{"id":"ee1e4d39-ef98-46db-9b78-ae0cf4fadc7e","arxiv_id":"2512.18781","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"In a 2D holographic CFT, half-line entanglement after a local operator quench grows as (c/6)log t for unitary (uniform-then-Rindler) evolution but saturates to (c/6)log(κO/aε) for non-unitary (Rindler-then-uniform) evolution, with the difference set by the partition function.","lead":"This paper asks whether the order of two types of time evolution — a probability-preserving one and a 'fake-time' one — changes how entanglement grows after a local burst of energy in a holographic system. The order decides: entanglement keeps growing logarithmically in one order and freezes to a steady value in the other, and the paper traces the freeze to a decaying normalization factor.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The e^{-2πi} branch for the anti-holomorphic cross-ratio at t = x1 − x is the pivotal assumption behind Eq. (3.55); the winding-geodesic check does not independently fix it for the semi-infinite interval.","rationale":"The reader’s weakest assumption is exactly the branch prescription for the anti-holomorphic cross-ratio, and I find this to be the most load-bearing point in the paper. Eq. (3.55) is the central claim, and the plateau/log dichotomy is not a minor detail: it drives the partition-function interpretation, the energy-density mechanism in Sec. 3.10, and the gravity-side discussion of horizons. The manuscript derives the finite-interval entanglement entropy by two methods and shows numerical agreement in Figs. 2–3, which supports the conformal-block plus geodesic framework in that regime. However, for the semi-infinite interval — the case where the dichotomy is strongest — the winding-geodesic computation is not shown to select the e^{−2πi} branch; the winding construction and the block formula are both part of the same analytic-continuation prescription, so they do not constitute an independent proof. The concern is concrete and addressable: a direct monodromy computation of the vacuum block, or a geodesic minimization with x2 → ∞, would settle whether the branch choice is correct. This does not force a rejection; it supports maintaining the conditional verdict, since the result is plausible but rests on a prescription that should be verified.","tokens_in":73653,"tokens_out":15150,"duration_ms":155198,"concrete_test":"Compute the anti-holomorphic vacuum Virasoro conformal block (e.g., via Zamolodchikov recursion) at c = 100, h_O = 5h_0, aε = 10^{-4}, for η̄ = 1 + i ε f̄, continuing t through t = x1 − x along the physical iε path. Check whether the logarithm of the full block including prefactors equals c/6 log[2κ_O/(ε f̄)] on the branch that keeps Im log continuous. Equivalently, evaluate the geodesic length (3.101) in the x2 → ∞ limit with different winding numbers (m, m̄) and take the minimum; if a pair other than the branch-equivalent (0,0) dominates for t > x1 − x, Eq. (3.55) changes.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The late-time dichotomy — saturation for i=1 and (c/6) log t growth for i=2 — is controlled by the branch prescription for η̄_i as it passes through infinity at t = x1 − x (Sec. 3.6.1). The paper uses η̄_i → e^{−2πi} η̄_i (Eqs. (3.52)–(3.53)); without this phase the factor in Eq. (3.50) tends to 1 and ΔS_{A;i} → 0, while with it one obtains the factor 2κ_O/(ε f̄_i) that produces Eq. (3.55). This branch choice is physically plausible and standard, but it is not derived from the monodromy of the semiclassical block. The claimed independent support from winding geodesics (Sec. 3.8.2) is not fully independent: the winding construction via (3.99)–(3.101) is formulated in terms of the same boundary maps f(z), f̄(z̄) that already encode the branch choice, and for the semi-infinite interval, where the central claim is made, no explicit geodesic minimization over winding numbers is presented. The identity-block formula (3.12) is also assumed to remain valid as η, η̄ → 1 on the chosen sheet. A different monodromy of the vacuum block, or a competing block contribution, would change the κ_O factor and hence which of the plateau/log behaviors is selected. The central claim is therefore conditional on an unproved analytic-continuation/manifold choice.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper analyzes a family of local-operator quenches in 2D holographic CFTs where the initial operator insertion is followed by a composite evolution consisting of a Euclidean Rindler Hamiltonian and a uniform Lorentzian Hamiltonian in two possible orders (Eq. (2.1)). Using holographic conformal blocks in the large central charge limit, the authors derive analytic expressions for the entanglement entropy of finite and semi-infinite intervals (Eqs. (3.44), (3.54)) and for mutual information. The central result is the late-time dichotomy for a semi-infinite interval: the non-unitary ordering i=1 gives ΔS_{A;1} ≈ (c/6) log(κ_O/aε), while the unitary ordering i=2 gives ΔS_{A;2} ≈ (c/6) log(κ_O t/(aε x)) (Eq. (3.55)). The authors also compute energy-momentum expectation values, construct the Bañados dual geometry, identify a black brane with a spacetime-dependent horizon, and propose a quasiparticle/energy-density mechanism. A holographic geodesic computation with winding numbers reproduces the CFT results for the finite interval.","tokens_in":73959,"tokens_out":6670,"duration_ms":59890,"significance":"If correct, the paper provides a concrete, falsifiable prediction about time-ordering effects: whether half-line entanglement entropy saturates or grows logarithmically is tied to unitarity of the composite evolution. The analytic formulas are explicit and internally consistent, with branch choices stated; the geodesic computation in Sec. 3.8.2 provides a genuine cross-check for the finite interval. The paper also derives the gravity dual and identifies the horizon shape, adding a geometric perspective. The main weakness is that the pivotal late-time dichotomy rests on an unproved analytic-continuation branch choice and on identity-block dominance, which need to be justified directly.","major_comments":[{"comment":"The late-time separation between ΔS_{A;1} and ΔS_{A;2} is entirely controlled by the phase shift ¯η_i → e^{-2πi} ¯η_i applied when t passes x_1 − x. This prescription is stated, not derived. The claimed independent support from winding geodesics (Sec. 3.8.2) does not fully close the gap: the maps in Eqs. (3.80)/(3.84) and the winding transformations (3.99)–(3.101) already contain the same branch choice, and for the semi-infinite interval no explicit minimization over winding numbers is presented. Please provide a direct derivation of the branch (e.g., from the Lorentzian iε continuation or from the monodromy of the vacuum block), or an explicit half-line geodesic computation, to make Eq. (3.55) unconditional.","section":"Sec. 3.6.1, Eqs. (3.52)–(3.55)"},{"comment":"The derivation assumes identity-block dominance of the semiclassical Virasoro block for η, η̄ ≃ 1 on the selected sheet. The late-time κ_O factor, and hence the plateau-vs-log selection, depends on this assumption. The paper does not specify the precise parameter regime where the approximation is controlled, nor does it quantify corrections from other blocks. Since the central claim is made for generic heavy operators, this dominance should be checked (analytically or numerically) rather than assumed.","section":"Sec. 3.2, Eq. (3.12)"}],"minor_comments":[{"comment":"Equation (4.20) inverts the square root relative to Eq. (4.19). From u'^min_{h;i} = L_AdS x a ε / (2 r_h) and r_h/L_AdS = sqrt(24 h_O/c − 1), the condition u'^min ≥ 1 reads 1 ≤ (x a ε / 2) / sqrt(24 h_O/c − 1), not 1 ≤ (x a ε / 2) sqrt(24 h_O/c − 1).","section":"Sec. 4.2, Eq. (4.20)"},{"comment":"The notation Z^0_{a;i} is ambiguous: the text and Eq. (3.45) indicate the relevant ratio is the right-moving (anti-holomorphic) partition function, but the subscript a is not defined. Please clarify which component is used and define Z^0_{a;i}.","section":"Sec. 3.10.2, Eq. (3.123)"},{"comment":"The post-selection interpretation requires the existence of a bounded Hermitian operator H_s satisfying cos(μH_s) = e^{-εH_R}. This is an ad hoc assumption; the paper should present it as a heuristic analogy or provide an argument for existence.","section":"Sec. 3.4, Eq. (3.38)"},{"comment":"The manuscript contains numerous typos and formatting artifacts (e.g., 'Bana˜ndos', inconsistent spacing, garbled subscripts in Appendix D). A careful proofread is needed.","section":"Throughout"}],"recommendation":"major_revision","confidential_remarks":"The branch-choice issue is the main obstacle to acceptance. If the authors can supply a derivation of the e^{-2πi} phase from the Lorentzian continuation or an independent half-line geodesic calculation, the paper would be a solid contribution. The mechanism section (3.10.2) relies on the companion paper [40]; the editors may wish to check the status of that reference. The manuscript is overlong; some appendices could be trimmed."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know. First, the paper cleanly demonstrates in an infinite-line holographic CFT that the late-time growth of entanglement after a local operator quench depends on whether the composite evolution is unitary: i=2 (e^{-iH0t}e^{-εH_R}) gives (c/6) log t, while i=1 (e^{-εH_R}e^{-iH0t}) gives a constant saturated value. The mechanism is the time dependence of the norm/partition function, and Eq. (3.55) is the key result. Second, the result is derived twice, via semiclassical conformal blocks and via holographic geodesics, and the agreement is genuine.\n\nWhat is new: the infinite-line realization of the ordering dichotomy, the explicit partition-function mechanism (Sec. 3.10.2), and the spacetime-dependent horizon shape for heavy operators. The paper credits its own earlier compact-system work [40,91] for the qualitative effect, which is honest.\n\nWhere the soft spots are: the branch choice for the anti-holomorphic cross-ratio at t = x1- x is the load-bearing step. The paper uses η̄ → e^{-2πi} η̄ to convert a vanishing factor into a finite log (Eqs. 3.52-3.54). This is a standard analytic continuation and physically plausible, but the winding-geodesic argument in Sec. 3.8.2 does not independently settle it for the semi-infinite limit: the finite-interval figures select (m,m)=0, and the semi-infinite limit is taken without an explicit minimization over windings. So the central plateau-vs-log claim is conditional on that branch choice. I do not think it is fatal—the choice is natural and consistent with the finite-interval analysis—but a referee should ask for a direct justification or an explicit asymptotic geodesic computation. Also the i=1 saturation value (c/6)log(κ_O/aε) depends on the regulator ε, and the paper does not contrast this with the universal quantum-dimension saturation seen in other local quench setups (Ref. [58]); that is a minor gap in discussion.\n\nOne thing in the reader's report does not hold up: the alleged algebraic slip in Eq. (4.20). Substituting r_h/L_AdS = sqrt(24h/c -1) into (4.19) gives exactly x aε/(2 sqrt(...)), so I think the equation is correct.\n\nOverall: this is a solid, well-written paper that makes a concrete prediction about ordering effects in local quenches. The math is mostly explicit, the limitations are disclosed, and the central mechanism is clean. It deserves a serious referee; the branch issue should be raised but is addressable. I would cite it if I worked on holographic quenches.","headline":"A mostly solid paper: the late-time plateau-vs-log dichotomy is a clean mechanism, but the central claim rests on a cross-ratio branch choice that is plausible yet not fully pinned down for the semi-infinite case.","tokens_in":74592,"tokens_out":6756,"would_cite":true,"duration_ms":62563,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["11.25.Hf","03.67.Mn"],"model":"deepseek-v4-flash","headline":"In a 2D holographic CFT, reversing the order of Euclidean and Lorentzian time evolutions flips late-time entanglement growth from logarithmic to saturated.","keywords":["entanglement entropy","local operator quench","holographic CFT","Rindler Hamiltonian","conformal blocks","Ryu-Takayanagi formula","BTZ black brane","non-unitary time evolution"],"falsifier":"Compute the exact late-time entanglement entropy for a semi-infinite interval in a solvable CFT (e.g., free boson or free fermion) under the same Rindler/uniform composite evolution: the branch-prescription mechanism predicts that the non-unitary (i=1) protocol saturates while the unitary (i=2) protocol grows logarithmically; if both orderings produce the same late-time scaling, the dichotomy would be an artifact of the holographic large-c approximation.","tokens_in":73400,"feed_emoji":"🌀","tokens_out":4923,"duration_ms":48753,"temperature":0.7,"pith_summary":"This paper studies entanglement growth in a 2D holographic CFT after acting on the vacuum with a primary operator and then evolving with a composite of the Rindler Euclidean Hamiltonian and the uniform Lorentzian Hamiltonian in two opposite orders. It claims that for a semi-infinite interval, the late-time entanglement entropy grows logarithmically when the Euclidean evolution is applied first and then the Lorentzian one (a unitary process), while it saturates to a constant when the order is reversed (a non-unitary process). The difference is traced to the time dependence of the norm (partition function) of the state. If correct, this shows that whether half-line entanglement keeps growing at late times is controlled simply by unitarity of the composite evolution, offering a general criterion for other quench protocols.","feed_headline":"Unitarity decides half-line entanglement growth after a local quench","feed_subtitle":"In a holographic CFT, reversing evolution order flips late-time entanglement from log growth to a plateau.","key_machinery":"The argument rests on the semi-classical expansion of holographic conformal blocks in the limit where the cross ratios η_i and η̄_i are close to one, with the identity operator and its descendants dominating. The late-time behavior is controlled by the analytic continuation of the anti-holomorphic cross-ratio: at t = x_1 - x, η̄_i passes through infinity and the paper shifts its phase by e^{-2πi}, converting the η̄ → 1 limit into a factor 2κ_O/(ε f̄_i). The winding geodesics in the Bañados/AdS3 gravity dual, computed via the Ryu-Takayanagi formula, provide support for this branch choice. The partition functions Z^0_i of the two protocols carry the unitary versus non-unitary distinction, and","core_discovery":"The paper's central discovery is a late-time dichotomy for the entanglement growth of a semi-infinite interval after a local operator quench with a composite evolution built from Euclidean Rindler and Lorentzian uniform Hamiltonians. When the Lorentzian evolution is applied first and then the Euclidean one (i=1), the protocol is non-unitary, the partition function decays as t^{-2h_O}, and the entanglement growth saturates to (c/6) log(κ_O/(aε)). When the Euclidean evolution is applied first (i=2), the protocol is unitary, the partition function is time-independent, and entanglement grows as (c/6) log(κ_O t/(aε x)). The ratio of partition functions fixes the difference between the two protoco","pith_inferences":["If unitarity of the composite evolution is the controlling factor, similar saturation-versus-log behaviors would be expected in other non-unitary protocols, such as monitored or post-selected dynamics, wherever the partition function decays in time.","The identification of the Euclidean evolution with a post-selecting projective measurement (Sec. 3.4) suggests the non-unitary protocol could be interpreted as a monitored evolution, and the late-time saturation might be a signature of measurement-induced dynamics in a holographic CFT.","The branch-prescription dependence is a potential weak point; computing the full Virasoro conformal block without assuming identity-dominance for moderate h_O/c values could test whether the dichotomy survives.","The horizon shape in the gravity dual, with two minima propagating at the speed of light, may serve as a bulk observable that distinguishes unitary from non-unitary quench protocols."],"forward_implications":["For a semi-infinite interval in a 2D holographic CFT, late-time entanglement after a local operator quench depends on the time-ordering of Euclidean and Lorentzian evolutions.","Unitary composite evolution produces logarithmic growth of half-line entanglement, while non-unitary evolution produces saturation to a constant determined by the operator's conformal dimension.","The difference is governed by the time dependence of the partition function (norm) of the state: a decaying norm cancels the would-be logarithmic growth.","For heavy primary operators, the gravity dual is a black brane with a spacetime-dependent horizon whose closest approach to the boundary occurs at the initial insertion point of the local operator.","The mutual information between two distant intervals also shows time-ordering effects, with time-dependent phase transitions between connected and disconnected Ryu-Takayanagi surfaces."],"fun_headline_variants":["Unitary quench gives log growth, non-unitary plateaus","Holographic quench: order flips entanglement growth from log to constant","Late-time entanglement: unitarity decides log vs plateau in CFT","Time-ordering in local quench turns log growth into saturation","Non-unitary evolution caps entanglement, unitary keeps growing"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The late-time plateau-versus-log dichotomy rests on a specific analytic-continuation branch choice for the anti-holomorphic cross-ratio at the moment it passes through infinity (the e^{-2πi} phase shift), which is supported but not proved by the winding-geodesic calculation.","fun_headline_variants_meta":{"raw":{"variants":["Unitary quench gives log growth, non-unitary plateaus","Holographic quench: order flips entanglement growth from log to constant","Late-time entanglement: unitarity decides log vs plateau in CFT","Time-ordering in local quench turns log growth into saturation","Non-unitary evolution caps entanglement, unitary keeps growing"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00019,"raw_usage":{"total_tokens":1186,"prompt_tokens":766,"completion_tokens":420,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":510,"completion_tokens_details":{"reasoning_tokens":341}},"tokens_in":510,"tokens_out":420,"duration_ms":4188,"temperature":1.0,"reasoning_tokens":341,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-03T14:55:12.057354+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the exact late-time entanglement entropy for a semi-infinite interval in a solvable CFT (e.g., free boson or free fermion) under the same Rindler/uniform composite evolution: the branch-prescription mechanism predicts that the non-unitary (i=1) protocol saturates while the unitary (i=2) protocol grows logarithmically; if both orderings produce the same late-time scaling, the dichotomy would be an artifact of the holographic large-c approximation.","supporting_citations":[],"review_version":1}