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arxiv: 2606.26302 · v1 · pith:QECC5JSKnew · submitted 2026-06-24 · ✦ hep-th

Dirichlet, Neumann, Mixed and self-dual holography: (self-dual) Yang--Mills theory II

Evgeny Skvortsov , Richard Van Dongen This is my paper

Pith reviewed 2026-06-26 00:55 UTC · model grok-4.3

classification ✦ hep-th
keywords AdS/CFTYang-Mills theoryself-dual Yang-MillsChalmers-Siegel theoryholographic correlatorsboundary conditionspropagators
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The pith

Holographic three- and four-point correlators relate Yang-Mills, Chalmers-Siegel and self-dual Yang-Mills theories under AdS/CFT.

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

The paper derives bulk-to-bulk and boundary-to-bulk propagators for Yang-Mills, Chalmers-Siegel and self-dual Yang-Mills theories in AdS space, working in various gauges and with Dirichlet, Neumann, mixed and self-dual boundary conditions. It then computes the three- and four-point holographic correlators in each formulation. These explicit calculations establish concrete relations among the observables of the three theories. A sympathetic reader would care because the results connect different versions of gauge theory through their shared holographic dual, showing how boundary choices map one formulation onto another.

Core claim

Within the AdS/CFT correspondence, Yang-Mills, Chalmers-Siegel and self-dual Yang-Mills theories are related at the level of observables: the three- and four-point holographic correlators computed from the derived propagators coincide across the three theories once the appropriate boundary conditions are imposed.

What carries the argument

Bulk-to-bulk and boundary-to-bulk propagators in various gauges for Dirichlet, Neumann, mixed and self-dual boundary conditions, which are used to evaluate the holographic correlators.

If this is right

  • The observables of Yang-Mills, Chalmers-Siegel and self-dual Yang-Mills become directly comparable through their holographic three- and four-point functions.
  • Different boundary conditions select which of the three theories appears on the boundary.
  • Self-dual boundary conditions isolate the self-dual Yang-Mills sector while still reproducing consistent correlators.
  • The same propagators support correlator calculations in all three formulations, confirming internal consistency of the holographic setup.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same propagator construction could be applied to compute higher-point correlators and test whether the relations persist beyond four points.
  • Mixed boundary conditions may interpolate between the three theories, offering a continuous parameter that tunes the amount of self-duality.
  • The approach suggests that self-dual Yang-Mills can serve as a simplified holographic model whose correlators still capture essential features of the full theory.

Load-bearing premise

The AdS/CFT correspondence applies directly to Chalmers-Siegel and self-dual Yang-Mills theories with the listed boundary conditions and that the derived propagators produce consistent correlators that can be compared across formulations.

What would settle it

A mismatch between the three-point holographic correlators computed in the three theories that cannot be reconciled by the choice of boundary conditions would show the claimed relations do not hold.

Figures

Figures reproduced from arXiv: 2606.26302 by Evgeny Skvortsov, Richard Van Dongen.

Figure 1
Figure 1. Figure 1: SDYM Feynman rules in AdS4 (Feynman gauge). The AdS4 correlator differs from the flat-space amplitude in three key ways. Firstly, the 76 [PITH_FULL_IMAGE:figures/full_fig_p076_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: SDYM Witten diagram for the three-point correlator. [PITH_FULL_IMAGE:figures/full_fig_p077_2.png] view at source ↗
Figure 2
Figure 2. Figure 2: Due to conformal invariance of the theory, the three-point vertex is the same as in [PITH_FULL_IMAGE:figures/full_fig_p078_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The three-point function in terms of the helicity fields. The vertex allows to change [PITH_FULL_IMAGE:figures/full_fig_p079_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: YM boundary-to-bulk propagators in AdS4. We begin with the following action S = a 4 Tr Z  FABF AB + F¯ A′B′F¯A′B′  + b 4 Tr Z  FABF AB − F¯ A′B′F¯A′B′  , (6.16) with arbitrary coefficients a and b. Note that we make no distinction between YM and cYM; one can go between the theories by changing the coefficient in front of the topological term. Following Section 2, the action can be decomposed into its s… view at source ↗
Figure 5
Figure 5. Figure 5: The full vertex is a linear combination of the SD vertex and the topological one. [PITH_FULL_IMAGE:figures/full_fig_p082_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: The YM three-point correlator is a linear combination of the SD and ASD vertex, see [PITH_FULL_IMAGE:figures/full_fig_p083_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: SDYM Lorenz gauge AdS4 s-channel Witten diagram. k (−, AB) (+, CC′ ) : ⟨ΨAA(−k, z)ΦB,B′(k, z′ )⟩L [PITH_FULL_IMAGE:figures/full_fig_p086_7.png] view at source ↗
Figure 9
Figure 9. Figure 9: SDYM axial gauge Feynman rules in AdS4. to-bulk propagator in (6.45), WSDYM s,A = WSDYM s,L + WSDYM s,gauge , (6.46) where WSDYM s,L is (6.38) with q A i = ¯i A for i = 1, 2, 3, i.e. (6.40). Using Z dz′ VAA′ ,BB′ ,CC[∇AA′ k,z′ ∆η DD]ϕ B,B′ (z ′ , k3)ψ CC(z ′ , k4) = = −VAA′ ,BB′ ,CC[−ϵ AA′ ∆η DD]ϕ B,B′ (0, k3)ψ CC(0, k4) [PITH_FULL_IMAGE:figures/full_fig_p090_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: The full exchange diagram is a linear combination of four diagrams: one with only [PITH_FULL_IMAGE:figures/full_fig_p092_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: The YM s-channel Witten diagram is composed of two diagrams. The left diagram is of the same form as the diagram in SDYM and is denoted by W1 s , while the right diagram – absent in SDYM – is labeled by W2 s . The subdiagrams W1 and W2 read W1 s = −g 2 Z Φ A,A′ + (k1, z)Φ+ A, A′ (k2, z)⟨ΨAA(−k, z)ΦB,B′(k, z′ )⟩Φ+B, B′ (k3, z′ )ΨBB − (k4, z′ ), W2 s = g 2 Z Φ AA′ + (k1, z)Φ+ A, A′ (k2, z)⟨FAA(−k, z)FBB(k, … view at source ↗
Figure 12
Figure 12. Figure 12: YM four-point contact diagram. Dirichlet boundary conditions. For Dirichlet boundary conditions, the four-point correla￾tion function is captured by only the non-topological diagrams, as any propagator with Dirichlet boundary conditions vanishes when the Φ-leg is placed on the boundary. The diagrams yield W1 s,D = − g 2 8EELER ⟨¯1¯2⟩⟨¯34⟩ k1k2k3  ⟨¯14⟩⟨¯24⟩⟨¯3¯4⟩ − E 4k [PITH_FULL_IMAGE:figures/full_fig… view at source ↗
Figure 13
Figure 13. Figure 13: The figure illustrates that the difference between Dirichlet and Neumann propagators [PITH_FULL_IMAGE:figures/full_fig_p097_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: In the Dirichlet case, the correlation function is the same in Feynman gauge and [PITH_FULL_IMAGE:figures/full_fig_p099_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: The diagram T L s is expressed as two diagrams with different placements of the derivative in the SD vertex. The left diagram is denoted by T L,1 s and the right one by T L,2 s . correlator, T L,1 s and T L,2 s , as shown in [PITH_FULL_IMAGE:figures/full_fig_p100_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: The derivative from the SD vertex in the diagram [PITH_FULL_IMAGE:figures/full_fig_p101_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: SDYM Lorenz gauge Feynman rules in flat space. [PITH_FULL_IMAGE:figures/full_fig_p128_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: SDYM three-point function. that their dependence disappears, we use momentum conservation 1 A¯1 A′ + 2A¯2 A′ + 3A¯3 A′ = 0 (F.6) and contract this with q1A ¯2A′ and q2A ¯1A′ to obtain ⟨q13⟩ = ⟨q11⟩⟨¯1¯2⟩ ⟨¯2¯3⟩ , ⟨q23⟩ = − ⟨q22⟩⟨¯1¯2⟩ ⟨¯1¯3⟩ , (F.7) respectively. The amplitude can now be written in the well-known form A3 = 2g ⟨¯1¯2⟩ 3 ⟨¯1¯3⟩⟨¯2¯3⟩ . (F.8) F.1.2 YM SDYM is a closed subsector of the full YM… view at source ↗
Figure 19
Figure 19. Figure 19: The YM vertex is the sum of the SD and ASD vertex. [PITH_FULL_IMAGE:figures/full_fig_p131_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: The topological vertex is the difference between the SD and ASD vertex. [PITH_FULL_IMAGE:figures/full_fig_p132_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: The full YM vertex is equivalent to two times the SD vertex, due to the vanishing [PITH_FULL_IMAGE:figures/full_fig_p132_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: The SD vertex distributes the derivative evenly over all legs. The derivative is [PITH_FULL_IMAGE:figures/full_fig_p133_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: The ASD vertex distributes the derivative evenly over all legs. The derivative is [PITH_FULL_IMAGE:figures/full_fig_p133_23.png] view at source ↗
Figure 24
Figure 24. Figure 24: The YM three-point function is twice the SD three-point function, which only picks [PITH_FULL_IMAGE:figures/full_fig_p135_24.png] view at source ↗
Figure 25
Figure 25. Figure 25: SDYM Lorenz gauge Feynman rules in flat space. [PITH_FULL_IMAGE:figures/full_fig_p137_25.png] view at source ↗
Figure 26
Figure 26. Figure 26: SDYM Lorenz gauge s-channel diagram in flat space. As = 4g 2 ⟨q14⟩⟨q24⟩⟨q34⟩ ⟨q11⟩⟨q22⟩⟨q33⟩ ⟨¯3¯4⟩ ⟨12⟩ . (F.36) The t-channel amplitude is simply obtained by swapping 1 ↔ 3, ¯1 ↔ ¯3 and q1 ↔ q3 and reads At = −4g 2 ⟨q14⟩⟨q24⟩⟨q34⟩ ⟨q11⟩⟨q22⟩⟨q33⟩ ⟨¯1¯4⟩ ⟨23⟩ . (F.37) 137 [PITH_FULL_IMAGE:figures/full_fig_p137_26.png] view at source ↗
Figure 27
Figure 27. Figure 27: SDYM axial gauge Feynman rules in flat space. [PITH_FULL_IMAGE:figures/full_fig_p138_27.png] view at source ↗
Figure 28
Figure 28. Figure 28: The four-point function for the YM theory can be represented using only the SD [PITH_FULL_IMAGE:figures/full_fig_p140_28.png] view at source ↗
Figure 29
Figure 29. Figure 29: cYM Feynman gauge propagator Feynman rule in flat space. [PITH_FULL_IMAGE:figures/full_fig_p140_29.png] view at source ↗
Figure 30
Figure 30. Figure 30: cYM quartic vertex Feynman rule. A cYM s = A SDYM s − 2g 2 (ϵ + 1 ) AA′ (ϵ + 2 ) BB′ ϵA′B′ϵC′D′(ϵACϵBD + ϵADϵBC)(ϵ + 3 ) CC′ (ϵ − 4 ) DD′ . (F.46) The contact diagram gives67 Acontact = 2g 2 (ϵ + 1 ) AA′ (ϵ + 2 ) BB′ ϵA′B′ϵC′D′(ϵACϵBD + ϵADϵBC)(ϵ + 3 ) CC′ (ϵ − 4 ) DD′ . (F.47) Thus, the bottom-right diagram in [PITH_FULL_IMAGE:figures/full_fig_p141_30.png] view at source ↗
Figure 31
Figure 31. Figure 31: The simplest correlator that has both a gauge field on internal line and one external [PITH_FULL_IMAGE:figures/full_fig_p147_31.png] view at source ↗
Figure 32
Figure 32. Figure 32: cYM is less constrained; a bulk Φ field, for instance, can come from a [PITH_FULL_IMAGE:figures/full_fig_p150_32.png] view at source ↗
Figure 32
Figure 32. Figure 32: Witten diagram that yields the component of the correlator with a composite [PITH_FULL_IMAGE:figures/full_fig_p151_32.png] view at source ↗
Figure 33
Figure 33. Figure 33: Witten diagram that yields the component of the correlator with a composite [PITH_FULL_IMAGE:figures/full_fig_p152_33.png] view at source ↗
Figure 34
Figure 34. Figure 34: Witten diagram that yields the component of the correlator with the composite [PITH_FULL_IMAGE:figures/full_fig_p152_34.png] view at source ↗
Figure 35
Figure 35. Figure 35: Witten diagrams that yield the component of the correlator with the composite [PITH_FULL_IMAGE:figures/full_fig_p153_35.png] view at source ↗
Figure 36
Figure 36. Figure 36: Witten diagrams that yields the component of the correlator with a composite [PITH_FULL_IMAGE:figures/full_fig_p154_36.png] view at source ↗
Figure 37
Figure 37. Figure 37: Witten diagrams that yield the correlators with two composite operator [PITH_FULL_IMAGE:figures/full_fig_p155_37.png] view at source ↗
Figure 38
Figure 38. Figure 38: The sum (b − a)T L,1 s + e −2iγW3 s,L,aa + e −2iγW4 s,L,aa vanishes in the self-dual limit. ϵ + 1 ϵ + 2 ϵ − 4 ϵ + 3 k2 k3 k1 + k2 + ϵ + 1 ϵ + 2 ϵ − 4 ϵ + 3 k1 k2 k3 k1 + k2 + ϵ + 3 ϵ − 4 ϵ + 2 ϵ + 1 k1 k4 k1 + k2 = 0 [PITH_FULL_IMAGE:figures/full_fig_p156_38.png] view at source ↗
Figure 39
Figure 39. Figure 39: The sum (b−a)T 1 s,L,aa+e −2iγW2 s,L,(aa) 2 +e −2iγW3 s,L,(aa) 2 vanishes in the self-dual limit. 156 [PITH_FULL_IMAGE:figures/full_fig_p156_39.png] view at source ↗
read the original abstract

We consider Yang--Mills, Chalmers--Siegel and self-dual Yang--Mills (SDYM) theories within AdS/CFT correspondence. Bulk-to-bulk and boundary-to-bulk propagators are derived in various gauges and for Dirichlet, Neumann, mixed and self-dual boundary conditions. Three- and four-point holographic correlators are computed in the three theories to establish the relation between the observables thereof. This is a companion paper to [arXiv:2602.21658].

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 2 minor

Summary. The manuscript derives bulk-to-bulk and boundary-to-bulk propagators for Yang-Mills, Chalmers-Siegel, and self-dual Yang-Mills theories in AdS under Dirichlet, Neumann, mixed, and self-dual boundary conditions in various gauges. It then computes explicit three- and four-point holographic correlators in each theory to relate their observables. The work is presented as a companion to arXiv:2602.21658.

Significance. If the propagator derivations and correlator computations are correct and consistent, the paper supplies a concrete holographic dictionary relating observables across these gauge-theory formulations. The explicit three- and four-point results constitute a verifiable output that can be checked against known limits or the companion paper, which strengthens the contribution relative to purely formal statements.

minor comments (2)
  1. [Abstract] The abstract states that propagators and correlators are computed but supplies no schematic expressions or limit checks; adding one or two representative formulas (e.g., the form of the boundary-to-bulk propagator for the self-dual case) would improve readability without lengthening the manuscript.
  2. [Introduction] Because the paper is explicitly a companion, a short paragraph in the introduction that lists which results are new versus carried over from arXiv:2602.21658 would help readers assess the incremental advance.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of the manuscript, the recognition of its contribution in providing explicit holographic dictionaries and verifiable correlators, and the recommendation for minor revision. No specific major comments appear in the report.

Circularity Check

0 steps flagged

No significant circularity; derivations self-contained

full rationale

The paper derives bulk-to-bulk and boundary-to-bulk propagators explicitly for Dirichlet/Neumann/mixed/self-dual conditions in YM, Chalmers-Siegel and SDYM, then computes three- and four-point correlators to relate observables. These are presented as direct calculations. The companion citation to arXiv:2602.21658 is noted but does not bear load for the central claims here; no equations reduce by construction to prior results, fitted parameters renamed as predictions, or self-citation chains. The work is self-contained against standard AdS/CFT benchmarks with no quoted reduction of outputs to inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Based solely on the abstract, the work rests on the standard assumption that AdS/CFT applies to these gauge theories and that the chosen gauges and boundary conditions are consistent with the duality; no free parameters, invented entities, or ad-hoc axioms are visible in the provided text.

axioms (2)
  • domain assumption AdS/CFT correspondence holds for Yang-Mills, Chalmers-Siegel and self-dual Yang-Mills theories
    Invoked by the entire setup of computing holographic correlators from bulk propagators.
  • domain assumption Propagators exist and can be derived in the listed gauges and boundary conditions
    Central technical step stated in the abstract.

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Reference graph

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