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Holographic correlation functions from wedge

T0 review · 2 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read 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…

desk verdict 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. read the letter →

arxiv 2411.12420 v2 pith:XRLCBDOZ submitted 2024-11-19 hep-th

Tengzhou Lai , Ya-Wen Sun , Jia Tian This is my paper · ORCID
classification hep-th
keywords holographiccorrelationfunctionsheavyoperatorsAdS/CFTcorrespondenceexcisedwedgeend-of-the-worldbranesconicaldefectsBTZblackholeFefferman-Grahamgauge
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

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.

What carries the argument

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.

What would settle it

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.

Watch

Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

  • 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.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • 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.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 5 minor

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.

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 (2)
  1. [Sec. 1, Eq. (1.3); Sec. 3.1, Eqs. (3.6)-(3.8); Sec. 4.1, Eq. (4.19); Appendix A, Eq. (A.9)] 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.
  2. [Secs. 3.2 and 3.3; Appendix C] 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.
minor comments (5)
  1. [Sec. 3.1, Eq. (3.7)] 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.
  2. [Secs. 2 and 3] 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.
  3. [Abstract and Sec. 3.1] 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).
  4. [Figures 6, 8, 9 and Tables 1, 2] 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.
  5. [Throughout] 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.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular derivation: the wedge actions are checked against known CFT two-point functions with Δ supplied as an input, and the only self-citation is a minor, non-load-bearing reference to the companion FG-gauge result.

full rationale

The paper's central relation (1.3) is an equivalence claim between the excised-wedge action and the backreacted conical action. It is not derived from the target correlators: the mass m is fixed by the deficit angle via m=(1−α)/(4GN), the Hayward corner term cancels the mass term geometrically, and the remaining boundary term is computed directly in each example. In the Poincaré, global, and BTZ cases, the logarithmically divergent coefficient is m times a boost-dependent insertion distance, yielding e^{-I} ~ (ε/|x12|)^{2Δ} after inserting the external input Δ≈m (Eq. 3.7). Thus the position dependence is a real output, while the overall scaling dimension is an input—standard in holographic correlator computations, and not a closed loop. The paper explicitly flags the lack of a general proof of the wedge/backreacted equivalence (Section 2), and Appendix A repeats the Caputa–Ge computation rather than treating it as an unexamined premise. The only self-citation is to the companion paper [21] for the FG-gauge discrepancy; here the Poincaré case is computed independently and the global/BTZ cases are supported by inequalities derived in the paper, so the self-citation is not load-bearing. No fitted parameter is renamed as a prediction, and no ansatz is smuggled in via citation. The possible failure of (1.3) beyond leading order in the Poincaré case is a quantitative accuracy concern, not a circularity. Overall: minor self-citation only, hence score 2.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The central claim rests on the standard AdS/CFT dictionary and AdS/BCFT actions rather than on new fitted parameters. The only free inputs are the mass (deficit angle) and the boost parameter that sets operator positions. No new entities are introduced. The main burden is the assumed equivalence between the excised wedge and the conical backreacted geometry, which is verified case by case.

free parameters (2)
  • Deficit angle α (wedge angle η)
    Sets the particle mass m=(1−α)/(4G_N) and, via Eq. (3.7), the conformal dimension Δ≈m of the heavy operator. The entire comparison with CFT correlation functions depends on this parameter, though it is a physical input, not fitted.
  • Boost parameter β
    Determines the insertion points u_a,u_b of the two operators on the boundary through Eq. (4.12). It is a kinematic parameter chosen by hand to set the positions; the final correlator depends on it through the separation |u_ab|.
assumptions (5)
  • domain assumption AdS/CFT correspondence (GKPW dictionary (1.1))
    The paper assumes the standard dictionary between the bulk on-shell action and CFT generating functional, which is the foundation of all computations.
  • domain assumption AdS/BCFT with end-of-the-world branes and Hayward corner terms (Eq. 2.9, 2.12)
    The wedge geometry is described by the generalized AdS/BCFT action, including the corner term at the tip. This is a construction from prior literature [31,32,36,39-43] that the paper adopts.
  • standard math Relation between particle mass and deficit angle (Eq. 2.4-2.5), m=(1−α)/(4G_N)
    Derived from the Einstein equation for a conical defect; it is used to translate the geometric parameter α into the CFT conformal dimension.
  • domain assumption Probe-limit relation Δ≈m (Eq. 3.7)
    Used to map the on-shell action of the excised wedge to the two-point function in the probe limit; this is an approximation that the paper explicitly uses in the wedge cases.
  • domain assumption Known forms of CFT two-point functions (Eqs. 2.21, 2.22, 3.25, 3.43)
    The paper compares its computed actions against the known CFT two-point functions on the plane, cylinder, and thermal state; these are external benchmarks, not derived here.

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Cite this review

Pith. "Pith review of Holographic correlation functions from wedge." pith.science (2026). https://pith.science/paper/XRLCBDOZ

@misc{pith2026241112420,
  author       = {Pith},
  title        = {Pith review of: Holographic correlation functions from wedge},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XRLCBDOZ}},
  note         = {Machine review of arXiv:2411.12420}
}
abstract

In this work, we propose a novel holographic method for computing correlation functions of operators in conformal field theories. This method refines previous approaches and is specifically aimed at being applied to heavy operators. For operators that correspond to particles in the bulk, we show that the correlation functions can be derived from the on-shell actions of excised geometries for heavy operators, using numerical and perturbative calculations. These excised geometries are constructed from various background solutions such as \Poincare AdS$_3$, global AdS$_3$, and BTZ by cutting out a wedge bounded by two intersecting End-of-the-world branes and the AdS boundary. The wedge itself can be interpreted as a dual to a BCFT with cusps in the AdS/BCFT framework. Additionally, we calculate the correlation functions for heavy operators directly by constructing backreacted bulk geometries for particle excitations through coordinate transformations from a conical solution. We find that the on-shell actions of these backreacted solutions accurately reproduce correlation functions, although they differ from those computed in Fefferman-Graham(FG) gauge. This discrepancy, previously noted and explained in our earlier work, is reinforced by additional examples presented here.

Figures

Figures reproduced from arXiv: 2411.12420 by the authors.

Figure 1
Figure 1. The bulk dual of a non-trivial BCC operator. [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. A simple gravity solution dual to the two-point correlation function of BCC [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. The bulk region in 2 is dual to a BCFT defined on the green-shaded region.. [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: Boundary region dual to the bulk wedge in Poincar´e AdS [PITH_FULL_IMAGE:figures/full_fig_p012_4.png]
Figure 5
Figure 5. Figure 5: Boundary region dual to the bulk wedge in global AdS [PITH_FULL_IMAGE:figures/full_fig_p014_5.png]
Figure 6
Figure 6. Figure 6: Numerical result of the integral in global AdS [PITH_FULL_IMAGE:figures/full_fig_p015_6.png]
Figure 7
Figure 7. Figure 7: Boundary region dual to the bulk wedge in BTZ black hole [PITH_FULL_IMAGE:figures/full_fig_p018_7.png]
Figure 8
Figure 8. Figure 8: Numerical result and analytical result at leading order perturbation when [PITH_FULL_IMAGE:figures/full_fig_p019_8.png]
Figure 9
Figure 9. Figure 9: Comparison between the numerical result and analytical result when [PITH_FULL_IMAGE:figures/full_fig_p021_9.png]
Figure 10
Figure 10. Figure 10: Image of the Wall in deformed Poincar´e AdS. [PITH_FULL_IMAGE:figures/full_fig_p026_10.png]
Figure 11
Figure 11. Figure 11: A naive attempt at constructing a wedge for a three-point function, represented [PITH_FULL_IMAGE:figures/full_fig_p033_11.png]
Figure 12
Figure 12. Figure 12: Two cases of the integral C Higher-order corrections In this appendix, we include the higher-order corrections to the on-shell action of both the global wedge and the BTZ wedge. Since the integrand is quite complicated, we will only present the result and compare it w…

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