Linearized $\mathcal{N}=2$ conformal supergravity in the harmonic approach

Evgeny Ivanov; Nikita Zaigraev

REVIEW 3 major objections 3 minor 2 cited by

Linearized $\mathcal{N}=2$ conformal supergravity in the harmonic approach

T0 review · 3 major / 3 minor · reviewed 2026-08-03 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read This paper constructs a linearized harmonic-superspace action for N=2 conformal supergravity from unconstrained analytic prepotentials and proves its invariance under rigid N=2 superconformal transformations; after gauge-fixing it reduces t

desk verdict First explicit harmonic-superspace action for linearized N=2 conformal supergravity; the construction and Appendix B reduction look right, but the superconformal invariance proof has a real gap at eqs. (4.36)-(4.37). read the letter →

arxiv 2511.16325 v2 pith:JYE2MSBX submitted 2025-11-20 hep-th gr-qc

Evgeny Ivanov , Nikita Zaigraev This is my paper

classification hep-thgr-qc PACS 04.65.+e11.30.Pb

keywords harmonicsuperspaceN=2conformalsupergravityWeylmultipletsuperconformalinvarianceanalyticprepotentialshalf-analyticitysuper-Weyltensorhigher-spin

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 establish that linearized N=2 conformal supergravity (the Weyl multiplet) admits a gauge-invariant and rigidly superconformal-invariant action in harmonic superspace, written directly in terms of unconstrained analytic prepotentials. The proposed action, S = ∫ d^4x d^8θ du H^{++(αβ)} H^{--}_{(αβ)} + c.c., is shown to be equivalent to the chiral action (1/16)∫ d^4x_L d^4θ W^{(αβ)} W_{(αβ)} + c.c., where W_{αβ} is the linearized N=2 super-Weyl tensor. If correct, this fills a gap in the literature: no dynamical harmonic-superspace action for the N=2 Weyl multiplet had been given before. The construction mirrors the free N=2 vector-multiplet action, with the half-analyticity condition playing the role of analyticity, and it reproduces the familiar Weyl-squared conformal supergravity upon fixing a harmonic-independent gauge. A reader should care because unconstrained prepotentials make possible harmonic-superspace quantization, effective-action computations, and a conjectured route to the full nonlinear N=2 Weyl theory.

What carries the argument

The central mechanism is the pair of zero-curvature equations D^{++}G^{--}=D^{--}G^{++} and D^{++}H^{--}_{(αβ)}=D^{--}H^{++}_{(αβ)}, whose unique solutions define the negatively charged potentials needed to form a gauge-invariant action. The other load-bearing element is the half-analyticity condition, a Grassmann-analyticity constraint on half the spinor coordinates; it fixes the relative coefficient in the definition of H^{++}, guarantees gauge invariance of the action, and ensures that W_{αβ} is a chiral superfield. These two ingredients convert the structure of the N=2 vector-multiplet action — analyticity plus zero curvature — into a spin-2 version, with the Weyl tensor sitting in the θ

What would settle it

Perform the component expansion of S_Weyl in a fully fixed harmonic-independent gauge and verify that the coefficient of the θ^4 component is exactly the linearized Weyl-squared invariant with no additional lower-derivative or lower-spin terms; alternatively, solve D^{++}H^{--}=D^{--}H^{++} for a nontrivial analytic source and exhibit a non-zero homogeneous solution H^{--}_0 with D^{++}H^{--}_0=0, which would make H^{--} non-unique.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is the action S_Weyl = ∫ d^4x d^8θ du H^{++(αβ)} H^{--}_{(αβ)} + c.c. = (1/16) ∫ d^4x_L d^4θ W^{(αβ)} W_{(αβ)} + c.c., constructed from analytic prepotentials h^{++α˙α}, h^{++α+}, h^{++˙α+}, h^{(+4)} that define the covariant harmonic derivative D^{++}. The superfield H^{++}_{(αβ)} is built from these prepotentials and satisfies the half-analyticity condition, which requires the conjugate spinor derivative to annihilate it; its negatively charged partner H^{--}_{(αβ)} is defined by the zero-curvature equation D^{++}H^{--}=D^{--}H^{++}. The superfield W_{αβ}=(conjugate D^+)^2 H^{--}_{(αβ)} is then a chiral, gauge-invariant object whose lowest component

Load-bearing premise

The load-bearing premise is that the zero-curvature equations have unique solutions for the negatively charged potentials G^{--} and H^{--}; the paper defers this check to a component gauge-fixing without presenting the proof, and any harmonic zero-mode or cohomology ambiguity would make the action ill-defined or introduce extra degrees of freedom.

Editorial extensions

If this is right

If the action is correct, it provides the first off-shell harmonic-superspace description of linearized N=2 conformal supergravity with unconstrained prepotentials, enabling manifestly supersymmetric quantization.
The equivalence to the chiral Weyl-squared action means all previously known linearized results are recovered after fixing a harmonic-independent gauge; no new physical degrees of freedom appear.
The structural parallel with the N=2 vector-multiplet theory yields a concrete conjectured form of the full nonlinear N=2 Weyl action (a trace-type integral over multiple harmonic coordinates), which can now be tested at cubic order.
The derived superconformal transformation laws of the prepotentials also specify the N=2 AdS supersymmetry subgroup, opening a route to constructing N=2 AdS supergravity in harmonic superspace.
The same half-analyticity mechanism is expected to generalize to N=2 higher-spin superconformal multiplets, providing gauge-invariant higher-derivative actions for integer spins.

Reading between the lines

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

A testable next step the paper leaves implicit: the cubic-order check of the conjectured nonlinear action. If the cubic vertex requires terms beyond the trace formula, the difference will pinpoint how the superconformal measure weight must be compensated by the prepotentials themselves.
The half-analyticity condition defines new superconformally closed subspaces of harmonic superspace (spaces with 3/4 of the Grassmann coordinates). If these spaces carry their own invariant measures, they may provide an alternative geometric arena for computing correlation functions in N=2 conformal supergravity.
The uniqueness of H^{--} and G^{--} is the algebraic hinge of the entire construction; a cohomological analysis of the zero-curvature equations on the harmonic sphere would either confirm the component-gauge argument or reveal hidden redundancies.
If the construction extends to arbitrary conformally flat backgrounds as the authors anticipate, it would give a harmonic-superspace derivation of the N=2 conformal supergravity action on curved spacetime, independent of the standard conformal-superspace approach.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Two things up front. The central construction is almost certainly right: a harmonic-superspace action S = ∫ H^{++(αβ)}H^{--}_{(αβ)} + c.c. built from unconstrained analytic prepotentials, gauge invariant via the half-analyticity condition, and reducible in Appendix B to the known linearized Weyl-squared supergravity. And the paper's proof of rigid superconformal invariance has a genuine gap at the step where it concludes that the field-dependent gauge parameter Λ^{(sc)} in (4.35) is half-analytic. That step is load-bearing.

What is actually new: the explicit linearized action for the N=2 Weyl multiplet in harmonic superspace, its chiral representation, and the sector-by-sector superconformal analysis. Footnote 2 is honest that the structure was already sketched in the authors' own review, so the novelty is the full construction and the invariance study, not the bare idea. The spin-1/spin-2 Maxwell analogy is well drawn and makes the paper readable for people inside the harmonic formalism. Appendix B is the strongest part: in the harmonic-independent gauge they recover W_{(αβ)} = −(D̄)⁴D_{(αβ)}H, matching Howe-Stelle-Townsend and Butter-Kuzenko; that grounds the whole thing in independent results and is a real consistency check.

Soft spots, in proportion. (1) The invariance proof: from (4.36) one gets D^{++}(D̄^+Λ^{(sc)}) = 0, and the paper infers D̄^+Λ^{(sc)} = 0. That inference is invalid — D^{++} has a nontrivial kernel on charge +1 (u^+_i f^i, for instance), so the variation being half-analytic does not force the gauge parameter to be half-analytic. The conclusion may be salvageable from the explicit form of Λ^{(sc)}, or by checking the action's invariance directly, but the paper does neither. The same issue feeds into δ_sc H^{--} via the source term in (4.38). I do not think the result is wrong — Appendix B is a strong anchor — but the invariance claim is not yet proven. (2) The uniqueness of solutions to the zero-curvature equations (4.12)/(4.16) is asserted with "directly checked in WZ gauge." This is standard (D^{++} has no kernel on negative charge) and probably fine, but it is load-bearing and should be written out. (3) Minor: (2.8) has the wrong commutator in the δ_sc D^{--} line, and several integration-by-parts chains in (3.13) and (4.19) are compressed.

For peer review: yes. This is a technical construction from people who know the framework, the appendix check is genuine, and the gap I flagged is fixable. The appropriate outcome is major revision — the invariance proof has to be completed, not cosmetic. For a reader: if you work in harmonic superspace or N=2 conformal supergravity, worth a careful read; the Maxwell/Weyl analogy and Appendix B carry value even if the invariance proof needs patching.

Referee Report

3 major / 3 minor

Summary. The paper constructs a linearized action for N=2 conformal supergravity in harmonic superspace, using unconstrained analytic prepotentials h^{++α\dot α}, h^{++α+}, h^{++\dot α+}, h^{(+4)}. The central object is H^{++}_{(αβ)} defined in (4.13), which satisfies the half-analyticity condition (4.14). The proposed action S_Weyl = ∫ d^4x d^8θ du H^{++(αβ)} H^{--}_{(αβ)} + c.c. (4.18) is shown to be gauge invariant, and a chiral representation (4.23) is derived in terms of the super-Weyl tensor W_{(αβ)}. The bulk of the paper (§4.3) is devoted to proving rigid N=2 superconformal invariance by decomposing the transformation into λ^-, \bar λ^-, and λ^{++} sectors and reducing the variation to a homogeneous rotation plus a field-dependent gauge transformation. Appendix B provides a consistency check by reducing to the known harmonic-independent formulation and reproducing the standard super-Weyl tensor.

Significance. If correct, the paper provides the first explicit harmonic-superspace action for the linearized N=2 Weyl multiplet, expressed in terms of unconstrained analytic prepotentials, and reproduces the known Weyl-squared supergravity after gauge-fixing. The detailed sector-by-sector derivation and the consistency check in Appendix B are valuable, and the Maxwell analogy offers a plausible blueprint for a nonlinear generalization and for higher-spin extensions. However, the central proof of superconformal invariance contains a logical gap in establishing the half-analyticity of the composite gauge parameter, as detailed below. The result is plausible and likely repairable, but the current manuscript does not fully support its main claim.

major comments (3)

[§4.3, eqs. (4.35)–(4.37)] The step from (4.36) to (4.37) is not valid. From (4.36) and the half-analyticity of the homogeneous terms in (4.35) one obtains only D^{++}(\bar D^+ Λ^{(sc)}_{(αβ)})=0, not \bar D^+ Λ^{(sc)}_{(αβ)}=0. The operator D^{++} has a nontrivial kernel on charge +1 superfields (e.g. u^+_i times a harmonic-independent superfield), so the conclusion (4.37) does not follow. This is load-bearing: the gauge invariance of S_Weyl in (4.19) relies on the gauge parameter being half-analytic, and without (4.37) the invariance under δ_sc is not established. Please provide a direct computation of \bar D^+ Λ^{(sc)}_{(αβ)} or a separate argument that the kernel contribution vanishes.
[§4.1 and §4.3, eqs. (4.12), (4.16), (4.38)] The uniqueness of the negative-charge potentials G^{--}, H^{--}, and of the solution for δ_sc H^{--} is asserted without proof. The statement after (4.12) that this "can be directly checked, e.g., in WZ gauge" is not a proof. The action (4.18), the chiral representation (4.23), and the transformation law (4.39) all rely on these potentials being well-defined and unique. For (4.12) and (4.16) an explicit argument should be straightforward using the absence of zero-modes of D^{++} on charge −2 superfields; for (4.38) it must be shown that the source term lies in the image of D^{++} on the appropriate space. These steps need to be written out.
[§4.3, eqs. (4.38)–(4.40)] The superconformal variation of W_{(αβ)} in (4.40) is derived from δ_sc H^{--} in (4.39), which in turn depends on the uniqueness of the solution to (4.38) and on the half-analyticity of Λ^{(sc)}. Since the previous two comments show that both of these ingredients are not rigorously established, the chiral-superspace proof of superconformal invariance inherits the same gap. The claim in the abstract and §5 that invariance is "proved" is therefore premature.

minor comments (3)

[§2.1, eq. (2.8)] The displayed transformation law for δ_sc D^{--} uses the commutator [\hatΛ_sc, D^{++}], which appears to be a typo; it should be [\hatΛ_sc, D^{--}]. The surrounding text and the result indicate this is a typographical error.
[§4.2, after eq. (4.23)] The statement that the action "contains the square of the linearized Weyl tensor" is not explicitly demonstrated by a component reduction. While the identification of W_{(αβ)} with the super-Weyl tensor in (4.21) and Appendix B is convincing, a brief component check (or a reference to where it appears) would strengthen the claim.
[Abstract] The abstract asserts that the paper "proves its invariance in both harmonic and chiral superspaces." Given the gaps in §4.3, this overstates the rigor of the proof. The wording should be softened unless the gaps are closed.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the harmonic action is checked against the known N=2 Weyl supertensor in Appendix B, and the self-citations are not load-bearing in a circular way.

full rationale

The construction of S_Weyl is an explicit ansatz in the harmonic prepotentials, not a fit masquerading as a prediction. The central identification of the action with linearized N=2 conformal supergravity is anchored externally: W_(αβ) is defined as (Dbar+)^2 H^--_(αβ), and in the harmonic-independent gauge the paper reproduces the standard expression W_(αβ) = -(Dbar)^4 D_(αβ) H (eq. B.15), which it explicitly identifies with the known N=2 Weyl supertensor in conventional N=2 superspace. This is an independent, externally falsifiable check, so the half-analyticity condition imported from the authors' earlier work [19] is not a circular input. Gauge invariance (4.19) is a direct integration-by-parts calculation using half-analyticity. The superconformal invariance proof is also a direct calculation with no fitted parameters. The self-citations [6,10,19] supply background machinery (superconformal Killing parameters, half-analyticity, sketches of the action structure), but the load-bearing physical identification is verified against known results [21,27,40], not assumed. The only flagged weakness is a proof gap, not a circularity: at eqs. (4.36)-(4.37) the inference from D^{++}(Dbar^+Lambda^(sc))=0 to Dbar^+Lambda^(sc)=0 is not justified, since D^{++} has a nontrivial kernel on harmonic charge +1. This is a correctness/incompleteness issue in the invariance proof, not a reduction of the claimed result to its own inputs. Similarly, the assertion that the zero-curvature solutions for G^-- and H^-- are unique is stated as 'directly checked, e.g., in WZ gauge' without showing the check; again an omitted proof, not a circular step. Therefore the derivation chain is not circular, and the score is 0.

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

The central claim rests on prior harmonic superspace technology: the superconformal Killing realization, the analytic prepotentials of the Weyl multiplet, and the half-analyticity condition introduced by the authors. No free parameters are fitted and no new physical entities are postulated. The main unproved assumption is the uniqueness of the zero-curvature solutions, which is standard but not demonstrated in the text.

assumptions (5)

domain assumption The harmonic superspace realization of N=2 superconformal transformations given in eq. (2.6), and the derivative transformation laws (2.9)-(2.11), are correct.
The entire invariance proof relies on these transformation laws; if they are wrong, the proof fails. They are taken from prior work [6] and derived in Section 2.
domain assumption The analytic prepotentials h^{++...} introduced as deviations in eq. (4.5) provide an off-shell description of the N=2 Weyl multiplet.
This is asserted from the WZ gauge (4.6) and references [6,10]. The central claim presupposes these prepotentials carry exactly the physical degrees of freedom with the correct gauge symmetries.
ad hoc to paper The zero-curvature equations (4.12) and (4.16) have unique solutions for the negative-charge potentials G^{--} and H^{--}.
Used to define G^{--} and H^{--}; the paper says 'This can be directly checked' without giving the proof. The action and its superconformal variation depend on these potentials being well-defined.
domain assumption The half-analyticity condition (4.14) fixes the relative coefficient in H^{++}_{(αβ)} and is preserved by the superconformal group in the sense used in eq. (4.36).
Introduced in ref. [19], this is the central structural input that replaces full analyticity and ensures gauge invariance of the action. Its superconformal covariance is argued in Section 4.3.
standard math The standard harmonic-superspace manipulations used to pass from the full action (4.18) to the chiral action (4.23) are valid, including integration by parts, harmonic identities, and the representation (3.14).
The derivation follows the known Maxwell theory pattern (3.13) and uses the algebra of covariant derivatives and zero-curvature relations. These are standard results in harmonic superspace.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Linearized $\mathcal{N}=2$ conformal supergravity in the harmonic approach." pith.science (2026). https://pith.science/paper/JYE2MSBX

@misc{pith2026251116325,
  author       = {Pith},
  title        = {Pith review of: Linearized $\mathcalN=2$ conformal supergravity in the harmonic approach},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JYE2MSBX}},
  note         = {Machine review of arXiv:2511.16325}
}

abstract

Using the harmonic superspace approach, we construct the superconformal harmonic action for $\mathcal{N}=2$ Weyl supermultiplet. The fundamental objects of the theory are unconstrained analytic potentials $h^{++\alpha\dot{\alpha}}, h^{++\alpha+}, h^{++\dot{\alpha}+}, h^{(+4)}$, which distinguishes our construction among the previously known ones. An important role is played by the ``half-analyticity'' conditions introduced in arXiv:2407.08524 [hep-th]. The structure of the harmonic linearized $\mathcal{N}=2$ Weyl action to large extent repeats the structure of the $\mathcal{N}=2$ Maxwell action, which suggests a conjecture on the possible structure of the complete nonlinear $\mathcal{N}=2$ Weyl theory action in the harmonic superspace. We provide a detailed study of the rigid superconformal properties of the proposed action and prove its invariance in both harmonic and chiral superspaces. First steps are also undertaken towards constructing the nonlinear $\mathcal{N}=2$ Weyl action, based on an analogy with $\mathcal{N}=2$ Maxwell action just mentioned and a generalization of the concept of half-analyticity to curved harmonic superspace.

Discussion (0). Sign in to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Novel $\mathcal{N}=2$ higher-spin supercurrents
hep-th 2026-06 unverdicted novelty 7.0 of 10

Constructs abelian (s,s1,s2) cubic vertices for N=2 higher-spin supermultiplets that exist only for s ≥ s1+s2 and take the universal form of a gauge prepotential coupled to a conserved supercurrent from Weyl supertens...
Structure of $\mathcal{N} = 2$ superfield higher-spin abelian cubic interactions
hep-th 2026-05 unverdicted novelty 7.0 of 10

The structure of N=2 abelian cubic higher-spin vertices is fully determined by three analytic supercurrents, and odd-spin (s,1,1) gauge transformations reduce to supersymmetric zilch symmetries.

Reference graph

Works this paper leans on

42 extracted references · 24 linked inside Pith · cited by 2 Pith papers

[1]

Galperin, E

A. Galperin, E. Ivanov, S. Kalitzin, V. Ogievetsky and E. Sokatchev,UnconstrainedN= 2Matter, Yang-Mills and Supergravity Theories in Harmonic Superspace, Class. Quant. Grav.1(1984), 469-498 [erratum: Class. Quant. Grav.2(1985), 127]

1984
[2]

A. S. Galperin, E. A. Ivanov, V. I. Ogievetsky, E. S. Sokatchev,Harmonic superspace, Cambridge Monographs on Mathematical Physics, Cambridge University Press, 2001, 306 p

2001
[3]

Quantum Field theory and Quantum Statistics

A. Galperin, E. Ivanov, V. Ogievetsky and E. Sokatchev,Conformal invariance in harmonic superspace, Dubna preprint JINR E2-85-363, (1985), published in "Quantum Field theory and Quantum Statistics", eds. I. Batalin, C. J. Isham, G. Vilkovisky, vol.2, Adam Hilger, Bristol, 1987, p. 233–248

1985
[4]

B. U. Eden, P. S. Howe, A. Pickering, E. Sokatchev and P. C. West,Four point functions inN= 2 superconformal field theories, Nucl. Phys. B581(2000), 523-558 [arXiv:hep-th/0001138]

arXiv 2000
[5]

E. A. Ivanov, A. V. Smilga and B. M. Zupnik,Renormalizable supersymmetric gauge theory in six dimensions, Nucl. Phys. B726(2005), 131-148 [arXiv:hep-th/0505082]

arXiv 2005
[6]

Buchbinder, E

I. Buchbinder, E. Ivanov and N. Zaigraev,N= 2superconformal higher-spin multiplets and their hypermultiplet couplings, JHEP08(2024), 120 [arXiv:2404.19016 [hep-th]]

arXiv 2024
[7]

Buchbinder, E

I. Buchbinder, E. Ivanov and N. Zaigraev,Unconstrained off-shell superfield formulation of 4D,N= 2supersymmetric higher spins, JHEP12(2021), 016 [arXiv:2109.07639 [hep-th]]

arXiv 2021
[8]

Buchbinder, E

I. Buchbinder, E. Ivanov and N. Zaigraev,Off-shell cubic hypermultiplet couplings toN= 2higher spin gauge superfields, JHEP05(2022), 104 [arXiv:2202.08196 [hep-th]]

arXiv 2022

Show all 42 references

[9]

Buchbinder, E

I. Buchbinder, E. Ivanov and N. Zaigraev,N= 2higher spins: superfield equations of motion, the hypermultiplet supercurrents, and the component structure, JHEP03(2023), 036 [arXiv:2212.14114 [hep-th]]

2023 arXiv
[10]

Buchbinder, E

I. Buchbinder, E. Ivanov and N. Zaigraev,TowardsN= 2higher-spin supergravity, [arXiv:2503.02438 [hep-th]]

arXiv
[11]

A. S. Galperin, E. A. Ivanov, V. I. Ogievetsky and E. Sokatchev,N= 2Supergravity in Superspace: Different Versions and Matter Couplings, Class. Quant. Grav.4(1987), 1255

1987
[12]

Ivanov and N

E. Ivanov and N. Zaigraev,N= 2superconformal gravitino in harmonic superspace, Phys. Lett. B 862(2025), 139333 [arXiv:2412.14822 [hep-th]]

2025 arXiv
[13]

A. S. Galperin, N. A. Ky and E. Sokatchev,N= 2Supergravity in Superspace: Solution to the Constraints, Class. Quant. Grav.4(1987), 1235

1987
[14]

Ivanov,N= 2Supergravities in Harmonic Superspace, in: Bambi, C., Modesto, L., Shapiro, I

E. Ivanov,N= 2Supergravities in Harmonic Superspace, in: Bambi, C., Modesto, L., Shapiro, I. (eds) Handbook of Quantum Gravity, Springer, 2024 [arXiv:2212.07925 [hep-th]]

2024 arXiv
[15]

S. M. Kuzenko and E. S. N. Raptakis,TowardsN= 2superconformal higher-spin theory, JHEP11 (2024), 013 [arXiv:2407.21573 [hep-th]]. – 21 –

2024 arXiv
[16]

Butter, B

D. Butter, B. de Wit, S. M. Kuzenko and I. Lodato,New higher-derivative invariants inN= 2 supergravity and the Gauss-Bonnet term, JHEP12(2013), 062 [arXiv:1307.6546 [hep-th]]

2013 arXiv
[17]

Butter,On conformal supergravity and harmonic superspace, JHEP03(2016), 107 [arXiv:1508.07718 [hep-th]]

D. Butter,On conformal supergravity and harmonic superspace, JHEP03(2016), 107 [arXiv:1508.07718 [hep-th]]

2016 arXiv
[18]

Butter, S

D. Butter, S. M. Kuzenko, J. Novak and S. Theisen,Invariants for minimal conformal supergravity in six dimensions, JHEP12(2016), 072 [arXiv:1606.02921 [hep-th]]

2016 arXiv
[19]

Ivanov and N

E. Ivanov and N. Zaigraev,Off-shell invariants of linearized4D,N= 2supergravity in the harmonic approach, Phys. Rev. D110(2024) no.6, 066020 [arXiv:2407.08524 [hep-th]]

2024 arXiv
[20]

E. A. Ivanov and N. M. Zaigraev,N= 2Supergravity and Harmonic Superspace: Linearized Supercurvatures, Phys. Part. Nucl.56(2025) no.2, 247-252

2025
[21]

P. S. Howe, K. S. Stelle and P. K. Townsend,Supercurrents, Nucl. Phys. B192(1981), 332-352

1981
[22]

S. J. Gates, Jr. and W. Siegel,LinearizedN= 2superfield supergravity,, Nucl. Phys. B195(1982), 39-60

1982
[23]

P. S. Howe,Supergravity in Superspace, Nucl. Phys. B199(1982), 309-364

1982
[24]

E. S. Fradkin and A. A. Tseytlin,Conformal supergravity, Phys. Rept.119(1985), 233-362

1985
[25]

M¨ uller,Consistent Classical Supergravity Theories, Lect.Notes Phys

M. M¨ uller,Consistent Classical Supergravity Theories, Lect.Notes Phys. 336 (1989)

1989
[26]

S. M. Kuzenko, U. Lindstrom, M. Rocek and G. Tartaglino-Mazzucchelli,4DN= 2Supergravity and Projective Superspace, JHEP09(2008), 051 [arXiv:0805.4683 [hep-th]]

2008 arXiv
[27]

S. M. Kuzenko and E. S. N. Raptakis,Extended superconformal higher-spin gauge theories in four dimensions, JHEP12(2021), 210 [arXiv:2104.10416 [hep-th]]

2021 arXiv
[28]

Hutchings, S

D. Hutchings, S. M. Kuzenko and E. S. N. Raptakis,TheN= 2superconformal gravitino multiplet, Phys. Lett. B845(2023), 138132 [arXiv:2305.16029 [hep-th]]

2023 arXiv
[29]

Butter,N= 2Conformal Superspace in Four Dimensions, JHEP10(2011), 030 [arXiv:1103.5914 [hep-th]]

D. Butter,N= 2Conformal Superspace in Four Dimensions, JHEP10(2011), 030 [arXiv:1103.5914 [hep-th]]

2011 arXiv
[30]

Ferber,Supertwistors and Conformal Supersymmetry, Nucl

A. Ferber,Supertwistors and Conformal Supersymmetry, Nucl. Phys. B132(1978), 55-64

1978
[31]

B. M. Zupnik,Background harmonic superfields inN= 2supergravity, Theor. Math. Phys.116 (1998), 964-977 [arXiv:hep-th/9803202 [hep-th]]

1998 arXiv
[32]

S. M. Kuzenko and S. Theisen,Correlation functions of conserved currents inN= 2superconformal theory, Class. Quant. Grav.17(2000), 665-696 [arXiv:hep-th/9907107]

2000 arXiv
[33]

Zaigraev,N= 2higher-spin supercurrents, Phys

N. Zaigraev,N= 2higher-spin supercurrents, Phys. Lett. B858(2024), 139056 [arXiv:2408.00668 [hep-th]]

2024 arXiv
[34]

B. M. Zupnik,The Action of the SupersymmetricN= 2Gauge Theory in Harmonic Superspace, Phys. Lett. B183(1987), 175-176

1987
[35]

F. A. Berends, G. J. H. Burgers and H. Van Dam,On Spin Three Self Interactions, Z. Phys. C24 (1984), 247-254

1984
[36]

E. S. Fradkin and M. A. Vasiliev,On the Gravitational Interaction of Massless Higher Spin Fields, Phys. Lett. B189(1987), 89-95

1987
[37]

Y. M. Zinoviev, On spin 3 interacting with gravity, Class. Quant. Grav.26(2009), 035022 [arXiv:0805.2226 [hep-th]]

2009 arXiv
[38]

Ivanov and N

E. Ivanov and N. Zaigraev,N= 2AdS hypermultiplets in harmonic superspace, Phys. Lett. B871 (2025), 139964 [arXiv:2509.01406 [hep-th]]

2025
[39]

J. H. Park,Superconformal symmetry and correlation functions, Nucl. Phys. B559(1999), 455-501 [arXiv:hep-th/9903230]. – 22 –

1999 arXiv
[40]

Butter and S

D. Butter and S. M. Kuzenko,N= 2supergravity and supercurrents, JHEP12(2010), 080 [arXiv:1011.0339 [hep-th]]

2010 arXiv
[41]

Mezincescu,On the superfield formulation ofO(2)-supersymmetry, Dubna preprint JINR-P2-12572 (1979)

L. Mezincescu,On the superfield formulation ofO(2)-supersymmetry, Dubna preprint JINR-P2-12572 (1979)

1979
[42]

V. O. Rivelles and J. G. Taylor,LinearisedN= 2superfield supergravity, J. Phys. A15(1982), 163. – 23 –

1982

Pith tools

Reviewed August 3, 2026 · model on record in the stance chip above.

[1] [1]

Galperin, E

A. Galperin, E. Ivanov, S. Kalitzin, V. Ogievetsky and E. Sokatchev,UnconstrainedN= 2Matter, Yang-Mills and Supergravity Theories in Harmonic Superspace, Class. Quant. Grav.1(1984), 469-498 [erratum: Class. Quant. Grav.2(1985), 127]

1984

[2] [2]

A. S. Galperin, E. A. Ivanov, V. I. Ogievetsky, E. S. Sokatchev,Harmonic superspace, Cambridge Monographs on Mathematical Physics, Cambridge University Press, 2001, 306 p

2001

[3] [3]

Quantum Field theory and Quantum Statistics

A. Galperin, E. Ivanov, V. Ogievetsky and E. Sokatchev,Conformal invariance in harmonic superspace, Dubna preprint JINR E2-85-363, (1985), published in "Quantum Field theory and Quantum Statistics", eds. I. Batalin, C. J. Isham, G. Vilkovisky, vol.2, Adam Hilger, Bristol, 1987, p. 233–248

1985

[4] [4]

B. U. Eden, P. S. Howe, A. Pickering, E. Sokatchev and P. C. West,Four point functions inN= 2 superconformal field theories, Nucl. Phys. B581(2000), 523-558 [arXiv:hep-th/0001138]

arXiv 2000

[5] [5]

E. A. Ivanov, A. V. Smilga and B. M. Zupnik,Renormalizable supersymmetric gauge theory in six dimensions, Nucl. Phys. B726(2005), 131-148 [arXiv:hep-th/0505082]

arXiv 2005

[6] [6]

Buchbinder, E

I. Buchbinder, E. Ivanov and N. Zaigraev,N= 2superconformal higher-spin multiplets and their hypermultiplet couplings, JHEP08(2024), 120 [arXiv:2404.19016 [hep-th]]

arXiv 2024

[7] [7]

Buchbinder, E

I. Buchbinder, E. Ivanov and N. Zaigraev,Unconstrained off-shell superfield formulation of 4D,N= 2supersymmetric higher spins, JHEP12(2021), 016 [arXiv:2109.07639 [hep-th]]

arXiv 2021

[8] [8]

Buchbinder, E

I. Buchbinder, E. Ivanov and N. Zaigraev,Off-shell cubic hypermultiplet couplings toN= 2higher spin gauge superfields, JHEP05(2022), 104 [arXiv:2202.08196 [hep-th]]

arXiv 2022