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Symmetric formulation for higher spin correlators, quantum effective action and anomaly

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Pith's one-line read The quantum trace anomaly is the single source of both gauge and trace violations in higher-spin conformal theories, and a current shift restores gauge invariance while leaving a $2s$-derivative trace anomaly.

desk verdict Clean single-source mechanism for HS anomalies, but the anomaly is not actually computed; worth sending to peer review with a demand for the spin-2 case. read the letter →

arxiv 2608.01125 v1 pith:SJK5BPGW submitted 2026-08-02 hep-th

Melik Karapetyan , Ruben Manvelyan This is my paper
classification hep-th
keywords higher-spingaugetheoryconformalcorrelationfunctionsquantumeffectiveactiontraceanomalydimensionalregularizationsingularityextractionsymmetricformulationWardidentities
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

The paper aims to show that in a conformal higher-spin gauge theory, the quantum anomaly of the cubic effective action has a single origin: the finite part of the variation of the singular local part. Using a symmetric rewriting of three-point correlators in terms of four building blocks $G$, $\Psi$, $F_1$, $F_2$, it extracts the principal singularity by dimensional regularization and shows that the $1/\epsilon$ pole can only be cancelled by linear-in-$\epsilon$ terms coming from trace contractions. The consequence is that the renormalized current violates both conservation and tracelessness, but the conservation violation is a gradient of the trace, so a shift of the current restores gauge invariance and leaves a pure trace anomaly. If true, the trace anomaly is quadratic in the linearized field, contains $2s$ derivatives, and in $d=4$ takes the form of a combination of squares of generalized HS Weyl and Ricci tensors; the same argument explains why anomaly detection in higher dimensions requires higher-point correlators.

What carries the argument

The argument runs on two pieces of machinery. First, the symmetric structural tensor of the three-point correlator is generated by four objects — $G$, $\Psi$, $F_1$, $F_2$; absorbing the inversion factors yields a manifestly symmetric kernel $\tilde t^{(s)}(a,b,c;\hat Z,\hat Y,\hat X)$. Second, singularity extraction uses the distribution identity $(x^2)^{-\lambda} = \hat C_\lambda \epsilon^{-1}(-\Box)^{\lambda-d/2}\delta^d(x)$ and its three-point analogue, turning the residue into a polynomial in Laplacians on delta functions. The decisive observation is that only trace-type contractions such as $\Box z^2 = 2(d-\epsilon)$ produce the linear-in-$\epsilon$ terms that cancel the pole, so the a

What would settle it

Classify all conserved three-point structural tensors for spin 5 in the same formulation. If an independent conserved combination exists that is not a polynomial in $G,\Psi,F_1,F_2$, or if the number of combinations is not $s+1=6$, the singularity decomposition (5.1) is incomplete and the anomaly content may differ. A direct check is to evaluate the spin-2 residue from (5.3) in $d=4$ and compare the resulting trace anomaly with the square of the linearized Weyl tensor.

Watch

Extended reading notes

Core claim

The anomaly has one source: the finite part of the variation of the singular local effective action. After splitting $W_{\mathrm{eff}} = \epsilon^{-1}W_{\mathrm{sing}} + W_{\mathrm{reg}}$, gauge invariance forces the $1/\epsilon$ pole to be cancelled by linear-in-$\epsilon$ terms, and only trace contractions such as $\Box_a a^2 = 2(d-\epsilon)$ produce those terms. Hence the renormalized current obeys $2_a J_R^{(s)} = T$ and $(\nabla_1\partial_a)J_R^{(s)} = -(d+2s-4)^{-1}(a\nabla_1)T$; the conservation violation is a gradient of the trace anomaly. Shifting $J_R^{(s)}$ by $\tfrac12(d+2s-4)^{-1}a^2T$ restores conservation, leaving a trace anomaly that is quadratic, has $2s$ derivatives, and in

Load-bearing premise

The general spin-$s$ claim assumes that the four building blocks $G$, $\Psi$, $F_1$, $F_2$ generate every conserved three-point structural tensor for arbitrary spin, with exactly $s+1$ independent combinations; the paper verifies this only for spins 3 and 4 and needs it for the singularity decomposition (5.1) and the anomaly argument.

Editorial extensions

If this is right

  • In $d=4$, the trace anomaly is second order in the linearized HS gauge field and contains $2s$ derivatives, so it can be written as a combination of squares of generalized Weyl and Ricci tensors and a scalar term.
  • The conservation anomaly is the gradient of the trace anomaly, so a shift of the renormalized current restores gauge invariance and leaves only the trace anomaly, with no separate HS gauge anomaly.
  • The $1/\epsilon$ pole in the singular local part of the effective action is cancelled by the finite part of its variation, so the anomaly is fixed entirely by the local residue without detailed knowledge of the regular nonlocal part.
  • In dimensions higher than four, the three-point function alone does not determine the anomaly; higher-point correlators are required, and their structure is not fixed by conformal symmetry.
  • The symmetric formulation turns the three-point correlator into a single manifestly symmetric object, simplifying the trace and conservation Ward identities for all equal spins.

Reading between the lines

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

  • If the four-building-block generation conjecture fails for some $s \ge 5$, new conserved combinations would add extra singular terms in (5.1) and could change the anomaly, although the gradient relation between conservation and trace anomalies would likely survive.
  • The same singularity-extraction machinery could be applied to arbitrary local cubic vertices, not just conserved-current correlators, yielding a systematic list of finite counterterms and anomalies for non-conserved higher-spin interactions; the paper does not pursue this.
  • The current shift (5.25) is the higher-spin analogue of the standard improvement transformation in conformal field theory, suggesting that the physical content of the anomaly is fully captured by the trace even though the unshifted quantization breaks conservation—an implicit conclusion, not stated in the paper.
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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

3 major / 5 minor

Summary. The paper develops a symmetric formulation of the three-point correlation function of equal-spin conserved higher-spin currents and uses it to study the singular part of the cubic quantum effective action. After reviewing the Osborn-Petkou formulation and the authors' constructive basis {G, Psi, F1, F2}, the paper introduces cyclic identities to symmetrize the structural tensor, then applies a dimensional-regularization singularity-extraction formula (attributed to Ruehl) to decompose the cubic effective action into a 1/epsilon local singular part and a finite nonlocal part. The central claim is that the quantum trace and gauge anomalies both originate from the finite O(epsilon) part of the variation of the singular local action: the divergence anomaly is a gradient of the trace anomaly, so shifting the current restores conservation while leaving a trace anomaly that is quadratic in the linearized spin-s field and contains 2s derivatives, expressible in d=4 as squares of generalized Weyl/Ricci tensors. Appendices provide an explicit spin-2 example and a detailed derivation of the singularity-extraction formula.

Significance. If the central mechanism were fully established, this would be a valuable constructive framework: it would connect the conformal-structure data of three-point functions to the anomaly structure of higher-spin gauge theories without a full loop computation, and it would give a general argument that the trace anomaly is governed by squares of generalized curvatures. The singularity-extraction derivation in Appendix B is careful and self-contained, and the spin-2 example in Appendix A is explicit and checks the conservation condition. However, the main anomaly claim is not actually computed: no O(epsilon) residue is evaluated, no explicit T(h) is exhibited, and the authors themselves state that even the spin-2 anomaly requires future computer calculations. The generality for arbitrary spin also rests on an unproved completeness assumption for the four-element basis. The significance is therefore conditional on completing and verifying these missing steps.

major comments (3)
  1. [Section 5, Eqs. (5.8)–(5.12), (5.18)–(5.24)] The central claim is asserted rather than demonstrated. The paper argues that O(epsilon) terms in the variation of the singular local action, coming only from trace-type sources (5.18)–(5.19), produce the anomaly, and then writes the trace anomaly as T(h) in (5.24). But no term of L_sing in (5.3) or (5.7) is actually evaluated; T(h) is never computed; and the statements that it contains 2s derivatives and is quadratic in h are justified only by 'careful consideration' (end of Section 5). Section 6 explicitly says that 'we need rather long and complicated computer calculations even for spin-two case.' This is a load-bearing gap: without at least the spin-2 anomaly computed explicitly (or a complete algebraic argument that the O(epsilon) terms cannot cancel), Eqs. (5.23)–(5.27) remain a proposed mechanism, not a result.
  2. [Section 2, Eq. (2.32); Section 5, Eq. (5.1)] The paper uses the completeness of {G, Psi, F1, F2} as generators of all conserved three-point structural tensors for arbitrary spin s, but the text notes this was proved only for spins 3 and 4 in reference [38]. The singularity decomposition (5.1), and hence the anomaly argument, uses this basis for general s. If additional conserved building blocks or additional conserved combinations exist for s>=5, the singular residue and the anomaly content could differ. The paper should either restrict the anomaly claims to s=3,4, where the basis is proven, or supply a proof of completeness for all s.
  3. [Section 4, Eqs. (4.9)–(4.14); Appendix B] The singularity-extraction formula is derived under the assumption that lambda, mu, nu are natural numbers ('Using the fact that lambda, mu, nu are natural numbers', Appendix B). However, in the three-point function the exponents are Delta(s)=d+s-2, Eq. (2.20), which depend on d. Under the replacement d -> d - epsilon (4.5), these exponents shift by -epsilon. The pole in (B.15) then has argument -m + c epsilon with c different from -1, which changes the residue coefficient; moreover m = lambda+mu+nu-d itself becomes epsilon-dependent. The paper does not explain whether lambda, mu, nu are held fixed at their d=4 integer values during regularization or continued with d. This affects the coefficient of the 1/epsilon pole and therefore the O(epsilon) terms that carry the anomaly. The application of (4.10)–(4.14) to the higher-spin correlator needs clarification and, if lambda is d-dependent,
minor comments (5)
  1. [Abstract and Introduction] There are several typos: 'tree-point' in reference [38] should be 'three-point'; 'We then we develop' in the Introduction is ungrammatical. Also, the Introduction's summary of Section 5 could be tightened to avoid repeating the same claim three times.
  2. [Section 3, Eq. (3.28)] Equation (3.28) is used to derive the conservation conditions (3.30)–(3.31), but no derivation or reference is given. Since this identity is central to the Ward-identity structure, a short derivation or a pointer to the previous papers would improve readability.
  3. [Section 5, Eqs. (5.13)–(5.17)] The notation in these equations is ambiguous: after the delta functions, expressions such as f(z,y,...)(nabla_2+nabla_3)^2 are written without specifying whether the derivatives act only on f or also on the external fields to the right. A convention (e.g., arrows or parentheses) would make the manipulation of partial integrations much clearer.
  4. [Section 5, Eq. (5.18)] The notation '2_a a^2 = 2(d-epsilon)' is confusing: the first '2_a' appears to be the auxiliary-space Laplacian/trace operator, while 'a^2' is a squared auxiliary vector. Please use distinct symbols for the trace operator and the norm squared to avoid conflating them.
  5. [Section 6] The sentence about d=4 and higher-point functions is interesting but compressed. Since the three-point function is fixed by conformal symmetry in any d, the claim that only d=4 can produce the trace anomaly from the three-point function should be substantiated with at least a scaling argument; otherwise it reads as an assertion.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular reduction found: the anomaly mechanism is argued from singular structure and Ward identities, not from the assumed answer; the main issues are unproved generality and deferred computation, not circularity.

full rationale

The paper's central derivation does not reduce to its inputs by construction. The singularity-extraction formulas (4.7)-(4.14) are taken from an external source [96] and re-derived in Appendix B, so they are an independent technical input. The four building blocks G, Psi, F1, F2 and the claim that they generate s+1 conserved three-point structures for arbitrary s are imported from the authors' own previous papers [37,38]; the paper explicitly states the completeness proof exists only for spins 3 and 4. This is a genuine gap in the general-s argument, but it is an unsupported generalization, not a circular one: the anomaly mechanism is argued from the structure of the singular kernel, the operator identity (5.17), translation invariance, and the requirement that the regularized effective action remain gauge invariant. No fitted parameters are used, and no 'prediction' is re-labeled fit. The relation (5.23) between the divergence anomaly and the trace T(h) follows from the operator identity and the observation that O(epsilon) terms arise only from trace-type contractions; the current shift (5.25) is a standard improvement construction, not a derivation of the anomaly from an assumed answer. The main weakness is that T(h) is never explicitly computed: the paper concludes with the statement that 'we need rather long and complicated computer calculations even for spin-two case,' so the claimed 2s-derivative trace anomaly remains conditional. That is a correctness/completeness concern, not circularity. The self-citations are load-bearing for the structural basis but do not smuggle in the anomaly result, and the central anomaly mechanism has independent content based on singular extraction plus Ward identities.

Assumptions & free parameters 0 free parameters · 6 assumptions · 0 invented entities

The central claim depends on the Osborn-Petkou conformal correlator framework, on the authors' constructive basis for the structural tensor (which is not proven for general spin), on Ruehl's singularity extraction, and on a specific assertion about which terms can produce O(epsilon) effects. No new particles or forces are introduced; the generalized Weyl and Ricci tensors are taken from prior literature. No free parameters are fitted: the coefficients in the structural tensor are undetermined, but the anomaly mechanism is claimed to be independent of their values.

assumptions (6)
  • domain assumption The Osborn-Petkou form of two- and three-point functions is fixed by conformal symmetry up to constants
    Section 2 uses this to justify the effective action built from two- and three-point correlators.
  • ad hoc to paper The four building blocks G, Psi, F1, F2 generate all conserved structural tensors for any spin s
    Proved only for s=3,4 in [38]; assumed for general s in Sections 3-5.
  • domain assumption Dimensional regularization preserves gauge invariance of the total effective action
    Section 5, eqs. (5.5)-(5.6); the cancellation argument requires the epsilon pole to vanish in the total variation.
  • standard math The principal singularity of F{lambda mu nu} is a single first-order pole given by Ruehl's formula
    Taken from [96] and derived in Appendix B; used to localize the singular part.
  • ad hoc to paper Only trace-type terms produce O(epsilon) contributions in the divergent variation; divergence terms do not
    Section 5 after (5.19): 'After some investigation we find...' asserted, not derived; central to the trace-as-single-source conclusion.
  • domain assumption Current dimensions are Delta(s)=d+s-2
    Section 2, eq. (2.20); used for power counting of singularities.

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Pith. "Pith review of Symmetric formulation for higher spin correlators, quantum effective action and anomaly." pith.science (2026). https://pith.science/paper/SJK5BPGW

@misc{pith2026260801125,
  author       = {Pith},
  title        = {Pith review of: Symmetric formulation for higher spin correlators, quantum effective action and anomaly},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SJK5BPGW}},
  note         = {Machine review of arXiv:2608.01125}
}
read the original abstract

We develop a constructive framework for the three-point higher spin conformal correlation function, originally introduced in our previous work, and apply it as the foundation for constructing the quantum effective action of the corresponding higher spin conformal gauge theory. Employing a symmetric refinement of the earlier construction, we analyze the principal singularity of the three-point function and the associated effective action. This leads to a general method for extracting the dominant singularity and investigating the anomalous local contributions to the effective action.

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Works this paper leans on

92 extracted references · 75 linked inside Pith

  1. [38]

    Constructive approach to solution of the conservation condition for conformal higher spin tree-point correlation function with equal spins,

    M. Karapetyan and R. Manvelyan, “Constructive approach to solution of the conservation condition for conformal higher spin tree-point correlation function with equal spins,” JHEP09(2025), 073 doi:10.1007/JHEP09(2025)073 [arXiv:2505.16634 [hep-th]]

    arXiv 2025

  2. [1]

    The Large N limit of superconformal field theories and supergravity,

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

    arXiv 1998

  3. [2]

    Anti-de Sitter space and holography,

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

    arXiv 1998

  4. [3]

    Conformal symmetry of critical fluctuations,

    A. M. Polyakov, “Conformal symmetry of critical fluctuations,” JETP Lett.12(1970), 381

    1970

  5. [4]

    Conformal symmetry and three-point functions,

    E. J. Schreier, “Conformal symmetry and three-point functions,” Phys. Rev. D3 (1971), 980

    1971

  6. [5]

    Conformal invariance and bootstrap,

    A. A. Migdal, “Conformal invariance and bootstrap,” Phys. Lett. B37(1971), 386

    1971

  7. [6]

    Tensor representations of conformal algebra and conformally covariant operator product expansion,

    S. Ferrara, A. F. Grillo and R. Gatto, “Tensor representations of conformal algebra and conformally covariant operator product expansion,” Annals Phys.76(1973), 161

    1973

  8. [7]

    Field representations of the conformal group with continuous mass spectrum,

    W. R¨ uhl, “Field representations of the conformal group with continuous mass spectrum,” Commun. Math. Phys.30(1973), 287

    1973

Show all 92 references
  1. [8]

    On conformal invariance of interacting fields,

    W. R¨ uhl, “On conformal invariance of interacting fields,” Commun. Math. Phys.34 (1973), 149

    1973

  2. [9]

    The Significance of Conformal Inversion in Quantum Field Theory,

    K. Koller, “The Significance of Conformal Inversion in Quantum Field Theory,” Commun. Math. Phys.40, 15; DESY-74-8

  3. [10]

    Convergence of Operator Product Expansions on the Vacuum in Conformal Invariant Quantum Field Theory,

    G. Mack, “Convergence of Operator Product Expansions on the Vacuum in Conformal Invariant Quantum Field Theory,” Commun. Math. Phys.53(1977), 155

    1977

  4. [11]

    Implications of conformal invariance in field theories for general dimensions,

    H. Osborn and A. C. Petkou, “Implications of conformal invariance in field theories for general dimensions,” Annals Phys.231(1994), 311; [hep-th/9307010]

    1994 arXiv

  5. [12]

    Implications of conformal invariance for quantum field theories in d>2,

    H. Osborn, “Implications of conformal invariance for quantum field theories in d>2,” [hep-th/9312176]. – 23 –

    arXiv

  6. [13]

    Conserved currents and the energy momentum tensor in conformally invariant theories for general dimensions,

    J. Erdmenger and H. Osborn, “Conserved currents and the energy momentum tensor in conformally invariant theories for general dimensions,” Nucl. Phys. B483(1997), 431; [hep-th/9605009]

    1997 arXiv

  7. [14]

    N=1 superconformal symmetry in four-dimensions,

    J. H. Park, “N=1 superconformal symmetry in four-dimensions,” Int. J. Mod. Phys. A 13(1998), 1743; [hep-th/9703191]

    1998 arXiv

  8. [15]

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

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

    1999 arXiv

  9. [16]

    Superconformal symmetry and correlation functions,

    J. H. Park, “Superconformal symmetry and correlation functions,” Nucl. Phys. B559 (1999), 455; [hep-th/9903230]

    1999 arXiv

  10. [17]

    Higher spin current multiplets in operator product expansions,

    D. Anselmi, “Higher spin current multiplets in operator product expansions,” Class. Quant. Grav.17(2000), 1383; [hep-th/9906167]

    2000 arXiv

  11. [18]

    Correlation functions of conserved currents in N=2 superconformal theory,

    S. M. Kuzenko and S. Theisen, “Correlation functions of conserved currents in N=2 superconformal theory,” Class. Quant. Grav.17(2000), 665; [hep-th/9907107]

    2000 arXiv

  12. [19]

    Superconformal symmetry in three-dimensions,

    J. H. Park, “Superconformal symmetry in three-dimensions,” J. Math. Phys.41 (2000), 7129; [hep-th/9910199]

    2000 arXiv

  13. [20]

    Higher Spin Gauge Theory and Holography: The Three-Point Functions,

    S. Giombi and X. Yin, “Higher Spin Gauge Theory and Holography: The Three-Point Functions,” JHEP09(2010), 115; [0912.3462]

    2010 arXiv

  14. [21]

    Higher Spins in AdS and Twistorial Holography,

    S. Giombi and X. Yin, “Higher Spins in AdS and Twistorial Holography,” JHEP04 (2011), 086; [1004.3736]

    2011 arXiv

  15. [22]

    A Note on CFT Correlators in Three Dimensions,

    S. Giombi, S. Prakash and X. Yin, “A Note on CFT Correlators in Three Dimensions,” JHEP07(2013), 105; [1104.4317]

    2013 arXiv

  16. [23]

    Spinning Conformal Correlators,

    M. S. Costa, J. Penedones, D. Poland and S. Rychkov, “Spinning Conformal Correlators,” JHEP11(2011), 071; [1107.3554]

    2011 arXiv

  17. [24]

    Spinning Conformal Blocks,

    M. S. Costa, J. Penedones, D. Poland and S. Rychkov, “Spinning Conformal Blocks,” JHEP11(2011), 154; [1109.6321]

    2011 arXiv

  18. [25]

    Constraining Conformal Field Theories with A Higher Spin Symmetry,

    J. Maldacena and A. Zhiboedov, “Constraining Conformal Field Theories with A Higher Spin Symmetry,” J. Phys. A46(2013), 214011; [1112.1016]

    2013 arXiv

  19. [26]

    Correlation Functions of Conserved Currents in Four Dimensional Conformal Field Theory,

    Y. S. Stanev, “Correlation Functions of Conserved Currents in Four Dimensional Conformal Field Theory,” Nucl. Phys. B865(2012), 200; [1206.5639]

    2012 arXiv

  20. [27]

    Conformal field theories with infinitely many conservation laws,

    I. Todorov, “Conformal field theories with infinitely many conservation laws,” J. Math. Phys.54(2013), 022303; [1207.3661]

    2013 arXiv

  21. [28]

    A note on three-point functions of conserved currents,

    A. Zhiboedov, “A note on three-point functions of conserved currents,” [1206.6370]

    arXiv

  22. [29]

    Constraining conformal field theories with a higher spin symmetry in d=4,

    V. Alba and K. Diab, “Constraining conformal field theories with a higher spin symmetry in d=4,” [1307.8092]. – 24 –

    arXiv

  23. [30]

    Conformal correlators of mixed-symmetry tensors,

    M. S. Costa and T. Hansen, “Conformal correlators of mixed-symmetry tensors,” JHEP02(2015), 151; [1411.7351]

    2015 arXiv

  24. [31]

    Constraining conformal field theories with a higher spin symmetry ind >3 dimensions,

    V. Alba and K. Diab, “Constraining conformal field theories with a higher spin symmetry ind >3 dimensions,” JHEP03(2016), 044; [1510.02535]

    2016 arXiv

  25. [32]

    Counting Conformal Correlators,

    P. Kravchuk and D. Simmons-Duffin, “Counting Conformal Correlators,” JHEP02 (2018), 096; [1612.08987]

    2018 arXiv

  26. [33]

    Light-Front Bootstrap for Chern-Simons Matter Theories,

    E. Skvortsov, “Light-Front Bootstrap for Chern-Simons Matter Theories,” JHEP06 (2019), 058; [1811.12333]

    2019 arXiv

  27. [34]

    Three-Point Functions of Higher-Spin Supercurrents in 4D N=1N= 1 Superconformal Field Theory,

    E. I. Buchbinder, J. Hutomo and G. Tartaglino-Mazzucchelli, “Three-Point Functions of Higher-Spin Supercurrents in 4D N=1N= 1 Superconformal Field Theory,” Fortsch. Phys.70(2022), 2200133; [2208.07057]

    2022 arXiv

  28. [35]

    Three-point functions of conserved currents in 3D CFT: General formalism for arbitrary spins,

    E. I. Buchbinder and B. J. Stone, “Three-point functions of conserved currents in 3D CFT: General formalism for arbitrary spins,” Phys. Rev. D107(2023) no.4, 046007; [2210.13135]

    2023 arXiv

  29. [36]

    Three-point functions of conserved currents in 4D CFT: general formalism for arbitrary spins,

    E. I. Buchbinder and B. J. Stone, “Three-point functions of conserved currents in 4D CFT: general formalism for arbitrary spins,” [2307.11435]

    arXiv

  30. [37]

    On correlation functions of higher spin currents in arbitrary dimensions d>3,

    M. Karapetyan, R. Manvelyan and K. Mkrtchyan, “On correlation functions of higher spin currents in arbitrary dimensions d>3,” JHEP03(2024), 161 doi:10.1007/JHEP03(2024)161 [arXiv:2309.05129 [hep-th]]

    2024 arXiv

  31. [39]

    Cubic Interaction Terms for Arbitrary Spin,

    A. K. H. Bengtsson, I. Bengtsson and L. Brink, “Cubic Interaction Terms for Arbitrary Spin,” Nucl. Phys. B227(1983), 31

    1983

  32. [40]

    On Spin Three Selfinteractions,

    F. A. Berends, G. J. H. Burgers and H. Van Dam, “On Spin Three Selfinteractions,” Z. Phys. C24(1984), 247

    1984

  33. [41]

    On the Theoretical Problems in Constructing Interactions Involving Higher Spin Massless Particles,

    F. A. Berends, G. J. H. Burgers and H. van Dam, “On the Theoretical Problems in Constructing Interactions Involving Higher Spin Massless Particles,” Nucl. Phys. B 260(1985), 295

    1985

  34. [42]

    On the Gravitational Interaction of Massless Higher Spin Fields,

    E. S. Fradkin and M. A. Vasiliev, “On the Gravitational Interaction of Massless Higher Spin Fields,” Phys. Lett. B189(1987), 89

    1987

  35. [43]

    Cubic Interaction in Extended Theories of Massless Higher Spin Fields,

    E. S. Fradkin and M. A. Vasiliev, “Cubic Interaction in Extended Theories of Massless Higher Spin Fields,” Nucl. Phys. B291(1987), 141

    1987

  36. [44]

    Interacting Higher Spin Gauge – 25 – Fields on the Light Front,

    A. K. H. Bengtsson, I. Bengtsson and N. Linden, “Interacting Higher Spin Gauge – 25 – Fields on the Light Front,” Class. Quant. Grav.4(1987), 1333

    1987

  37. [45]

    A Cubic interaction of totally symmetric massless representations of the Lorentz group in arbitrary dimensions,

    E. S. Fradkin and R. R. Metsaev, “A Cubic interaction of totally symmetric massless representations of the Lorentz group in arbitrary dimensions,” Class. Quant. Grav.8 (1991), L89

    1991

  38. [46]

    Poincare invariant dynamics of massless higher spins: Fourth order analysis on mass shell,

    R. R. Metsaev, “Poincare invariant dynamics of massless higher spins: Fourth order analysis on mass shell,” Mod. Phys. Lett. A6(1991), 359

    1991

  39. [47]

    S matrix approach to massless higher spins theory. 2: The Case of internal symmetry,

    R. R. Metsaev, “S matrix approach to massless higher spins theory. 2: The Case of internal symmetry,” Mod. Phys. Lett. A6(1991), 2411

    1991

  40. [48]

    Cubic interactions of bosonic higher spin gauge fields in AdS 5,

    M. A. Vasiliev, “Cubic interactions of bosonic higher spin gauge fields in AdS 5,” Nucl. Phys. B616(2001), 106-162 [erratum: Nucl. Phys. B652(2003), 407-407]; [hep-th/0106200]

    2001 arXiv

  41. [49]

    N=1 supersymmetric theory of higher spin gauge fields in AdS(5) at the cubic level,

    K. B. Alkalaev and M. A. Vasiliev, “N=1 supersymmetric theory of higher spin gauge fields in AdS(5) at the cubic level,” Nucl. Phys. B655(2003), 57; [hep-th/0206068]

    2003 arXiv

  42. [50]

    Conformal coupling of higher spin gauge fields to a scalar field in AdS(4) and generalized Weyl invariance,

    R. Manvelyan and W. R¨ uhl, “Conformal coupling of higher spin gauge fields to a scalar field in AdS(4) and generalized Weyl invariance,” Phys. Lett. B593(2004), 253; [hep-th/0403241]

    2004 arXiv

  43. [51]

    Spin three gauge theory revisited,

    X. Bekaert, N. Boulanger and S. Cnockaert, “Spin three gauge theory revisited,” JHEP 01(2006), 052; [hep-th/0508048]

    2006 arXiv

  44. [52]

    Cubic interaction vertices of massive and massless higher spin fields,

    R. R. Metsaev, “Cubic interaction vertices of massive and massless higher spin fields,” Nucl. Phys. B759(2006), 147; [hep-th/0512342]

    2006 arXiv

  45. [53]

    On killing tensors and cubic vertices in higher spin gauge theories,

    X. Bekaert, N. Boulanger, S. Cnockaert and S. Leclercq, “On killing tensors and cubic vertices in higher spin gauge theories,” Fortsch. Phys.54(2006), 282; [hep-th/0602092]

    2006 arXiv

  46. [54]

    Consistent couplings between spin-2 and spin-3 massless fields,

    N. Boulanger and S. Leclercq, “Consistent couplings between spin-2 and spin-3 massless fields,” JHEP11(2006), 034; [hep-th/0609221]

    2006 arXiv

  47. [55]

    Current Exchanges and Unconstrained Higher Spins,

    D. Francia, J. Mourad and A. Sagnotti, “Current Exchanges and Unconstrained Higher Spins,” Nucl. Phys. B773(2007), 203; [hep-th/0701163]

    2007 arXiv

  48. [56]

    higher spin Gauge Fields Interacting with Scalars: The Lagrangian Cubic Vertex,

    A. Fotopoulos, N. Irges, A. C. Petkou and M. Tsulaia, “higher spin Gauge Fields Interacting with Scalars: The Lagrangian Cubic Vertex,” JHEP10(2007), 021; [0708.1399]

    2007 arXiv

  49. [57]

    Cubic interaction vertices for fermionic and bosonic arbitrary spin fields,

    R. R. Metsaev, “Cubic interaction vertices for fermionic and bosonic arbitrary spin fields,” Nucl. Phys. B859(2012), 13; [0712.3526]

    2012 arXiv

  50. [58]

    Gauge Invariant Lagrangians for Free and Interacting Higher Spin Fields. A Review of the BRST formulation,

    A. Fotopoulos and M. Tsulaia, “Gauge Invariant Lagrangians for Free and Interacting Higher Spin Fields. A Review of the BRST formulation,” Int. J. Mod. Phys. A24 (2009), 1; [0805.1346]. – 26 –

    2009 arXiv

  51. [59]

    On spin 3 interacting with gravity,

    Y. M. Zinoviev, “On spin 3 interacting with gravity,” Class. Quant. Grav.26(2009), 035022; [0805.2226]

    2009 arXiv

  52. [60]

    On The Uniqueness of Minimal Coupling in higher spin Gauge Theory,

    N. Boulanger, S. Leclercq and P. Sundell, “On The Uniqueness of Minimal Coupling in higher spin Gauge Theory,” JHEP08(2008), 056; [0805.2764]

    2008 arXiv

  53. [61]

    Conformal invariant interaction of a scalar field with the higher spin field in AdS(D),

    R. Manvelyan and K. Mkrtchyan, “Conformal invariant interaction of a scalar field with the higher spin field in AdS(D),” Mod. Phys. Lett. A25(2010), 1333; [0903.0058]

    2010 arXiv

  54. [62]

    Off-shell construction of some trilinear higher spin gauge field interactions,

    R. Manvelyan, K. Mkrtchyan and W. R¨ uhl, “Off-shell construction of some trilinear higher spin gauge field interactions,” Nucl. Phys. B826(2010), 1; [0903.0243]

    2010 arXiv

  55. [63]

    On higher spin interactions with matter,

    X. Bekaert, E. Joung and J. Mourad, “On higher spin interactions with matter,” JHEP 05(2009), 126; [0903.3338]

    2009 arXiv

  56. [64]

    Direct Construction of A Cubic Selfinteraction for Higher Spin gauge Fields,

    R. Manvelyan, K. Mkrtchyan and W. R¨ uhl, “Direct Construction of A Cubic Selfinteraction for Higher Spin gauge Fields,” Nucl. Phys. B844(2011), 348; [1002.1358]

    2011 arXiv

  57. [65]

    General trilinear interaction for arbitrary even higher spin gauge fields,

    R. Manvelyan, K. Mkrtchyan and W. R¨ uhl, “General trilinear interaction for arbitrary even higher spin gauge fields,” Nucl. Phys. B836(2010), 204; [1003.2877]

    2010 arXiv

  58. [66]

    String Lessons for higher spin Interactions,

    A. Sagnotti and M. Taronna, “String Lessons for higher spin Interactions,” Nucl. Phys. B842(2011), 299; [1006.5242]

    2011 arXiv

  59. [67]

    Spin 3 cubic vertices in a frame-like formalism,

    Y. M. Zinoviev, “Spin 3 cubic vertices in a frame-like formalism,” JHEP08(2010), 084; [1007.0158]

    2010 arXiv

  60. [68]

    On the Tensionless Limit of String theory, Off - Shell Higher Spin Interaction Vertices and BCFW Recursion Relations,

    A. Fotopoulos and M. Tsulaia, “On the Tensionless Limit of String theory, Off - Shell Higher Spin Interaction Vertices and BCFW Recursion Relations,” JHEP11(2010), 086; [1009.0727]

    2010 arXiv

  61. [69]

    A Generating function for the cubic interactions of higher spin fields,

    R. Manvelyan, K. Mkrtchyan and W. R¨ uhl, “A Generating function for the cubic interactions of higher spin fields,” Phys. Lett. B696(2011), 410; [1009.1054]

    2011 arXiv

  62. [70]

    Higher Spins and Open Strings: Quartic Interactions,

    D. Polyakov, “Higher Spins and Open Strings: Quartic Interactions,” Phys. Rev. D83 (2011), 046005; [1011.0353]

    2011 arXiv

  63. [71]

    Solving Noether’s equations for gauge invariant local Lagrangians of N arbitrary higher even spin fields,

    W. R¨ uhl, “Solving Noether’s equations for gauge invariant local Lagrangians of N arbitrary higher even spin fields,” [1108.0225]

    arXiv

  64. [72]

    Cubic Vertices for Symmetric higher spin Gauge Fields in (A)dS d,

    M. A. Vasiliev, “Cubic Vertices for Symmetric higher spin Gauge Fields in (A)dS d,” Nucl. Phys. B862(2012), 341; [1108.5921]

    2012 arXiv

  65. [73]

    Cubic interactions of massless higher spins in (A)dS: metric-like approach,

    E. Joung and M. Taronna, “Cubic interactions of massless higher spins in (A)dS: metric-like approach,” Nucl. Phys. B861(2012), 145; [1110.5918]

    2012 arXiv

  66. [74]

    On the Structure of Quartic Vertices for Massless Higher Spin Fields on Minkowski Background,

    P. Dempster and M. Tsulaia, “On the Structure of Quartic Vertices for Massless Higher Spin Fields on Minkowski Background,” Nucl. Phys. B865(2012), 353; [1203.5597]

    2012 arXiv

  67. [75]

    On the cubic interactions of massive and – 27 – partially-massless higher spins in (A)dS,

    E. Joung, L. Lopez and M. Taronna, “On the cubic interactions of massive and – 27 – partially-massless higher spins in (A)dS,” JHEP07(2012), 041; [1203.6578]

    2012 arXiv

  68. [76]

    Cubic interaction vertex of higher spin fields with external electromagnetic field,

    I. L. Buchbinder, T. V. Snegirev and Y. M. Zinoviev, “Cubic interaction vertex of higher spin fields with external electromagnetic field,” Nucl. Phys. B864(2012), 694; [1204.2341]

    2012 arXiv

  69. [77]

    higher spin Fermionic Gauge Fields and Their Electromagnetic Coupling,

    M. Henneaux, G. Lucena G´ omez and R. Rahman, “higher spin Fermionic Gauge Fields and Their Electromagnetic Coupling,” JHEP08(2012), 093; [1206.1048]

    2012 arXiv

  70. [78]

    Solving the Noether procedure for cubic interactions of higher spins in (A)dS,

    E. Joung, L. Lopez and M. Taronna, “Solving the Noether procedure for cubic interactions of higher spins in (A)dS,” J. Phys. A46(2013), 214020; [1207.5520]

    2013 arXiv

  71. [79]

    Radial Reduction and Cubic Interaction for Higher Spins in (A)dS space,

    R. Manvelyan, R. Mkrtchyan and W. R¨ uhl, “Radial Reduction and Cubic Interaction for Higher Spins in (A)dS space,” Nucl. Phys. B872(2013), 265; [1210.7227]

    2013 arXiv

  72. [80]

    Generating functions of (partially-)massless higher spin cubic interactions,

    E. Joung, L. Lopez and M. Taronna, “Generating functions of (partially-)massless higher spin cubic interactions,” JHEP01(2013), 168; [1211.5912]

    2013 arXiv

  73. [81]

    Non-abelian cubic vertices for higher spin fields in anti-de Sitter space,

    N. Boulanger, D. Ponomarev and E. D. Skvortsov, “Non-abelian cubic vertices for higher spin fields in anti-de Sitter space,” JHEP05(2013), 008; [1211.6979]

    2013 arXiv

  74. [82]

    Gravitational Interactions of higher spin Fermions,

    M. Henneaux, G. Lucena G´ omez and R. Rahman, “Gravitational Interactions of higher spin Fermions,” JHEP01(2014), 087; [1310.5152]

    2014 arXiv

  75. [83]

    Cubic-interaction-induced deformations of higher spin symmetries,

    E. Joung and M. Taronna, “Cubic-interaction-induced deformations of higher spin symmetries,” JHEP03(2014), 103; [1311.0242]

    2014 arXiv

  76. [84]

    Spinor-Helicity Three-Point Amplitudes from Local Cubic Interactions,

    E. Conde, E. Joung and K. Mkrtchyan, “Spinor-Helicity Three-Point Amplitudes from Local Cubic Interactions,” JHEP08(2016), 040; [1605.07402]

    2016 arXiv

  77. [85]

    Investigations into Light-front Quartic Interactions for Massless Fields (I): Non-constructibility of Higher Spin Quartic Amplitudes,

    A. K. H. Bengtsson, “Investigations into Light-front Quartic Interactions for Massless Fields (I): Non-constructibility of Higher Spin Quartic Amplitudes,” JHEP12(2016), 134; [1607.06659]

    2016 arXiv

  78. [86]

    Cubic interactions of Maxwell-like higher spins,

    D. Francia, G. L. Monaco and K. Mkrtchyan, “Cubic interactions of Maxwell-like higher spins,” JHEP04(2017), 068; [1611.00292]

    2017 arXiv

  79. [87]

    On the Non-Local Obstruction to Interacting Higher Spins in Flat Space,

    M. Taronna, “On the Non-Local Obstruction to Interacting Higher Spins in Flat Space,” JHEP05(2017), 026; [1701.05772]

    2017 arXiv

  80. [88]

    On four-point interactions in massless higher-spin theory in flat space,

    R. Roiban and A. A. Tseytlin, “On four-point interactions in massless higher-spin theory in flat space,” JHEP04(2017), 139; [1701.05773]

    2017 arXiv

  81. [89]

    higher-spin Gauge Theories and Bulk Locality,

    C. Sleight and M. Taronna, “higher-spin Gauge Theories and Bulk Locality,” Phys. Rev. Lett.121(2018), 171604; [1704.07859]

    2018 arXiv

  82. [90]

    Feynman rules for higher spin gauge fields on AdS d+1,

    C. Sleight and M. Taronna, “Feynman rules for higher spin gauge fields on AdS d+1,” JHEP01(2018), 060; [1708.08668]

    2018 arXiv

  83. [91]

    Cubic interaction for higher spins in AdSd+1 space in the explicit covariant form,

    M. Karapetyan, R. Manvelyan and R. Poghossian, “Cubic interaction for higher spins in AdSd+1 space in the explicit covariant form,” Nucl. Phys. B950(2020), 114876; – 28 – [1908.07901]

    2020 arXiv

  84. [92]

    A note on higher-order vertices of higher-spin fields in flat and (A)dS space,

    E. Joung and M. Taronna, “A note on higher-order vertices of higher-spin fields in flat and (A)dS space,” JHEP09(2020), 171; [1912.12357]

    2020 arXiv

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