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REVIEW 3 major objections 4 minor 3 cited by

The paper claims that twistor-space variables, with Penrose and super-Penrose transforms, make 3d CFT correlators—conserved, scalar, generic, and supersymmetric—simple and systematic.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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Lecture notes recapping off-shell spinor helicity, twistor, and super-twistor methods for 3d CFT correlators, with 55 exercises and no substantial new research result.

T0 review reviewed 2026-08-05 challenge →

load-bearing objection Useful lecture-note compilation, not a new research result; the scalar/generic-operator twistor extension in Section 13 has a real gap at the Δ=1/2 unitarity bound. the 3 major comments →

arxiv 2508.21633 v1 pith:TQUFH6IQ submitted 2025-08-29 hep-th math-phmath.MP

Lectures on the Spinor and Twistor Formalism in 3D Conformal Field Theory

Dhruva K.S This is my paper
classification hep-th math-phmath.MP PACS 11.25.Hf11.30.Pb
keywords 3d conformal field theoryspinor helicitytwistor spacePenrose transformsuper-twistorssuperconformal field theoryAdS4/CFT3chiral higher spin theory
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The reading

These lecture notes argue that 3d conformal field theory has a natural kinematic formulation in spinor and twistor variables. The author establishes off-shell spinor helicity variables for conserved currents in R^2,1, uses them to organize two- and three-point correlators, and then derives the Penrose transform that maps twistor-space functions to position-space currents. The construction is extended from conserved currents to scalars and arbitrary non-conserved operators, at the cost of non-local conformal generators, and then to superconformal theories via super-twistors and a super-Penrose transform. The recurring claim is that correlators of (super)currents become simple functions of symplectic invariants and projective delta functions in (super-)twistor space, exposing structure that is obscured in position space. Applications include double-copy relations, the flat-space limit of AdS4 correlators, Chern-Simons matter theories, and the holographic dual of chiral higher spin theory.

Core claim

The notes' central claim is that twistor space is the natural kinematic home for 3d CFT correlators. Building on the Penrose transform, a conserved spin-s current in R^2,1 can be written as a projective integral of an unconstrained twistor-space function, with conservation automatic. The same construction extends to scalars and generic operators, at the cost of non-local conformal generators. In super-twistor space with coordinates (λ, μbar, ψ), the super-Penrose transform packages the whole super-current multiplet into one projective integral, and the resulting super-correlators are literally the non-supersymmetric ones with twistors replaced by super-twistors. Correlators of conserved curr

What carries the argument

The Penrose transform and its super-version: position-space operators are recovered by integrating twistor-space functions over RP^1 (or RP^{1|N}) with the incidence relation μbar = -xλ (and, supersymmetrically, ψ = -√2 e^{-iπ/4} θ·λ, with a θ^2 correction to μbar). The Witten half-Fourier transform connects these twistor variables to the spinor helicity variables of the first part, and the infinity twistor encodes the flat-space metric and the parity-odd sector.

Load-bearing premise

The load-bearing premise is that the inverse derivative (λ·∂/∂μbar)^{-1} is well defined on twistor-space operators, with boundary terms vanishing at μbar→∞; the notes explicitly state that higher-point Ward identities with this non-local generator remain unsolved.

What would settle it

Compute a four-point scalar correlator in a free 3d CFT in position space and then try to reproduce it through the generalized Penrose transform (13.14) using the non-local special conformal generator (13.10)-(13.11). If the integrals defining (λ·∂/∂μbar)^{-1} need a boundary contribution at μbar→∞, or the twistor result disagrees with the known position-space answer, the generalized transform for generic operators is not well defined.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • Twistor-space two- and three-point Wightman functions of conserved currents are determined by simple Sp(4)-invariant objects—symplectic dot products and projective delta functions—and Wick-rotate to known momentum-space results.
  • The parity-odd sector of 3d CFT, including epsilon transforms and contact terms, is encoded by the infinity twistor, with sign factors producing conformally invariant contact terms.
  • Scalars and generic non-conserved operators admit a generalized Penrose transform, opening the door to twistor-space descriptions of massive and spinning AdS4 fields; the notes state that higher-point Ward identities for such operators remain unsolved.
  • Super-correlators of conserved super-currents are obtained by replacing twistors with super-twistors: integer-spin three-point functions are homogeneous, half-integer-spin ones are non-homogeneous, and the component correlators arrange themselves to be super-covariant.
  • Spinor-helicity applications give double-copy relations among CFT three-point functions, a flat-space limit of AdS4 correlators, and identify a chiral/anti-chiral limit of Chern-Simons matter theories with the holographic dual of chiral higher spin theory.

Where Pith is reading between the lines

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

  • Inference: The non-local inverse derivative used for scalars and generic operators suggests that higher-point twistor-space correlators will require a careful prescription to control boundary terms at μbar→∞; the two-point success does not guarantee the four-point case.
  • Inference: If the 'replace twistors by super-twistors' rule holds at higher points, a superconformal block decomposition in twistor space could be built from the non-supersymmetric blocks with graded symplectic invariants, potentially giving a compact spinning superconformal bootstrap.
  • Inference: The chiral/anti-chiral limits of Chern-Simons matter theories point toward a family of parity-selected, non-unitary holographic CFTs whose four-point functions could be tested by explicit bulk-loop computations in chiral higher spin gravity.
  • Inference: The twistor-space epsilon transform for super-currents may generate parity-odd super-correlators and super contact terms relevant to 3d supersymmetric anomalies; the notes derive the parity-odd two-point super-correlator but leave higher-point parity-odd integrals open.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The manuscript is a set of lecture notes applying spinor-helicity and twistor methods to three-dimensional CFT. Part I reviews off-shell spinor-helicity variables, conformal Ward identities, two- and three-point correlators of conserved currents, conformal partial waves, double-copy relations, flat-space limits, Chern-Simons matter theories, and the holography of chiral higher-spin theory. Part II introduces twistor space for R^{2,1}, the Penrose and Witten transforms, twistor-space Ward identities, parity-odd structures via the infinity twistor, and extensions to scalars and generic non-conserved operators. Part III develops a super-twistor formalism for 3d SCFT, including a super-Penrose transform, super-conformal Ward identities, and two- and three-point super-correlators. The advertised central claim is that conserved and superconformal correlators become simple, natural expressions in twistor space. The notes are self-consciously based on the author's recent papers [74?76] and contain 55 exercises.

Significance. If the constructions are valid, this is a useful pedagogical and technical contribution: it consolidates spinor-helicity and twistor descriptions of 3d CFT, gives compact forms for current and supercurrent correlators, and provides a clear bridge between the momentum-space and twistor-space approaches. The many worked examples and exercises make it a potentially valuable reference for students and researchers entering the subject. The main weaknesses are that the most novel claims are not fully established within the notes: the scalar/generic-operator extension relies on a non-local inverse derivative that fails at the Δ=1/2 endpoint, and the super-Penrose results are largely taken from, and delegated to, the author's own earlier papers. These issues are local and fixable, so they do not invalidate the conserved-current material, but they do require revision of the abstract and the presentation of the generalized transforms.

major comments (3)
  1. [Section 13.2, Eq. (13.11)] The definition (λ·∂/∂μbar)^{-1} f = -∫_0^∞ ds f(λ, μbar+sλ) is load-bearing for the claim that the Penrose transform extends to scalars of arbitrary dimension, because it enters the special conformal generator (13.10). The text asserts that the inverse is well-defined for the unitary bound Δ ≥ (d−2)/2, but at the endpoint Δ=1/2 the two-point function (13.4) gives f(λ1, μbar1+sλ1) ~ |⟨12⟩|^{-1} (Z1·Z2 − s⟨12⟩)^{-1} up to constants, which decays only as 1/s. The defining integral therefore diverges logarithmically, in addition to the possible pole. No regularization or analytic continuation is supplied, and Exercise 13.2 is left to the reader. Thus the 'arbitrary scaling dimension' statement is unsupported at Δ=1/2. Please either exclude the endpoint, supply a convergent definition, or prove convergence in a distributional sense.
  2. [Sections 13.2–13.3] The abstract says the notes derive the Penrose transform for 'generic non-conserved operators', but Section 13.2 ends with the statement that higher-point Ward identities with the non-local SCT generator are still unsolved, and Section 13.3's transform (13.14) is presented through Exercise 13.3, with the position-space check delegated to Exercise 13.4. The two-point function (13.15) is an ansatz by dimensional analysis and projectiveness rather than a derivation. This is acceptable for lecture notes, but the abstract and the summaries should be scaled back to 'formal transform and two-point structure' for generic operators.
  3. [Sections 16–21] The super-Penrose transform and the super-correlator solutions are among the paper's main advertised novelties, but the text states that the super-Penrose transform 'was developed by the authors of [76]' and that the flow is 'heavily based on [76]'. Reference [76] shares the author of the present manuscript, and the consistency checks (super-conservation in Exercise 16.1, component expansion in Exercise 19.5, Ward identities in Exercise 19.6) are all assigned as exercises rather than demonstrated. This is not an internal inconsistency, and lecture notes may review the author's own work, but the abstract's 'we derive' and 'we find' overstate the incremental content. Please rewrite the contribution statement to distinguish new exposition from results taken from [74–76].
minor comments (4)
  1. [Eq. (1.89)] There are unmatched parentheses in the conformal partial wave expression, for example in the factors written as (1 − 3s/(p1+p2+s))(1 − 3s/(p3+p4+s)). These should be corrected.
  2. [Section 3 and Appendix A] The text contains placeholder phrases 'references to be provided soon' and 'a reference to be provided soon'. These need to be filled before submission.
  3. [Throughout] Typos and notation inconsistencies: 'Ads' should be 'AdS' in the Part I summary; 'ST 4' should be 'ST^4'; the unitary bound is written as Δ ≥ d−2/2 but should be Δ ≥ (d−2)/2; Eq. (11.8) has a garbled bracket in the finite rescaling identity.
  4. [Section 13, footnote and Eq. (13.4)] The claim that Z1·Z2 is dimensionless is only true under a simultaneous rescaling convention; under Z1→rZ1 it scales as r. The absolute value in (13.4) also needs a short comment on its definition for Lorentzian signature and for complex/conjugate spinors.

Circularity Check

2 steps flagged

Moderate circularity: the generic-operator and super-Witten results are imported from the author's own [76], and the advertised 'natural generalization' of super-correlators is a direct substitution.

specific steps
  1. self citation load bearing [Section 13.3, Exercise 13.3; Section 13.2, Eq. (13.10)-(13.11)]
    "As an application of what we have learnt so far, derive the Penrose transform for the non-conserved operator: ... where ck are coefficients that can easily be determined by an explicit calculation and performing the Witten transform (13.13) for each component."

    The notes advertise a derivation of the generalized Penrose transform for generic non-conserved operators, but the formula is not derived in the text; it is assigned as an exercise. The underlying non-local Sp(4) representation, including the inverse derivative (lambda . d/dmu-bar)^{-1} of Eq. (13.11), is introduced by the sentence 'First steps in this direction were taken in [76] which we recount below.' Since [76] shares the author Dhruva K.S. and no independent check, code, or external benchmark is supplied, the advertised generic-operator construction rests on a self-citation rather than on an in-notes derivation.

  2. renaming known result [Section 19.3; abstract (last sentence)]
    "The first thing to notice from the form of the invariants (19.9) and (19.10) is that is that tey are simply the same as their non supersymmetric counterparts (11.9) and (11.12)! Supplementing this by the super-helicity identities (19.6) and (19.8), we see that super-correlators can be obtained from their non-susy just by replacing twistors by super-twistors."

    The super-invariants (19.9) are the graded extensions of the non-supersymmetric invariants (11.9), and the super-helicity identities impose the same projective-weight conditions. Therefore the abstract's 'We find that the supersymmetric correlators are simple and natural generalizations of their non-supersymmetric counterparts' is a restatement of the construction: the super-correlators (e.g., Eq. (19.13)) are obtained from the non-susy ones (Eq. (11.22)) by substituting super-twistors and graded dot products. The claimed 'finding' is a renaming/substitution consequence rather than an independent result.

full rationale

The paper is not globally circular: the conserved-current Penrose transform is derived in the text from Fourier plus Witten transforms (Section 10), the conformal Ward identities for currents are solved with ingredients that have external support [72], and the super-Penrose transform of Section 16 is derived by matching the known component Penrose transforms with the superfield expansion. There is no fitted-input-called-prediction step. However, two load-bearing pieces are less independent. First, the extension to scalars and generic non-conserved operators in Section 13 uses a non-local inverse derivative (13.11) and the generic transform (13.14) imported from [76], an author-overlapping paper, with the derivation left as an exercise; no independent validation is given. Second, the advertised simplicity of super-correlators is explicitly obtained by 'replacing twistors by super-twistors', so the central 'natural generalization' statement reduces by construction to a substitution. The ill-definedness of the inverse derivative at the Delta=1/2 unitary bound (flagged by the skeptic) and the unsolved higher-point Ward identities with the non-local generator (stated in Section 13.2) are correctness/completeness concerns rather than circularity. On balance, the central Penrose and super-Penrose transforms retain independent content, but the generic-operator extension and the 'natural generalization' headline are substantially self-citing or definitional, giving a score of 4.

Axiom & Free-Parameter Ledger

0 free parameters · 6 axioms · 0 invented entities

The notes introduce no new free parameters or invented physical entities; the formalism, including the infinity twistor, is inherited from prior literature. The main unstated assumptions are standard CFT and AdS/CFT dictionary entries plus the non-local inverse-derivative assumption in Section 13.2.

axioms (6)
  • domain assumption Conserved symmetric traceless currents in 3d CFT have scaling dimension Δ=s+1 and only two independent helicity components.
    Used throughout Part I to construct the helicity basis and Ward identities, Section 1.3.
  • domain assumption The conformal generators in spinor-helicity variables take the forms in Eqs. (1.31)-(1.35), with the special conformal generator a second-order differential operator.
    Presented as an ansatz in Section 1.4 and verified through exercises, not derived from first principles in the notes.
  • domain assumption The incidence relations (7.3) and the Penrose transform (8.1) give a valid representation of conserved currents in R^{2,1}.
    Central to Part II; the geometry is reviewed from [72,74,76].
  • ad hoc to paper The inverse derivative (λ·∂/∂μbar)^{-1} is well-defined and the required boundary terms vanish, so the non-local special conformal generator (13.10) acts correctly on generic operators.
    Explicit assumption in Section 13.2; higher-point Ward identities remain unsolved.
  • domain assumption The super-incidence relations (16.10) and the super-Penrose transform (16.9) correctly describe conserved super-currents.
    Taken from [76], presented as review in Section 16.
  • domain assumption The AdS4/CFT3 dictionary maps bulk cubic vertices to homogeneous and non-homogeneous current correlators.
    Used for interpretation of correlators in Sections 1.5 and 5.

reviewed 2026-08-05 · how reviews work

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Cite this review

Pith. "Pith review of Lectures on the Spinor and Twistor Formalism in 3D Conformal Field Theory." pith.science (2026). https://pith.science/paper/TQUFH6IQ

@misc{pith2026250821633,
  author       = {Pith},
  title        = {Pith review of: Lectures on the Spinor and Twistor Formalism in 3D Conformal Field Theory},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TQUFH6IQ}},
  note         = {Machine review of arXiv:2508.21633}
}
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abstract

These notes are based on my lectures given at $\text{ST}^4$ 2025 held at IISER Bhopal. We study the application of spinor and twistor methods to three dimensional conformal field theories in these notes. They are divided into three parts dealing with spinor helicity, twistors and super-twistors respectively. In the first part, we introduce the off-shell spinor helicity formalism and apply it in several contexts including double copy relations, connection to four dimensional scattering amplitudes, correlators in Chern-Simons matter theories and the holography of chiral higher spin theory. The second part of the notes introduces the twistor space formalism. After discussing the geometry of twistor space, we derive the Penrose transform for conserved currents, scalars with arbitrary scaling dimension as well as generic non-conserved operators. We also explicitly show how the spinor and twistor approaches are related. We discuss how correlators of these operators and conserved currents in particular drastically simplify in twistor space unveiling their hidden simplicity. We also extend our construction to super-conformal field theories and develop a manifest super-twistor space formalism and derive the supersymmetric Penrose transform. We find that the supersymmetric correlators are simple and natural generalizations of their non-supersymmetric counterparts. The notes are made to be self-contained and also include over $50$ exercises that illustrate the formalism.

discussion (0)

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Reference graph

Works this paper leans on

139 extracted references · 27 canonical work pages · cited by 3 Pith papers · 27 internal anchors

  1. [1]

    Elvang and Y.-t

    H. Elvang and Y.-t. Huang, Scattering Amplitudes, 1308.1697

    Pith/arXiv arXiv

  2. [2]

    Maldacena, The Large N limit of superconformal field theories and supergravity , Adv

    J.M. Maldacena, The Large N limit of superconformal field theories and supergravity , Adv. Theor. Math. Phys. 2 (1998) 231 [ hep-th/9711200]

    Pith/arXiv arXiv 1998

  3. [3]

    Gubser, I.R

    S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory , Phys. Lett. B 428 (1998) 105 [ hep-th/9802109]

    Pith/arXiv arXiv 1998

  4. [4]

    Witten, Anti de Sitter space and holography , Adv

    E. Witten, Anti de Sitter space and holography , Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150]

    Pith/arXiv arXiv 1998

  5. [5]

    Belavin, A.M

    A.A. Belavin, A.M. Polyakov and A.B. Zamolodchikov, Infinite Conformal Symmetry in Two-Dimensional Quantum Field Theory , Nucl. Phys. B 241 (1984) 333

    1984

  6. [6]

    Rattazzi, V.S

    R. Rattazzi, V.S. Rychkov, E. Tonni and A. Vichi, Bounding scalar operator dimensions in 4D CFT , JHEP 12 (2008) 031 [ 0807.0004]

    Pith/arXiv arXiv 2008

  7. [7]

    Poland and D

    D. Poland and D. Simmons-Duffin, Snowmass White Paper: The Numerical Conformal Bootstrap, in Snowmass 2021 , 3, 2022 [ 2203.08117]

    Pith/arXiv arXiv 2021

  8. [8]

    Hartman, D

    T. Hartman, D. Mazac, D. Simmons-Duffin and A. Zhiboedov, Snowmass White Paper: The Analytic Conformal Bootstrap , in Snowmass 2021 , 2, 2022 [ 2202.11012]

    Pith/arXiv arXiv 2021

  9. [9]

    Maldacena and G.L

    J.M. Maldacena and G.L. Pimentel, On graviton non-Gaussianities during inflation , JHEP 09 (2011) 045 [ 1104.2846]

    Pith/arXiv arXiv 2011

  10. [10]

    McFadden and K

    P. McFadden and K. Skenderis, Cosmological 3-point correlators from holography, JCAP 06 (2011) 030 [ 1104.3894]

    Pith/arXiv arXiv 2011

  11. [11]

    Coriano, L

    C. Coriano, L. Delle Rose, E. Mottola and M. Serino, Solving the Conformal Constraints for Scalar Operators in Momentum Space and the Evaluation of Feynman ’s Master Integrals, JHEP 07 (2013) 011 [ 1304.6944]

    Pith/arXiv arXiv 2013

  12. [12]

    Bzowski, P

    A. Bzowski, P. McFadden and K. Skenderis, Implications of conformal invariance in momentum space, JHEP 03 (2014) 111 [ 1304.7760]

    Pith/arXiv arXiv 2014

  13. [13]

    Ghosh, N

    A. Ghosh, N. Kundu, S. Raju and S.P. Trivedi, Conformal Invariance and the Four Point Scalar Correlator in Slow-Roll Inflation , JHEP 07 (2014) 011 [ 1401.1426]

    Pith/arXiv arXiv 2014

  14. [14]

    Bzowski, P

    A. Bzowski, P. McFadden and K. Skenderis, Scalar 3-point functions in CFT: renormalisation, beta functions and anomalies , JHEP 03 (2016) 066 [ 1510.08442]

    Pith/arXiv arXiv 2016

  15. [15]

    Bzowski, P

    A. Bzowski, P. McFadden and K. Skenderis, Renormalised 3-point functions of stress tensors and conserved currents in CFT , JHEP 11 (2018) 153 [ 1711.09105]

    Pith/arXiv arXiv 2018

  16. [16]

    Bzowski, P

    A. Bzowski, P. McFadden and K. Skenderis, Renormalised CFT 3-point functions of scalars, currents and stress tensors , JHEP 11 (2018) 159 [ 1805.12100]

    Pith/arXiv arXiv 2018

  17. [17]

    Farrow, A.E

    J.A. Farrow, A.E. Lipstein and P. McFadden, Double copy structure of CFT correlators, JHEP 02 (2019) 130 [ 1812.11129]

    Pith/arXiv arXiv 2019

  18. [18]

    Isono, T

    H. Isono, T. Noumi and T. Takeuchi, Momentum space conformal three-point functions of conserved currents and a general spinning operator , JHEP 05 (2019) 057 [1903.01110]. 60

    Pith/arXiv arXiv 2019

  19. [19]

    Bautista and H

    T. Bautista and H. Godazgar, Lorentzian CFT 3-point functions in momentum space, JHEP 01 (2020) 142 [ 1908.04733]

    Pith/arXiv arXiv 2020

  20. [20]

    Gillioz, Conformal 3-point functions and the Lorentzian OPE in momentum space, Commun

    M. Gillioz, Conformal 3-point functions and the Lorentzian OPE in momentum space, Commun. Math. Phys. 379 (2020) 227 [ 1909.00878]

    Pith/arXiv arXiv 2020

  21. [21]

    Baumann, C

    D. Baumann, C. Duaso Pueyo, A. Joyce, H. Lee and G.L. Pimentel, The cosmological bootstrap: weight-shifting operators and scalar seeds , JHEP 12 (2020) 204 [1910.14051]

    Pith/arXiv arXiv 2020

  22. [22]

    Lipstein and P

    A.E. Lipstein and P. McFadden, Double copy structure and the flat space limit of conformal correlators in even dimensions , Phys. Rev. D 101 (2020) 125006 [1912.10046]

    Pith/arXiv arXiv 2020

  23. [23]

    Baumann, C

    D. Baumann, C. Duaso Pueyo, A. Joyce, H. Lee and G.L. Pimentel, The Cosmological Bootstrap: Spinning Correlators from Symmetries and Factorization , SciPost Phys. 11 (2021) 071 [ 2005.04234]

    Pith/arXiv arXiv 2021

  24. [24]

    Jain, R.R

    S. Jain, R.R. John and V. Malvimat, Momentum space spinning correlators and higher spin equations in three dimensions , JHEP 11 (2020) 049 [ 2005.07212]

    Pith/arXiv arXiv 2020

  25. [25]

    Jain, R.R

    S. Jain, R.R. John and V. Malvimat, Constraining momentum space correlators using slightly broken higher spin symmetry , JHEP 04 (2021) 231 [ 2008.08610]

    Pith/arXiv arXiv 2021

  26. [26]

    Jain, R.R

    S. Jain, R.R. John, A. Mehta, A.A. Nizami and A. Suresh, Momentum space parity-odd CFT 3-point functions , JHEP 08 (2021) 089 [ 2101.11635]

    Pith/arXiv arXiv 2021

  27. [27]

    Jain, R.R

    S. Jain, R.R. John, A. Mehta, A.A. Nizami and A. Suresh, Double copy structure of parity-violating CFT correlators, JHEP 07 (2021) 033 [ 2104.12803]

    Pith/arXiv arXiv 2021

  28. [28]

    Jain, R.R

    S. Jain, R.R. John, A. Mehta, A.A. Nizami and A. Suresh, Higher spin 3-point functions in 3d CFT using spinor-helicity variables , JHEP 09 (2021) 041 [2106.00016]

    Pith/arXiv arXiv 2021

  29. [29]

    Baumann, W.-M

    D. Baumann, W.-M. Chen, C. Duaso Pueyo, A. Joyce, H. Lee and G.L. Pimentel, Linking the singularities of cosmological correlators , JHEP 09 (2022) 010 [2106.05294]

    Pith/arXiv arXiv 2022

  30. [30]

    Jain and R.R

    S. Jain and R.R. John, Relation between parity-even and parity-odd CFT correlation functions in three dimensions , JHEP 12 (2021) 067 [ 2107.00695]

    Pith/arXiv arXiv 2021

  31. [31]

    Jain, R.R

    S. Jain, R.R. John, A. Mehta and D.K. S, Constraining momentum space CFT correlators with consistent position space OPE limit and the collider bound , JHEP 02 (2022) 084 [ 2111.08024]

    Pith/arXiv arXiv 2022

  32. [32]

    Gillioz, Conformal field theory for particle physicists , SpringerBriefs in Physics, Springer (2023), 10.1007/978-3-031-27086-4, [ 2207.09474]

    M. Gillioz, Conformal field theory for particle physicists , SpringerBriefs in Physics, Springer (2023), 10.1007/978-3-031-27086-4, [ 2207.09474]

    Pith/arXiv arXiv 2023

  33. [33]

    Caloro and P

    F. Caloro and P. McFadden, Shift operators from the simplex representation in momentum-space CFT, JHEP 03 (2023) 106 [ 2212.03887]

    Pith/arXiv arXiv 2023

  34. [34]

    Marotta, K

    R. Marotta, K. Skenderis and M. Verma, Momentum space CFT correlators of non-conserved spinning operators, JHEP 03 (2023) 196 [ 2212.13135]

    Pith/arXiv arXiv 2023

  35. [35]

    Bzowski, Handbook of derivative AdS amplitudes , JHEP 04 (2024) 082 [2312.11625]

    A. Bzowski, Handbook of derivative AdS amplitudes , JHEP 04 (2024) 082 [2312.11625]

    Pith/arXiv arXiv 2024

  36. [36]

    D.K. S, D. Mazumdar and S. Yadav, n-point functions in conformal quantum mechanics: a momentum space odyssey , JHEP 08 (2024) 085 [ 2402.16947]

    Pith/arXiv arXiv 2024

  37. [37]

    Gupta and Meenu, Non-relativistic conformal field theory in momentum space , Eur

    R.K. Gupta and Meenu, Non-relativistic conformal field theory in momentum space , Eur. Phys. J. C 85 (2025) 422 [ 2403.01933]

    Pith/arXiv arXiv 2025

  38. [38]

    Jain, D.K

    S. Jain, D.K. S and E. Skvortsov, Hidden sectors of Chern-Simons matter theories and exact holography , Phys. Rev. D 111 (2025) 106017 [ 2405.00773]

    arXiv 2025

  39. [39]

    Marotta, K

    R. Marotta, K. Skenderis and M. Verma, Flat space spinning massive amplitudes from momentum space CFT , JHEP 08 (2024) 226 [ 2406.06447]. 61

    Pith/arXiv arXiv 2024

  40. [40]

    Corian´ o and S

    C. Corian´ o and S. Lionetti,CFT constraints on parity-odd interactions with axions and dilatons , Phys. Rev. D 110 (2024) 125008 [ 2408.02580]

    Pith/arXiv arXiv 2024

  41. [41]

    Gillioz, The momentum-space conformal bootstrap in 2d , 2502.21227

    M. Gillioz, The momentum-space conformal bootstrap in 2d , 2502.21227

    Pith/arXiv arXiv

  42. [42]

    Arkani-Hamed and J

    N. Arkani-Hamed and J. Maldacena, Cosmological Collider Physics , 1503.08043

    Pith/arXiv arXiv

  43. [43]

    Arkani-Hamed, D

    N. Arkani-Hamed, D. Baumann, H. Lee and G.L. Pimentel, The Cosmological Bootstrap: Inflationary Correlators from Symmetries and Singularities , JHEP 04 (2020) 105 [ 1811.00024]

    Pith/arXiv arXiv 2020

  44. [44]

    Baumann, D

    D. Baumann, D. Green, A. Joyce, E. Pajer, G.L. Pimentel, C. Sleight et al., Snowmass White Paper: The Cosmological Bootstrap , in Snowmass 2021 , 3, 2022 [2203.08121]

    Pith/arXiv arXiv 2021

  45. [45]

    Raju, BCFW for Witten Diagrams , Phys

    S. Raju, BCFW for Witten Diagrams , Phys. Rev. Lett. 106 (2011) 091601 [1011.0780]

    Pith/arXiv arXiv 2011

  46. [46]

    Raju, Recursion Relations for AdS/CFT Correlators , Phys

    S. Raju, Recursion Relations for AdS/CFT Correlators , Phys. Rev. D 83 (2011) 126002 [1102.4724]

    Pith/arXiv arXiv 2011

  47. [47]

    Raju, Four Point Functions of the Stress Tensor and Conserved Currents in AdS4/CFT3, Phys

    S. Raju, Four Point Functions of the Stress Tensor and Conserved Currents in AdS4/CFT3, Phys. Rev. D 85 (2012) 126008 [ 1201.6452]

    Pith/arXiv arXiv 2012

  48. [48]

    Albayrak and S

    S. Albayrak and S. Kharel, Towards the higher point holographic momentum space amplitudes, JHEP 02 (2019) 040 [ 1810.12459]

    Pith/arXiv arXiv 2019

  49. [49]

    Albayrak and S

    S. Albayrak and S. Kharel, Towards the higher point holographic momentum space amplitudes. Part II. Gravitons , JHEP 12 (2019) 135 [ 1908.01835]

    Pith/arXiv arXiv 2019

  50. [50]

    Gadde and T

    A. Gadde and T. Sharma, A scattering amplitude for massive particles in AdS , JHEP 09 (2022) 157 [ 2204.06462]

    Pith/arXiv arXiv 2022

  51. [51]

    Armstrong, H

    C. Armstrong, H. Gomez, R. Lipinski Jusinskas, A. Lipstein and J. Mei, New recursion relations for tree-level correlators in anti–de Sitter spacetime , Phys. Rev. D 106 (2022) L121701 [ 2209.02709]

    Pith/arXiv arXiv 2022

  52. [52]

    Albayrak and S

    S. Albayrak and S. Kharel, All plus four point (A)dS graviton function using generalized on-shell recursion relation , JHEP 05 (2023) 151 [ 2302.09089]

    Pith/arXiv arXiv 2023

  53. [53]

    Mei, Amplitude Bootstrap in (Anti) de Sitter Space And The Four-Point Graviton from Double Copy , 2305.13894

    J. Mei, Amplitude Bootstrap in (Anti) de Sitter Space And The Four-Point Graviton from Double Copy , 2305.13894

    Pith/arXiv arXiv

  54. [54]

    Chowdhury and K

    C. Chowdhury and K. Singh, Analytic results for loop-level momentum space Witten diagrams, JHEP 12 (2023) 109 [ 2305.18529]

    Pith/arXiv arXiv 2023

  55. [55]

    Albayrak, S

    S. Albayrak, S. Kharel and X. Wang, Momentum-space formulae for AdS correlators for diverse theories in diverse dimensions , 2312.02154

    Pith/arXiv arXiv

  56. [56]

    Chowdhury, A

    C. Chowdhury, A. Lipstein, J. Mei and Y. Mo, Soft limits of gluon and graviton correlators in Anti-de Sitter space , JHEP 10 (2024) 070 [ 2407.16052]

    Pith/arXiv arXiv 2024

  57. [57]

    Chopping, C

    A.J. Chopping, C. Sleight and M. Taronna, Cosmological correlators for Bogoliubov initial states , JHEP 09 (2024) 152 [ 2407.16652]

    Pith/arXiv arXiv 2024

  58. [58]

    Chowdhury, P

    C. Chowdhury, P. Chowdhury, R.N. Moga and K. Singh, Loops, recursions, and soft limits for fermionic correlators in (A)dS , JHEP 10 (2024) 202 [ 2408.00074]

    Pith/arXiv arXiv 2024

  59. [59]

    Chowdhury, G

    C. Chowdhury, G. Doran, A. Lipstein, R. Monteiro, S. Nagy and K. Singh, Light-cone actions and correlators of self-dual theories in AdS 4, 2411.04172

    Pith/arXiv arXiv

  60. [60]

    Raju, New Recursion Relations and a Flat Space Limit for AdS/CFT Correlators , Phys

    S. Raju, New Recursion Relations and a Flat Space Limit for AdS/CFT Correlators , Phys. Rev. D 85 (2012) 126009 [ 1201.6449]

    Pith/arXiv arXiv 2012

  61. [61]

    Corian` o, S

    C. Corian` o, S. Lionetti and M.M. Maglio, Parity-odd 3-point functions from CFT in momentum space and the chiral anomaly , Eur. Phys. J. C 83 (2023) 502 [2303.10710]. 62

    Pith/arXiv arXiv 2023

  62. [62]

    CFT Correlators and CP-Violating Trace Anomalies

    C. Corian` o, S. Lionetti and M.M. Maglio, CFT correlators and CP-violating trace anomalies, Eur. Phys. J. C 83 (2023) 839 [ 2307.03038]

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  63. [63]

    Corian` o, S

    C. Corian` o, S. Lionetti and M.M. Maglio, Parity-violating CFT and the gravitational chiral anomaly, Phys. Rev. D 109 (2024) 045004 [ 2309.05374]

    Pith/arXiv arXiv 2024

  64. [64]

    Hartman and G

    T. Hartman and G. Mathys, Averaged null energy and the renormalization group , JHEP 12 (2023) 139 [ 2309.14409]

    Pith/arXiv arXiv 2023

  65. [65]

    Hartman and G

    T. Hartman and G. Mathys, Null energy constraints on two-dimensional RG flows , JHEP 01 (2024) 102 [ 2310.15217]

    Pith/arXiv arXiv 2024

  66. [66]

    Light-ray sum rules and the c-anomaly

    T. Hartman and G. Mathys, Light-ray sum rules and the c-anomaly , JHEP 08 (2024) 008 [ 2405.10137]

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  67. [67]

    Penrose, Twistor algebra, J

    R. Penrose, Twistor algebra, J. Math. Phys. 8 (1967) 345

    1967

  68. [68]

    Nair, A Current Algebra for Some Gauge Theory Amplitudes , Phys

    V.P. Nair, A Current Algebra for Some Gauge Theory Amplitudes , Phys. Lett. B 214 (1988) 215

    1988

  69. [69]

    Witten, Perturbative gauge theory as a string theory in twistor space , Commun

    E. Witten, Perturbative gauge theory as a string theory in twistor space , Commun. Math. Phys. 252 (2004) 189 [ hep-th/0312171]

    Pith/arXiv arXiv 2004

  70. [70]

    Mason and D

    L.J. Mason and D. Skinner, Scattering Amplitudes and BCFW Recursion in Twistor Space, JHEP 01 (2010) 064 [ 0903.2083]

    Pith/arXiv arXiv 2010

  71. [71]

    Arkani-Hamed, F

    N. Arkani-Hamed, F. Cachazo, C. Cheung and J. Kaplan, The S-Matrix in Twistor Space, JHEP 03 (2010) 110 [ 0903.2110]

    Pith/arXiv arXiv 2010

  72. [72]

    Baumann, G

    D. Baumann, G. Mathys, G.L. Pimentel and F. Rost, A New Twist on Spinning (A)dS Correlators, 2408.02727

    Pith/arXiv arXiv

  73. [73]

    Jain, D.K

    S. Jain, D.K. S, D. Mazumdar and S. Yadav, A foray on SCFT 3 via super spinor-helicity and Grassmann twistor variables , JHEP 09 (2024) 027 [ 2312.03059]

    Pith/arXiv arXiv 2024

  74. [74]

    A. Bala, S. Jain, D.K. S., D. Mazumdar and V. Singh, 3D Conformal Field Theory in Twistor Space , 2502.18562

    Pith/arXiv arXiv

  75. [75]

    A. Bala, S. Jain, D.K. S., D. Mazumdar, V. Singh and B. Thakkar, A Supertwistor Formalism for N = 1, 2, 3, 4 SCFT3, 2503.19970

    Pith/arXiv arXiv

  76. [76]

    Bala and D.K

    A. Bala and D.K. S, An Ode to the Penrose and Witten transforms in Twistor space for 3D CFT , 2505.14082

    Pith/arXiv arXiv

  77. [77]

    Rost, A novel language for spinning (A)dS correlators , Ph.D

    F.E. Rost, A novel language for spinning (A)dS correlators , Ph.D. thesis, 2025

    2025

  78. [78]

    Mazumdar, Super-Penrose & Witten Transforms for SCFT 3, 2508.02672

    D. Mazumdar, Super-Penrose & Witten Transforms for SCFT 3, 2508.02672

    Pith/arXiv arXiv

  79. [79]

    Osborn, N=1 superconformal symmetry in four-dimensional quantum field theory , Annals Phys

    H. Osborn, N=1 superconformal symmetry in four-dimensional quantum field theory , Annals Phys. 272 (1999) 243 [ hep-th/9808041]

    Pith/arXiv arXiv 1999

  80. [80]

    Park, Superconformal symmetry and correlation functions , Nucl

    J.-H. Park, Superconformal symmetry and correlation functions , Nucl. Phys. B 559 (1999) 455 [ hep-th/9903230]

    Pith/arXiv arXiv 1999

Showing first 80 references.

This paper was first reviewed by deepseek-v4-flash on August 5, 2026.