The author honestly flags both issues in Section 8, but they sit exactly on the claim of consistency.\n\nThe global geometry only covers two patches that don't connect smoothly; a shock wave at t = ±z is conjectured, and all computations are done inside one patch. That makes the quench interpretation conditional on an unconstructed gluing. Similarly, the stability result covers a massless scalar with a specific boundary condition, not metric perturbations.\n\nWhat's genuinely good: the exact solution (2.15)–(2.17) is clean, the O(γ) one-point match works up to an overall normalization a, the finite-temperature and higher-dimensional generalizations are natural and likely correct. This is a meaningful step in the Janus program and a plausible toy model for holographic quenches.\n\nWho should read it: anyone working on holographic ICFTs, quenches, or pseudo-entropy; they'll find the construction useful and the open problems concrete. It deserves a serious referee—this should be reviewed, not desk-rejected—but the referee should require the stress tensor issue and the EE comparison to be addressed, or the claims toned down to match what is actually shown.\n\nMy recommendation: send it out, with a referee who will push on those two mismatches.","headline":"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.","tokens_in":26751,"tokens_out":2423,"would_cite":true,"duration_ms":26411,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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.","keywords":["time-like Janus solution","holographic global quantum quench","conformal perturbation theory","holographic entanglement entropy","null energy condition","Einstein-dilaton gravity","interface conformal field theory","scalar perturbation stability"],"falsifier":"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.","tokens_in":25388,"feed_emoji":"⏳","tokens_out":13125,"duration_ms":140947,"temperature":0.7,"pith_summary":"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.","feed_headline":"Time-like Janus geometry matches a global quantum quench","feed_subtitle":"An exact AdS3 solution matches quench one-point functions and late-time entropy despite violating energy conditions.","key_machinery":"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","core_discovery":"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","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Supplies the Einstein–dilaton Janus ansatz, the ODE reduction, and the finite-temperature black-hole construction this paper extends.","marker":"[8]"},{"why":"The earlier time-like Janus solution with a naked singularity that the paper cures by taking the deformation parameter imaginary.","marker":"[16]"},{"why":"Defines the global quantum quench and its time-dependent correlation functions, motivating the interface/quench interpretation.","marker":"[19]"},{"why":"Provides the conformal perturbation theory and splitting regularization used to derive the first-order one-point function ⟨O⟩.","marker":"[21]"},{"why":"Gives the three-point function involving the stress tensor and two operators, used to constrain the second-order CFT stress tensor.","marker":"[22]"},{"why":"Supplies the covariant HRT prescription needed because the boundary metric is time-dependent.","marker":"[23]"},{"why":"Provides the AdS₃ spacelike-geodesic distance formula used to evaluate the extremal surface in Section 4.","marker":"[25]"},{"why":"Supplies the central-charge dictionary c = 3/(2G_N) used to convert geodesic length into entanglement entropy.","marker":"[26]"},{"why":"Provides the CFT computation of entanglement growth after a quench that the holographic late-time result is compared with.","marker":"[27]"},{"why":"Supplies the BF bound in AdS₃ used to conclude that massless scalar perturbations are stable.","marker":"[29]"}],"fun_headline_variants":["Time-like Janus models global quantum quench","Janus with complex dilaton fits quench data","Exact AdS3 Janus solution as quench toy","Time-like Janus matches quench entropy and correlators","NEC violation but valid quench holography"],"cache_read_input_tokens":2688,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Time-like Janus models global quantum quench","Janus with complex dilaton fits quench data","Exact AdS3 Janus solution as quench toy","Time-like Janus matches quench entropy and correlators","NEC violation but valid quench holography"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000406,"raw_usage":{"total_tokens":1944,"prompt_tokens":740,"completion_tokens":1204,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":484,"completion_tokens_details":{"reasoning_tokens":1126}},"tokens_in":484,"tokens_out":1204,"duration_ms":12604,"temperature":1.0,"reasoning_tokens":1126,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-05T12:06:11.828667+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"Breitenlohner and D.Z","cited_arxiv_id":null,"evidence_quote":"Supplies the BF bound in AdS₃ used to conclude that massless scalar perturbations are stable."}],"review_version":1}