{"id":"412cb0db-0262-4cab-beeb-792de707f9ee","arxiv_id":"2501.18386","paper_version":2,"verdict":"ACCEPT","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Explicit bulk derivations yield two- and three-point stress tensor correlators in AdS3/BCFT2 and scalar and stress tensor correlators for XCFT2 on RP2, with tension independence and finite-cutoff deformations.","lead":"This paper computes explicit holographic stress tensor correlators for two-dimensional boundary conformal field theories and for crosscap CFTs on the real projective plane, including effects of brane tension and finite cutoff. It extends the holographic dictionary to boundary and non-orientable geometries and gives concrete benchmarks for CFT boundary and crosscap studies.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"RP2 stress tensor two-point function is not checked against the crosscap Ward identity; the displayed result (158) appears to miss the image-channel singular terms required by the crosscap involution.","rationale":"The reader's weakest_assumption is that the RP2 saddle choice is not proven dominant or unique. I agree this is the primary external assumption, and it is explicitly stated, but my concern is sharper and more testable: the paper's RP2 stress tensor two-point function (158) lacks a check against the local crosscap Ward identity and the OPE of the stress tensor with its own one-point function. For a CFT on RP2, the crosscap involution z -> -1/bar{z} generates a non-trivial image contribution; the two-point function must have a w'-dependent singular term arising from the image of the second insertion. Equation (158) contains the 'bulk' term (w-w')^{-4} and a contact term proportional to delta^(2)(w + bar{w}'^{-1}), which is the correct crosscap-image contact structure, but the singular part proportional to 1/(w + bar{w}'^{-1})^2 is absent. If the authors' convention (where Tww is the holomorphic stress tensor and the one-point function is constant) is standard, the Ward identity requires a 1/(z-w)^2 term proportional to the one-point function <T(w)>. Unless the paper defines away this term by using traceless-transverse components or a different normalization, the displayed result is incomplete. This is precisely the kind of internal consistency check the authors did perform for the BCFT sector: recurrence relations matched Ward identities, and two BCFT methods agreed. The absence of such a check for the RP2 stress tensor is a genuine gap. The fix is computational: derive the Ward identity and test (158). This does not undermine the scalar results, which are checked against geodesics, and it does not challenge the BCFT results, which are internally verified. Hence ACCEPT should become CONDITIONAL, pending the Ward-identity check or an explicit statement that Tww is not the holomorphic stress tensor but a component of a trace-free tensor with modified Ward identities.","tokens_in":1320,"tokens_out":1457,"duration_ms":33074,"concrete_test":"Derive the holomorphic Ward identity for the stress tensor on RP2 using the crosscap involution z -> -1/bar{z}, expressing <T(z)T(w)> in terms of the one-point function <T(w)> = constant on RP2. Substitute equation (158) into this identity and check whether the 1/(z-w)^2 and crosscap-image 1/(z + 1/bar{w})^2 terms match. Also verify the coefficient of the leading (z-w)^{-4} OPE pole equals c/2 = 3/(32 pi G) given the paper's normalization; if the Ward identity fails or the pole coefficient differs, the RP2 stress tensor result requires correction.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"Section 3 inherits from [56] the assumption that the dominant bulk saddle for the RP2 crosscap CFT is the Z2 quotient of global AdS3 with fixed point at eta=0, resolved by a single EOW brane of tension T<-1 (stated in Sec. 3.1: 'we assume that the dominant saddle is constructed by the identification with a fixed point at eta=0'). That assumption is load-bearing: all scalar and stress tensor correlators in Section 3 are computed on this one background, and the paper offers no independent CFT-side check of the resulting two-point functions. There is a concrete internal test available, however. In a 2D crosscap CFT with a single stress tensor, the holomorphic Ward identity under the crosscap involution relates the two-point function to the one-point function: schematically <T(z)T(w)> on RP2 should satisfy the involution z -> -1/bar{z} with the appropriate Schwarzian, while the leading singularity ~ 1/(z-w)^4 has coefficient c/2. The paper's equation (158) gives <Tww(w)Tww(w')> = (3/(16 pi^2 G)) (w-w')^{-4} + contact terms, with coefficient c/2 if c=3/(2G), matching the holomorphic OPE coefficient. But the crosscap Ward identity imposes a specific one-point-function source term: <T(z)T(w)> should have a singular term of the form (1/2)c T_crosscap(w) / (z-w)^2 plus regular terms, where T_crosscap is the one-point function on RP2, which from (171) and (137) is a constant. The displayed formula (158) has no w'-dependent 1/(w-w')^2 singular term, suggesting either the convention is that T is a trace/improved tensor and the check is subtle, or the RP2 result is missing the crosscap-image contribution that would arise from the antipodal image OPE. Since the authors verify their BCFT results against the Cardy/Ward identities and the heavy-scalar one-point function against geodesics, but do not perform the analogous stress tensor check on RP2, the risk is that the crosscap two-point function is incomplete.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper computes holographic stress tensor correlators in AdS3/BCFT2 for both tensionless and tensionful end-of-the-world branes, deriving explicit two- and three-point functions and recurrence relations. It then extends the holographic approach to two-dimensional crosscap CFTs on RP2, computing exact scalar one- and two-point functions, stress tensor two-point functions, and their finite-cutoff (TTbar-deformed) versions. The methodology follows standard GKPW holographic renormalization with Neumann boundary conditions on the EOW brane. The BCFT section is checked by matching two independent coordinate frames and by comparing recurrence relations to BCFT Ward identities. The heavy-dimension scalar one-point function is matched to a geodesic approximation. The RP2 results rely on the model of [56], in which the quotient singularity is resolved by a single EOW brane.","tokens_in":38095,"tokens_out":31402,"duration_ms":270156,"significance":"If the results are correct, the paper provides concrete holographic predictions for boundary and non-orientable CFTs in two dimensions, including explicit exact correlators that are not yet available from other methods. The BCFT part is a solid extension of earlier work and contains useful consistency checks. The crosscap part is novel and addresses an underdeveloped area, but its correctness hinges on the two-point function of the stress tensor on RP2, which is not independently verified. The paper is clearly written and the derivations are mostly unambiguous, but the RP2 stress tensor sector needs scrutiny.","major_comments":[{"comment":"The two-point function ⟨Tww(w)Tww(w')⟩ in Eq. (158) contains only the direct-channel pole (3/(16π²G)) (w−w')⁻⁴ and a contact term supported at the image point w = −1/\\bar{w}'. The crosscap Ward identity, which follows from the involution w → −1/\\bar{w}, requires a non-contact image-channel singularity at w = −1/\\bar{w}' of the form (3/(16π²G)) (w + 1/\\bar{w}')⁻⁴ (up to the appropriate tensor factor). This is also what one expects from the covering-space expression (156), which explicitly contains four singular terms, two at the direct point and two at the antipodal image. After the coordinate change (157), those image terms do not disappear; they should appear as a fourth-order pole at the image point. Its absence in (158) means either the conversion from (156) to (158) is incorrect, or (158) is incomplete. Since the later finite-cutoff results in §3.4 are built on this two-point function, this is a load-bearing issue.","section":"§3.3, Eq. (158)"},{"comment":"The RP2 stress tensor two-point functions are not checked against any independent CFT-side criterion. In the BCFT section, the recurrence relations are explicitly compared to the BCFT Ward identities (§2.2.2), and the scalar one-point function is checked against a geodesic approximation (§3.2). For the crosscap stress tensor, no analogous check is provided. I request that the authors verify that the final expressions, e.g. (158)–(161), satisfy the Ward identity associated with the crosscap involution, including the correct singular behaviour at the image point. This is necessary to exclude the possibility that the holographic computation missed an image contribution.","section":"§3.3"}],"minor_comments":[{"comment":"The assumption that the dominant bulk saddle is the Z2 quotient of global AdS3 with a single EOW brane of tension T<−1 is clearly stated, but it is an assumption inherited from [56]. If other saddles contribute, the RP2 correlators would change. I suggest making this caveat more prominent, e.g., in the introduction or at the start of §3.","section":"§3.1"},{"comment":"In several places, terms like \"e−|ω(x−x0)|\" should read \"e^{−|ω|(x−x0)}\"; the absolute value sign is missing on ω.","section":"Eq. (90)"},{"comment":"The notation δ(2)(w + ¯w′−1) is confusing; I suggest writing δ^{(2)}(w + 1/\\bar{w}') to make the support of the delta explicit.","section":"Eqs. (158)–(160)"},{"comment":"The assumption that the brane tension T does not flow with the cutoff is stated without discussion. A sentence justifying this, or at least pointing to a reference where it is discussed, would be helpful.","section":"§3.4, footnote 7"},{"comment":"The paper sometimes uses \"correlators\" without specifying connectedness; since Eq. (13) defines connected correlators, please be consistent in the terminology.","section":"Various"}],"recommendation":"major_revision","confidential_remarks":"The BCFT part of the paper appears correct and well-checked, and the scalar crosscap results are supported by the geodesic check. The main issue is the RP2 stress tensor two-point function, which appears to miss required image-channel singularities. This is a technical error that is likely fixable by carefully performing the coordinate transformation from the covering-space expression, but until it is fixed, the RP2 stress tensor results are not reliable. If the authors can provide the corrected expressions and a Ward-identity check, the paper would be a strong contribution."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The BCFT part of this paper is the real meat and it holds up well. The two-point and three-point stress tensor correlators for the tensionless and tensionful brane cases are new, the recurrence relations are a useful addition, and the two independent methods (Poincare vs. hyperbolic slicing) matching for the two-point functions is a genuine internal check. The consistency with BCFT Ward identities and the geodesic check for the heavy scalar one-point function give me confidence that the computation is doing what it claims. I also appreciate that the paper states its assumptions plainly, especially the saddle choice for the RP2 calculation.\n\nThe RP2 section is where I am less comfortable. The paper inherits from Wei [56] the assumption that the Z2 quotient with a fixed point at eta=0, resolved by a single EOW brane, is the dominant saddle. That is a load-bearing assumption, and the paper does not justify dominance or uniqueness. More concretely, the stress-test note has a point about equation (158). For a CFT on RP2, the two-point function of the holomorphic stress tensor should satisfy the crosscap Ward identity, which relates singular terms in <T(z)T(w)> to the one-point function <T>. The displayed result (158) has the expected 1/(z-w)^4 term with the right central charge coefficient, but no 1/(z-w)^2 term proportional to the constant one-point function. That is exactly the term the crosscap image channel would produce. The authors verify their BCFT results against Ward identities, but they do not perform the analogous check here. It is possible the convention is such that the term is absorbed into the contact terms or the trace part of the stress tensor, but that needs to be spelled out. As it stands, I would not trust the RP2 stress tensor two-point functions without this check.\n\nThe finite-cutoff section is a nice bonus, though it assumes the brane tension does not flow; that is a minor caveat, not a fatal one.\n\nWho is this for? Holographers working on AdS/BCFT and on non-orientable CFTs. The BCFT correlators and recurrence relations are likely to become useful benchmarks. The RP2 results are worth having on the record, but they are conditional on the saddle and on the Ward identity question.\n\nRecommendation: send it to peer review. A good referee should push the authors on the crosscap Ward identity and on saddle dominance; with those addressed, I would accept.","headline":"A solid analytic tour de force for BCFT stress tensor correlators, with a more conditional RP2 crosscap section that needs a Ward identity check before I'd take its two-point functions at face value.","tokens_in":38765,"tokens_out":1491,"would_cite":false,"duration_ms":17123,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["11.25.Tq","11.25.Hf"],"model":"deepseek-v4-flash","headline":"Applying the GKPW dictionary to AdS3 with a Neumann end-of-the-world brane yields exact two- and three-point stress tensor correlators for BCFT2, and the same construction on a Z2 quotient of global AdS3 gives exact scalar and stress…","keywords":["AdS/BCFT","crosscap CFT","end-of-the-world brane","stress tensor correlators","real projective plane","holographic renormalization","T-Tbar deformation","GKPW relation"],"falsifier":"Evaluate the Euclidean on-shell actions of the proposed RP2 saddle (Z2 quotient of global AdS3 with fixed point at eta=0, resolved by an EOW brane of tension T<-1) and of the alternative smooth saddles for the same RP2 boundary, and check which has the lower action; the Section 3 correlators are only the answer if the proposed saddle dominates.","tokens_in":37507,"feed_emoji":"🌀","tokens_out":11507,"duration_ms":98414,"temperature":0.7,"pith_summary":"This paper derives exact holographic correlators for two classes of two-dimensional CFTs with defects: boundary CFTs (BCFT2) and crosscap CFTs on the real projective plane (RP2). Working in semiclassical AdS3/CFT2, it computes two- and three-point stress tensor correlators in AdS3/BCFT2, derives recurrence relations for higher-point correlators, and shows that the two- and three-point functions are independent of the end-of-the-world brane tension. On the non-orientable side, it obtains exact scalar one- and two-point functions and stress tensor two-point functions on RP2 from a Z2 quotient of global AdS3 whose fixed-point singularity is resolved by a brane, and it also gives the finite-cutoff (T-Tbar deformed) versions of these correlators. The BCFT recurrence relations match the boundary Ward identities, and the heavy-operator limit of the RP2 one-point function matches the geodesic approximation, so the paper supplies concrete holographic predictions for CFTs on manifolds with boundaries and on non-orientable surfaces.","feed_headline":"Derived exact correlators for boundary and crosscap CFTs","feed_subtitle":"Two- and three-point stress correlators from AdS3, plus RP2 crosscap predictions; brane tension drops out.","key_machinery":"The engine of the calculation is the GKPW relation, which equates the bulk on-shell gravitational action to the boundary CFT generating functional; in the semiclassical limit all correlators are functional derivatives of that action. The stress tensor computations use the Fefferman-Graham expansion of the bulk metric, whose first non-trivial coefficient g(2) encodes the Brown-York stress tensor, and the Neumann boundary condition (K_ij - K gamma_ij + T gamma_ij = 0) on the end-of-the-world brane, which determines the brane profile and relates it to the correlators. For the crosscap case the central object is the RP2 bulk saddle: global AdS3 quotiented by the antipodal map ($\\theta$,phi) -> (pi-$\\theta$, phi+pi), with the fixed point at eta=0 excised by an EOW brane of tension T<-1; scalar correlators follow from a Robin boundary condition on that brane and a spherical-harmonic decomposition restricted to even l, while stress tensor correlators follow from solving the perturbed Neumann condition on the sphere. At finite cutoff, the dictionary is the generalized GKPW relation for AdS3 truncated at z=z_c, whose dual is the T-Tbar deformed CFT (the solvable irrelevant deformation generated by the determinant of the stress tensor).","core_discovery":"The central claim is that the standard GKPW dictionary, applied to pure gravity in AdS3 with Neumann boundary conditions on an end-of-the-world brane, yields exact connected stress tensor correlators for BCFT2. Concretely, the paper obtains explicit two-point and three-point correlators for the tensionless brane, recurrence relations that generate higher-point correlators from lower-point ones, and a separate computation in hyperbolic slicing coordinates showing that general-tension two- and three-point correlators equal the tensionless ones. For crosscap CFT2, the claim is that the Z2 quotient of global AdS3 with antipodal identification fixed at the center, with the fixed-point singularity excised by an end-of-the-world brane of tension T<-1, is the holographic dual of the CFT on RP2; using it the paper computes exact scalar one- and two-point functions and stress tensor two-point functions, and shows the heavy-scalar one-point function agrees with the geodesic approximation. The same construction is then moved to a hard radial cutoff, giving deformed one- and two-point stress tensor correlators.","pith_inferences":["A natural extension the paper leaves implicit is the same Z2-quotient-plus-brane construction on the Klein bottle and on higher non-orientable surfaces; if the saddle-dominance assumption holds there, the method yields concrete Klein-bottle correlators that could be checked against known universal entropy results.","The demonstrated tension independence of BCFT two- and three-point correlators suggests a stronger conjecture: in AdS3/BCFT2 all higher-point stress tensor correlators, and possibly correlators involving boundary operators, are tension-independent; computing one four-point or boundary-operator correlator would test this.","The scalar two-point function (133) is an explicit infinite series over even spherical harmonics, so a direct boundary computation of the crosscap OPE, or a numerical simulation of a crosscap state in a lattice CFT, could check the coefficients A_l^(1) term by term.","If the finite-cutoff dictionary is exactly T-Tbar, the deformed RP2 one-point function should satisfy the T-Tbar flow equation in the large-central-charge limit, which is a concrete check of the cutoff construction beyond the correlators reported here."],"forward_implications":["If the BCFT results are correct, the recurrence relations (62)-(64) constitute a direct confirmation that the GKPW dictionary with a Neumann brane reproduces the boundary Ward identity structure of BCFT2.","Because the two- and three-point BCFT correlators do not depend on brane tension, tension-free calculations capture these boundary observables in AdS3/BCFT2, and tension only enters through the brane profile itself.","The RP2 scalar one- and two-point functions and stress tensor two-point functions become concrete holographic predictions for crosscap CFTs, with the heavy-dimension limit of the one-point function anchored by the geodesic approximation.","The finite-cutoff results give explicit T-Tbar-deformed versions of the RP2 stress tensor correlators, showing exactly how a hard radial cutoff deforms one- and two-point functions on the projective plane.","The explicit infinite-sum form of the RP2 scalar two-point function can be directly compared with boundary crosscap OPE data."],"supporting_citations":[{"why":"Supplies the GKPW dictionary that turns the bulk on-shell action into boundary correlators; every holographic correlator in the paper is derived through it.","marker":"[2, 3]"},{"why":"Defines AdS/BCFT with the Neumann condition on the end-of-the-world brane, the setup used throughout Section 2.","marker":"[23, 24]"},{"why":"Provides the brane-bending treatment that relates stress tensor correlators to variations of the brane profile, a central step for the BCFT computation.","marker":"[39, 40]"},{"why":"Gives the boundary Ward identity and Cardy condition that the BCFT recurrence relations are checked against.","marker":"[41, 42]"},{"why":"Provides the holographic dual of crosscap CFT on RP2 through Z2 quotient and EOW brane resolution; Section 3 is built on this construction.","marker":"[56]"},{"why":"Supplies the holographic renormalization counterterm and the renormalized one-point function prescription used in the scalar and stress tensor computations.","marker":"[59]"},{"why":"Is the boundary CFT result for the stress tensor two-point function at the edge that the tensionless BCFT computation reproduces.","marker":"[72]"},{"why":"Prescribes the Dirichlet boundary condition at a hard radial cutoff, the starting point of the finite-cutoff computation.","marker":"[78]"},{"why":"Gives the generalized GKPW relation for cutoff AdS3 that defines the deformed correlators.","marker":"[79]"},{"why":"Defines the T-Tbar flow equation identifying the deformed field theory dual to the cutoff AdS3.","marker":"[80, 81]"}],"fun_headline_variants":["Exact holographic correlators for boundary and crosscap CFTs","Brane tension drops out of exact stress correlators in BCFT2","AdS3 holography yields RP2 crosscap correlators","Finite cutoff deforms holographic stress correlators"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"For the RP2 results, the load-bearing premise is that the dominant bulk saddle is the Z2 quotient of global AdS3 whose antipodal identification has a fixed point at the center, with that singularity resolved by a single end-of-the-world brane of tension T<-1; the paper assumes this rather than proving it, and if another saddle contributes or the resolution differs, every crosscap correlator in Section 3 changes.","fun_headline_variants_meta":{"raw":{"variants":["Exact holographic correlators for boundary and crosscap CFTs","Brane tension drops out of exact stress correlators in BCFT2","AdS3 holography yields RP2 crosscap correlators","Finite cutoff deforms holographic stress correlators"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000393,"raw_usage":{"total_tokens":2066,"prompt_tokens":946,"completion_tokens":1120,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":562,"completion_tokens_details":{"reasoning_tokens":1045}},"tokens_in":562,"tokens_out":1120,"duration_ms":10762,"temperature":1.0,"reasoning_tokens":1045,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-09T23:40:35.303936+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Evaluate the Euclidean on-shell actions of the proposed RP2 saddle (Z2 quotient of global AdS3 with fixed point at eta=0, resolved by an EOW brane of tension T<-1) and of the alternative smooth saddles for the same RP2 boundary, and check which has the lower action; the Section 3 correlators are only the answer if the proposed saddle dominates.","supporting_citations":[],"review_version":1}