{"id":"fb0f1610-ea36-4e16-a204-52db117b3d38","arxiv_id":"2411.12420","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"Correlation functions of heavy operators can be computed from the on-shell action of a wedge excised from AdS3, verified in Poincaré, global, and BTZ backgrounds.","lead":"This paper proposes a new way to compute correlation functions of very heavy operators in a holographic CFT, using the gravitational action of a wedge-shaped slice of the curved spacetime. It checks the method in three different backgrounds and reports that one common coordinate choice gives wrong answers, a subtlety that matters for future calculations.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Exact equality (1.3) fails in Poincaré AdS beyond leading order: wedge action gives coefficient 2m, backreacted action gives 2Δ, differing at O((1−α)^2 log ε).","rationale":"The reader's conditional verdict and weakest-assumption both focus on the unproven wedge/conical equivalence at the level of the on-shell action. My stress-test agrees with that focus but sharpens it: in the one case where an exact comparison is possible, the proposed exact equality (1.3) is demonstrably false beyond leading order. This is an internal consistency check, not an outside-consensus objection: the exact backreacted calculation (Section 4), the exact wedge calculation (Appendix A), and the perturbative/numerical checks in Section 3 and Appendix C are all internally coherent. The problem is that the two sides of Eq. (1.3) are not actually equal: the wedge action carries the geodesic/probe exponent 2m, while the backreacted action carries the exact conformal exponent 2Δ = 2m(1−2G_N m). The difference is a self-energy correction of order G_N m². The paper's explicit probe-limit statements (Eqs. (3.8), (3.24), (3.43)) are therefore safe, but the exact formulation in Eq. (1.3) overstates the equivalence. Since the paper is otherwise careful and provides substantial numerical support, this concern does not overturn the conditional verdict; it does require either weakening Eq. (1.3) or identifying the missing subleading terms. I set agreement to 'partial' because the reader identified the same region of the argument but did not claim a concrete failure in the exactly solvable case.","tokens_in":28533,"tokens_out":29514,"duration_ms":282752,"concrete_test":"Evaluate Eq. (A.9) exactly, without expanding in η, for e.g. α = 1/2, β = 1, 8πG_N = 1, and compare −I_gravity,W with Eq. (4.19), I_BR = 4h log(2 csch β/ε), at the same cutoff ε. If the two differ at O((1−α)² log ε) for arbitrarily small ε, then Eq. (1.3) is only a probe-limit relation. A useful second check is to test whether adding the tip Hayward term with a different angle convention, or a boundary term at the FG wall (the surface of Eq. (4.24)), restores the equality; if no local boundary term removes the O((1−α)² log ε) mismatch, the wedge proposal must be reformulated as a leading-order construction.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing step is Eq. (1.3), which asserts an exact action-level equality between the excised wedge and the backreacted conical geometry. The Poincaré case is the one place where both sides can be evaluated in closed form, and the equality does not survive beyond leading order in the deficit angle. The direct backreacted on-shell action is Eq. (4.19): I_BR = 4h log(2 csch β/ε), with 4h = (1−α²)/(4G_N), so the correlation-function exponent is 2Δ = (1−α²)/(4G_N). Expanding the exact wedge computation in Appendix A in η = π(1−α) gives −I_gravity,W = η/(2πG_N) log(2 csch β/ε) + O(η³) = 2m log(2 csch β/ε) + O(η³), where 2m = (1−α)/(2G_N). Since 2Δ − 2m = −(1−α)²/(4G_N) ≠ 0, the dilogarithm and boundary Hayward terms in Eq. (A.9) do not supply the missing O((1−α)² log ε) contribution. Thus Eq. (1.3) is at best a leading-order/probe-limit identity; the exact backreacted computation and the wedge computation are computing different quantities beyond leading order. This should be stated explicitly in the paper, or the missing subleading terms identified.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a holographic method for computing two-point correlation functions of heavy scalar operators in AdS3/CFT2. The method replaces the backreacted conical geometry of a massive particle by an excised wedge bounded by two intersecting tensionless end-of-the-world branes and the AdS boundary, and extracts the correlator from the on-shell action of this excised geometry. This is tested in Poincaré AdS3, global AdS3, and BTZ, using exact, perturbative, and numerical computations. In a second, independent part, the paper constructs the backreacted geometries by coordinate transformations from the conical AdS3 solution and computes their on-shell actions in both the physical coordinate patch and Fefferman-Graham gauge. The authors find that the physical-patch actions reproduce the two-point functions, while the FG-gauge actions do not, extending a discrepancy reported in their earlier work.","tokens_in":28821,"tokens_out":8691,"duration_ms":91797,"significance":"If the wedge proposal were exact, it would provide a technically simple way to compute holographic correlators of heavy operators without constructing the full backreacted geometry, and the detailed case studies in this paper would be a useful toolbox. The paper has real strengths: the backreacted on-shell action computations in Section 4 are explicit and analytic; the integral computations are documented in appendices; and the numerical/perturbative cross-checks in Figures 6, 8, 9 and Tables 1, 2 are a valuable feature. The FG-gauge discrepancy is a concrete and interesting claim that is supported by several examples. However, the central identity Eq. (1.3) is presented as an exact action-level equality, and the paper's own Poincaré computation shows that it fails beyond leading order in the deficit angle. Because this identity is the basis of the wedge proposal, the significance of the wedge part depends on reframing it as a probe-limit/leading-order statement.","major_comments":[{"comment":"The central equality I_BR = I_AdS3 - I_gravity,W + I_m is not exact in the Poincaré case, where both sides can be evaluated in closed form. The wedge computation in Eq. (A.9) gives a leading logarithmic coefficient 2m = (1-α)/(2G_N), whereas the backreacted on-shell action Eq. (4.19) gives 4h = (1-α^2)/(4G_N) = 2Δ, using Eq. (3.7). Since 2Δ - 2m = -(1-α)^2/(4G_N), the two actions differ by an O((1-α)^2 log ε) term. The dilogarithm and boundary Hayward terms in Eq. (A.9) are of order η^3 or are finite, so they do not supply the missing contribution. Consequently Eq. (1.3) can only hold at leading order in the deficit angle, i.e., in the probe limit G_N m << 1. The authors should qualify Eq. (1.3) and the statements built on it, and either identify the subleading terms that would restore the equality or state explicitly that the wedge proposal is a probe-limit/leading-order statement in the present form.","section":"Sec. 1, Eq. (1.3); Sec. 3.1, Eqs. (3.6)-(3.8); Sec. 4.1, Eq. (4.19); Appendix A, Eq. (A.9)"},{"comment":"For global AdS and BTZ, the analytic verification of the wedge proposal is performed only at leading order in η, with higher-order corrections tested numerically in a limited parameter range (Tables 1 and 2). In view of the exact Poincaré discrepancy found in Major Comment 1, the same order of mismatch is expected beyond leading order in these cases. The text should therefore restrict the claim that the wedge on-shell action 'precisely reproduces' the two-point function to the leading-order/probe-limit regime in Sections 3.2 and 3.3 as well, not only in Section 3.1, and should note that the numerical checks cannot rule out an O(η^2 log ε) discrepancy of the kind present in the Poincaré case.","section":"Secs. 3.2 and 3.3; Appendix C"}],"minor_comments":[{"comment":"The relation Δ = m(1 - 2G_N m) is exact given Eq. (2.5) and c = 3/(2G_N); writing 'Δ = m(1 - 2G_N m) ≈ m' can obscure the fact that the exact relation already encodes the backreaction. The text should separate the exact formula from the probe-limit approximation Δ ≈ m.","section":"Sec. 3.1, Eq. (3.7)"},{"comment":"The sign conventions for I_gravity,W are confusing: Eq. (1.3) has a minus sign, while Section 3.1 defines I_grav = -I_gravity,W and later compares with -I_gravity,W. Please state the convention once, explicitly, so that Eqs. (3.6), (3.24), and (3.41) can be compared without re-deriving signs.","section":"Secs. 2 and 3"},{"comment":"The terminology 'heavy operators' should be reconciled with the probe limit: in the wedge computation, small η means α close to 1 and Δ is small compared with 1/G_N, not of order c. Please clarify the intended regime, both in the abstract and when introducing Eq. (3.7).","section":"Abstract and Sec. 3.1"},{"comment":"The numerical integration method and its precision are not specified. Please state the quadrature scheme, the handling of the ε cutoffs, and an estimate of the numerical error, so the claimed agreement with the perturbative expansions is reproducible.","section":"Figures 6, 8, 9 and Tables 1, 2"},{"comment":"There are several typographical issues, such as 'din stinction' in Section 3.3 and inconsistent spacing around 'Bañados'. A careful proofreading pass would improve readability.","section":"Throughout"}],"recommendation":"major_revision","confidential_remarks":"The main weakness is the exactness claim attached to Eq. (1.3). The paper's own Poincaré computation shows an O((1-α)^2 log ε) mismatch between the wedge and backreacted actions, so the wedge proposal should be reframed as a leading-order/probe-limit consistency check rather than an exact action-level equivalence. The backreacted computation and the FG-gauge discrepancy are more solid and could stand as the main contribution if the wedge claims are appropriately qualified. I recommend major revision rather than rejection, because the issue is fixable by amending the claims and explicitly acknowledging the subleading discrepancy."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"This paper has two distinct parts. The first is the wedge proposal for two-point functions of heavy operators in AdS3: excise a wedge bounded by two EOW branes, compute the on-shell action, and read off the correlation function. The second is a direct construction of backreacted geometries by coordinate transformations on the conical AdS3 solution, with computation of their on-shell actions in the physical patch and in Fefferman-Graham gauge.\n\nThe backreacted part is the genuinely new content and it is solid. The computations are explicit, the integrals are in the appendices, and the numerical/perturbative tables support the analytic results. The demonstration that the on-shell action in the physical patch reproduces the two-point function, while the FG-gauge computation does not, is a useful and somewhat surprising observation, consistent with the companion paper [21]. The wedge part is less new: the cut-and-glue construction is in [27] and [33], and the Poincare case was already computed there. What is new is the explicit formulation, the extension to global AdS and BTZ, and the systematic perturbative+numerical verification. That is a reasonable increment, not a breakthrough.\n\nThe soft spot is the status of Eq. (1.3). The paper states this as an exact action-level equality between the excised wedge and the backreacted conical geometry. The authors do note, in Section 2, that a rigorous proof is lacking, and the case studies are explicitly in the probe limit. But the equation itself is presented as exact, and the abstract says correlation functions 'can be derived' from the excised geometry without the probe-limit caveat. The Poincare case is the one place both sides can be evaluated in closed form, and the equality fails beyond leading order in the deficit angle. The wedge action gives coefficient 2m = (1-alpha)/(2G_N), while the backreacted action gives 2Delta = (1-alpha^2)/(4G_N); the difference is order (1-alpha)^2 log(epsilon), and the dilogarithm and Hayward terms in Appendix A do not cancel it. So Eq. (1.3) is at best a leading-order identity. The paper should state this explicitly, either by weakening the claim or by identifying the missing subleading terms.\n\nThe FG-gauge discrepancy is also argued mostly by example and by showing that the surface reproducing the inverse two-point function lies outside the wall. That is suggestive but not a general proof; the paper's own language ('may reveal deeper insights', 'leave this question to the future') is appropriately cautious there.\n\nWho is this for? AdS3/CFT2 practitioners working on heavy operators, local quenches, and BCFT. It deserves a serious referee — the backreacted computations are worth checking and citing — but it needs a major revision that clearly delimits the wedge proposal to leading order and either proves or explicitly bounds the subleading corrections. I would send it to peer review, with the expectation of revision rather than acceptance as is.","headline":"The backreacted action computations are the solid, new part; the wedge proposal is a useful leading-order tool, but Eq. (1.3) is not exact and the paper should say so.","tokens_in":29372,"tokens_out":2894,"would_cite":true,"duration_ms":28240,"reading_group":"maybe","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 proposes that heavy-operator correlation functions can be computed from the on-shell action of an AdS3 geometry with a wedge excised by two end-of-the-world branes, and verifies the proposal in Poincaré, global, and BTZ…","keywords":["holographic correlation functions","heavy operators","AdS/CFT correspondence","excised wedge","end-of-the-world branes","conical defects","BTZ black hole","Fefferman-Graham gauge"],"falsifier":"Compute the excised-wedge on-shell action for a configuration with three intersecting EOW branes and compare it with the semiclassical Virasoro conformal block for a three-point function of heavy operators; a mismatch in the logarithmic divergence would falsify the wedge proposal.","tokens_in":28307,"feed_emoji":"📐","tokens_out":7132,"duration_ms":67818,"temperature":0.7,"pith_summary":"This paper proposes a holographic shortcut: instead of building the backreacted bulk geometry sourced by a heavy scalar operator, compute the on-shell action of the same AdS3 spacetime with a wedge excised by two intersecting end-of-the-world branes. The claim, summarized in Eq. (1.3), is that this excised-wedge action equals the backreacted action, so the two-point correlation function of the dual heavy operator can be read off directly. The proposal is tested in Poincaré AdS3, global AdS3, and BTZ, with analytic, perturbative, and numerical checks. In the direct backreacted computation, the physical coordinate patch reproduces the expected two-point function while the Fefferman-Graham gauge patch does not, sharpening a discrepancy from earlier work.","feed_headline":"Cut a wedge out of AdS3 and read off heavy-operator correlators","feed_subtitle":"The excised-wedge action equals the backreacted action in Poincare, global, and BTZ; Fefferman-Graham gauge misses it.","key_machinery":"The load-bearing identity is Eq. (1.3): $I_{\\rm BR} = I_{\\rm AdS_3} - I_{\\rm gravity,W} + I_m$, equating the on-shell action of the backreacted conical geometry with bulk particle excitations to the on-shell action of the excised wedge. The machinery is a cut-and-glue construction: a conical defect with deficit angle $2\\pi(1-\\alpha)$ is equivalent to the global AdS3 geometry with a wedge of angle $2\\pi(1-\\alpha)$ excised and its two edges identified. The wedge's two tensionless end-of-the-world branes intersect along the particle worldline; because they are tensionless and perpendicular to the boundary, only the Hayward term (the gravitational boundary term at a nonsmooth corner) survives at the tip, and it cancels $I_m$ exactly. After a boost, the wedge becomes a spindle whose boundary intersection points are the two operator insertions, so the regularized on-shell action yields the two-point function.","core_discovery":"The paper's central claim is that for a heavy scalar operator dual to a point particle in the bulk, the two-point correlation function can be obtained from the on-shell action of the background AdS3 geometry with a wedge removed, rather than from the full backreacted geometry. The wedge is bounded by two intersecting tensionless end-of-the-world branes and the asymptotic boundary; its tip is the particle's worldline. The equivalence is expressed by $I_{\\rm BR} = I_{\\rm AdS_3} - I_{\\rm gravity,W} + I_m$, where the left side is the backreacted conical action and the right side is the excised-wedge action, with the particle mass term $I_m$ cancelling the Hayward corner term at the tip. The paper verifies the proposal in Poincaré AdS3, global AdS3, and BTZ, both by direct computation of the wedge action and by constructing the backreacted geometry through coordinate transformations of the conical solution. In the direct construction, the on-shell action computed in the physical coordinate patch reproduces the CFT two-point function, while the same geometry in Fefferman-Graham gauge does not.","pith_inferences":["If the wedge/backreacted equivalence holds generally, it supplies a cheaper route to higher-point correlators: assemble a configuration from several intersecting EOW branes and compute the wedge action, instead of solving nonlinear backreaction; the paper notes the naive three-wedge overlap fails, so a corrected construction (e.g. holographic polygons) would be the test.","The FG-gauge failure suggests that correlation functions should be computed in the coordinate patch tied to the operator insertions, and that boundary-fixed gauges can lead to the wrong observable; a generalized FG gauge may restore the correct answer, a direction the paper flags.","The same cut-and-glue logic may apply to spinning particles or to defect CFTs dual to 3D C-metrics, since the only ingredients are EOW branes and corner terms."],"forward_implications":["In all three backgrounds examined, the excised-wedge partition function $e^{-I_{\\rm grav}}$ reproduces the CFT two-point function at leading order, including the thermal two-point function in BTZ.","The on-shell action of the directly backreacted geometry in the physical coordinate patch also gives the two-point function, so no probe-limit approximation is needed there.","The same backreacted geometry in Fefferman-Graham gauge gives a different on-shell action (the inverse, or otherwise too large), so FG-gauge actions misidentify correlation functions for heavy operators.","The particle mass term always cancels against the conical-singularity/Hayward corner term, so practical wedge computations can omit both."],"supporting_citations":[{"why":"Provides the specific example where a two-point correlation function is read from the on-shell action of an excised geometry, the basis for the wedge proposal.","marker":"[27]"},{"why":"Supplies the insight that heavy-operator correlation functions or conformal blocks come from on-shell actions of conical or backreacted geometries.","marker":"[19-21]"},{"why":"Previous companion work where the discrepancy between backreacted and Fefferman-Graham on-shell actions was noted, which this paper reinforces with additional examples.","marker":"[21]"},{"why":"Establishes that a conical geometry can be interpreted as global AdS with a wedge excised, the cut-and-glue construction used throughout.","marker":"[11, 25, 26]"},{"why":"Provides coordinate transformations used to construct backreacted geometries from the conical solution, enabling direct verification of the wedge result.","marker":"[28]"},{"why":"First articulated the wedge idea with caveats and supplied local-quench transformations that this paper adapts.","marker":"[33]"},{"why":"AdS/BCFT formalism with end-of-the-world branes, used to treat the wedge boundaries and their actions.","marker":"[31, 32]"},{"why":"Hayward's gravitational action for nonsmooth boundaries, needed for the corner term at the wedge tip.","marker":"[36]"},{"why":"Relates the particle mass to the deficit angle, used to identify and cancel the mass term in the on-shell action.","marker":"[34]"}],"fun_headline_variants":["AdS3 wedge: heavy correlators without backreaction","Cut a wedge, get heavy correlators: FG gauge not needed","Wedge action matches backreacted: heavy correlators in AdS3","Heavy operator correlators from AdS3 wedge excision","FG gauge fails: wedge action yields heavy correlators in AdS3"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The central bet is that an excised wedge and the backreacted conical geometry have exactly the same on-shell action, with the particle's mass term canceling the corner contribution at the wedge tip; the paper checks this in each example but proves no general identity.","fun_headline_variants_meta":{"raw":{"variants":["AdS3 wedge: heavy correlators without backreaction","Cut a wedge, get heavy correlators: FG gauge not needed","Wedge action matches backreacted: heavy correlators in AdS3","Heavy operator correlators from AdS3 wedge excision","FG gauge fails: wedge action yields heavy correlators in AdS3"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000932,"raw_usage":{"total_tokens":4017,"prompt_tokens":1003,"completion_tokens":3014,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":619,"completion_tokens_details":{"reasoning_tokens":2933}},"tokens_in":619,"tokens_out":3014,"duration_ms":21772,"temperature":1.0,"reasoning_tokens":2933,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T17:32:46.367561+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the excised-wedge on-shell action for a configuration with three intersecting EOW branes and compare it with the semiclassical Virasoro conformal block for a three-point function of heavy operators; a mismatch in the logarithmic divergence would falsify the wedge proposal.","supporting_citations":[],"review_version":1}