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arxiv: 2605.30276 · v1 · pith:BUCVQQYUnew · submitted 2026-05-28 · ✦ hep-th

Self-dual holography: four-point AdS/CFT correlators in higher-spin gravity

Evgeny Skvortsov , Richard Van Dongen This is my paper

Pith reviewed 2026-06-29 06:18 UTC · model grok-4.3

classification ✦ hep-th
keywords self-dual theorieshigher-spin gravityAdS/CFT correlatorsFefferman-Graham expansionchiral higher-spin gravitybulk-to-bulk propagatorsholographic dictionaryself-dual Yang-Mills
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0 comments X

The pith

Self-dual higher-spin theories receive a Fefferman-Graham expansion and holographic dictionary that yields explicit three- and four-point AdS/CFT correlators.

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

The paper develops the Fefferman-Graham expansion for self-dual theories of arbitrary spin to establish a holographic dictionary. It applies this to derive bulk-to-bulk propagators and compute three- and four-point correlators in a contraction of Chiral higher-spin gravity. The work treats this contraction as a higher-spin extension of self-dual Yang-Mills theory. A reader would care because the construction supplies concrete AdS/CFT data for UV-finite self-dual models whose duals are expected to be simpler than those of full higher-spin gravity.

Core claim

By constructing the Fefferman-Graham expansion and holographic dictionary for arbitrary-spin self-dual theories, bulk-to-bulk propagators can be derived and three- and four-point AdS/CFT correlators can be computed explicitly in a contraction of Chiral higher-spin gravity.

What carries the argument

The Fefferman-Graham expansion adapted to self-dual theories of arbitrary spin, which supplies the holographic dictionary and enables propagator and correlator calculations.

If this is right

  • Bulk-to-bulk propagators exist for arbitrary-spin self-dual theories.
  • Three- and four-point AdS/CFT correlators become computable in the contracted Chiral higher-spin gravity.
  • The same dictionary applies to the full class of self-dual higher-spin models.
  • Self-dual Yang-Mills theory extends to a higher-spin version with an AdS/CFT description.

Where Pith is reading between the lines

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

  • The dictionary may extend directly to the uncontracted Chiral higher-spin gravity and its proposed duality with subsectors of Chern-Simons matter theories.
  • Higher-point functions could be obtained by iterating the same propagator and vertex rules.
  • The approach offers a route to test self-dual holography by comparing bulk correlators against explicit CFT computations on the boundary.
  • Similar Fefferman-Graham constructions might apply to other UV-finite self-dual models beyond gravity.

Load-bearing premise

Self-dual theories should possess their own AdS/CFT dualities.

What would settle it

Computed four-point correlators in the contracted theory that fail to match independent boundary CFT calculations would falsify the dictionary.

Figures

Figures reproduced from arXiv: 2605.30276 by Evgeny Skvortsov, Richard Van Dongen.

Figure 1
Figure 1. Figure 1: The “map” of self-dual theories. Along x we plot spin and along y we display the “number of derivatives” in cubic vertices. The smallest theories are SDYM and SDGR, which admit higher-spin extensions: HS-SDYM and HS-SDGR. The maximal self-dual theory is chiral higher-spin gravity. There are many intermediate cases [12, 16] and the complete classification is not yet available. The x-line itself is forbidden… view at source ↗
Figure 2
Figure 2. Figure 2: In fact, the existence of (anti)-Chiral theories implies that the vector models should [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
read the original abstract

Self-dual theories, being UV-finite, should have their own AdS/CFT dualities. Higher-spin extensions of self-dual theories are attractive to simplify the CFT duals. The maximal self-dual theory is Chiral higher-spin gravity, which should be dual to a subsector of Chern--Simons matter theories. As a step toward establishing self-dual holography, we develop the Fefferman--Graham expansion and holographic dictionary for arbitrary spin self-dual theories. As an application, we derive bulk-to-bulk propagators and compute three- and four-point AdS/CFT correlators in a contraction of Chiral higher-spin gravity, which is a higher-spin extension of self-dual Yang--Mills theory.

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

1 major / 0 minor

Summary. The paper develops the Fefferman-Graham expansion and holographic dictionary for arbitrary-spin self-dual theories. As an application, it derives bulk-to-bulk propagators and computes three- and four-point AdS/CFT correlators in a contraction of Chiral higher-spin gravity (a higher-spin extension of self-dual Yang-Mills), presented as a step toward self-dual holography in which the maximal self-dual theory is dual to a subsector of Chern-Simons matter theories.

Significance. If the dictionary construction and correlator computations are internally consistent and correctly derived, the work would supply concrete holographic tools for UV-finite self-dual higher-spin theories, potentially simplifying dual CFTs and enabling explicit higher-point function calculations in this setting.

major comments (1)
  1. [Abstract] Abstract: the statement that Chiral higher-spin gravity 'should be dual to a subsector of Chern--Simons matter theories' is asserted without derivation, explicit operator mapping, or verification that the computed three- and four-point functions match CFT expectations. This premise is load-bearing for interpreting the results as progress toward self-dual holography.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the detailed report and constructive feedback. We address the single major comment below.

read point-by-point responses

  1. Referee: the statement that Chiral higher-spin gravity 'should be dual to a subsector of Chern--Simons matter theories' is asserted without derivation, explicit operator mapping, or verification that the computed three- and four-point functions match CFT expectations. This premise is load-bearing for interpreting the results as progress toward self-dual holography.

    Authors: We agree that the full duality between Chiral higher-spin gravity and a subsector of Chern-Simons matter theories is not derived, mapped, or verified in this work. The phrasing in the abstract is intended as contextual motivation, drawing on existing results in higher-spin holography and the UV-finiteness of self-dual theories; it is not presented as a claim established here. Our manuscript develops the Fefferman-Graham expansion and holographic dictionary for arbitrary-spin self-dual theories and computes explicit three- and four-point correlators in a contraction of Chiral higher-spin gravity (a higher-spin extension of self-dual Yang-Mills). These bulk computations are offered as a concrete step toward self-dual holography rather than a verification of the maximal duality. To address the concern, we will revise the abstract to clarify the conjectural status of the duality statement and the limited scope of the present calculations. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper develops the Fefferman-Graham expansion, holographic dictionary, bulk-to-bulk propagators, and explicit three- and four-point correlators for a contraction of chiral higher-spin gravity. These steps are presented as independent technical constructions applied to the theory. The duality to a subsector of Chern-Simons matter theories is stated as an expected property ('should be dual') rather than a result derived or used as an input within the paper's equations. No self-definitional reductions, fitted inputs renamed as predictions, or load-bearing self-citations that collapse the computed correlators back to the premise are present. The work is therefore self-contained against external benchmarks for the calculations performed.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claims rest on the domain assumption that self-dual theories admit AdS/CFT dualities and on the further assumption that chiral higher-spin gravity is dual to a Chern-Simons subsector; no free parameters or invented entities are visible in the abstract.

axioms (2)
  • domain assumption Self-dual theories, being UV-finite, should have their own AdS/CFT dualities
    Opening sentence of abstract
  • domain assumption The maximal self-dual theory is dual to a subsector of Chern-Simons matter theories
    Abstract states this as background for the application

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discussion (0)

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Forward citations

Cited by 2 Pith papers

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

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