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REVIEW 3 major objections 5 minor 71 references

Massless fermions of any spin admit two inequivalent Carrollian limits, electric and magnetic, derived from the Fang–Fronsdal action.

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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2026-08-01 08:22 UTC pith:NYKIVCIZ

load-bearing objection A serious, mostly convincing extension of Carrollian limits to arbitrary-spin fermions; the arbitrary-spin step rests on an operator identity stated without derivation. the 3 major comments →

arxiv 2607.21124 v1 pith:NYKIVCIZ submitted 2026-07-23 hep-th

Carroll fermions of arbitrary spin

Andrea Campoleoni , Lea Mele This is my paper
classification hep-th
keywords Carrollian symmetryFang–Fronsdal actionarbitrary spin fermionselectric and magnetic limitsHamiltonian formalismnull hypersurfaceshigher-spin gauge theoryc to 0 limit
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.

This paper establishes that every free massless fermion of arbitrary half-integer spin, described by the Fang–Fronsdal action, has two inequivalent Carrollian limits obtained by sending the speed of light to zero. The electric limit rescales the fields so that the second-class constraints survive, producing an action with vanishing Hamiltonian in which conjugate momenta are eliminated. The magnetic limit removes the second-class constraints, doubling the number of independent spinor fields and turning the conjugate momenta into genuine dynamical variables. The central technical step is a set of operator identities that transfer the c-dependence into a new first-class constraint, and an explicit truncation showing that the magnetic action's equations reduce to the directly-projected relativistic equations. The result gives a uniform, dimension-independent treatment of Carrollian fermions at all spins, relevant for physics on null hypersurfaces.

Core claim

The paper claims that the relativistic Fang–Fronsdal action for a free massless fermion of spin s+1/2 in any spacetime dimension D ≥ 3 admits two inequivalent c → 0 limits. The electric limit, obtained by rescaling the canonical fields by c^{1/2} and the Lagrange multipliers by c^{-1/2}, preserves the second-class constraints and yields a Carroll-invariant action with vanishing Hamiltonian, in which the conjugate momenta are eliminated algebraically. The magnetic limit, obtained by a field redefinition of the Lagrange multipliers N = χ + c^{-1} ζ and a rescaling of the second-class constraint multipliers, removes the second-class constraints entirely, so that the conjugate momenta become ind

What carries the argument

The machinery is the Hamiltonian form of the Fang–Fronsdal action, built from canonical variables Ψ_A (the spatial components of the spinor-tensor and the combination Ξ that absorbs temporal components), their conjugate momenta Π_A, a symplectic form ω_AB, first-class constraints F generating the gauge symmetry, and second-class constraints C_A relating Π_A to Ψ^†_B ω_BA. The crucial operatorial identity is −2(D^*_A) C^†_A = c^{−1} F − G, where D is the differential operator that defines the gauge transformations and D^* its formal adjoint; this identity transfers the c-dependence from the second-class constraints into the new first-class constraint G and guarantees that the magnetic limit i

Load-bearing premise

The entire construction rests on the correctness of the arbitrary-spin Hamiltonian decomposition in appendix B — the explicit symplectic form, the Hamiltonian, and the operator identities (4.17)–(4.20) — which are adapted from an earlier paper and not re-derived here; if any of those formulas is wrong, the magnetic action and the truncation proof fail.

What would settle it

Verify the truncation for the first non-checked case, for example spin 7/2 in D=4: substitute the explicit ω_AB, D, and H from appendix B into the magnetic equations (4.28) and the truncation (4.29), and check whether the P_− projection of (4.28b) reproduces (4.27b) exactly; a single mismatched term would falsify the claimed equivalence.

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

If this is right

  • Every half-integer spin field has a magnetic Carrollian action in which the conjugate momentum is an independent dynamical variable, not eliminable through its equation of motion.
  • The electric and magnetic actions are genuinely inequivalent: the electric one has zero Hamiltonian, while the magnetic one retains spatial gradients and a doubled spinor content.
  • The equations of the magnetic action can be truncated to the smaller set obtained by projecting the relativistic Fang–Fronsdal equations, so the two descriptions agree on the minimal sector.
  • The gauge symmetry of the relativistic theory survives both limits; in the magnetic limit the number of independent gauge parameters doubles, matching the doubled field content.

Where Pith is reading between the lines

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

  • If the magnetic action is taken as the fundamental Carrollian fermion theory, the doubled spinor content suggests a natural coupling to Carrollian gravity that could produce novel supergravity theories distinct from those obtained by direct limits of known supergravities.
  • The operator identities resemble a duality structure; one might expect a canonical transformation relating the electric and magnetic Carroll theories at finite c that becomes singular in the c → 0 limit, a relation not explored in the paper.
  • The same Hamiltonian machinery could be applied to massive fermions using the Singh–Hagen actions, yielding massive Carrollian fermions with electric and magnetic sectors — an extension the paper leaves open.

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 / 5 minor

Summary. This paper constructs electric and magnetic Carrollian actions for massless fermions of arbitrary half-integer spin as inequivalent c→0 limits of the relativistic Fang–Fronsdal actions. The electric limit is obtained by rescaling the canonical variables so that the second-class constraints survive, the Hamiltonian vanishes, and the first-class gauge constraints remain. The magnetic limit introduces conjugate momenta, removes the second-class constraints in the limit, doubles the number of independent spinor fields, and retains the spatial Hamiltonian and first-class constraints. The resulting magnetic equations have a triangular structure, and the paper shows that they can be truncated to the equations obtained by directly projecting the relativistic Fang–Fronsdal field equations. The construction is worked out explicitly for spin 3/2 and 5/2, then generalized to arbitrary spin using the Hamiltonian formulation of Appendix B, where the symplectic form and Hamiltonian are displayed.

Significance. If the arbitrary-spin claims are correct, this is the first systematic treatment of electric and magnetic Carrollian limits for massless fermions of any half-integer spin, complementing earlier work on scalar, vector, and spin-1/2 Carroll theories. The results are explicit, parameter-free, and reduce to known cases; the magnetic truncation gives a clear relation between the doubled Lagrangian formulation and the directly projected equations. The low-spin sections are especially clean and convincing. The main caveat is that the arbitrary-spin step relies on lengthy operator identities and Hamiltonian data that are stated without derivation, so the central claim is not yet fully established as it stands.

major comments (3)
  1. [Section 4, eqs. (4.17)–(4.20) and Appendix B] The identities F = -D*ωΨ and G = 2D*π†, together with the symplectic form (B.3)–(B.6) and the Hamiltonian (B.8), are load-bearing for the magnetic action (4.21) and for the truncation matching (4.27)–(4.29). These identities are asserted rather than derived. The explicit checks for spin 3/2 and 5/2 in Sections 2 and 3 do not cover generic s, since the gamma-trace manipulations depend on s. Please provide a derivation, or a verification scheme such as an inductive proof in s, and clarify which parts of Appendix B are new relative to [61].
  2. [Section 4, eq. (4.24a) and footnote 7] The equations of motion are obtained from H = Ψ† H_AB Ψ_B using the self-adjointness of H_AB in the sense of eq. (4.18). This property is assumed, not demonstrated. If H_AB is not self-adjoint under the stated integration by parts, the variation of H would produce different terms and eq. (4.24a) would need modification. Please state the precise domain of integration by parts and prove or justify the self-adjointness.
  3. [Section 4, after eq. (4.21)] For arbitrary spin the paper does not explicitly verify the Carroll-invariance criteria of [38]. The low-spin examples check the constraint algebra and the absence of secondary constraints (eqs. (2.21)–(2.23) and (3.22)–(3.23)), but for general s only the gauge transformations are displayed. Since the action is a gauge theory, one should show that the Hamiltonian weakly commutes with the first-class constraints, {F[ϵ],H}≈0 and {G[ϵ],H}≈0, and state explicitly that {H(x),H(x')}=0. The latter is trivial because H is independent of momenta, but the former should be demonstrated, ideally as a corollary of (4.17)–(4.20).
minor comments (5)
  1. [Eq. (1.14)] The notation ∙̇¯ψ¯π is confusing; adding parentheses or reordering the factors would improve clarity.
  2. [Section 2, eq. (2.15)] The field redefinition Ψ0=χ+c−1ζ and the resulting reducible shift (2.19) are introduced quickly; a sentence explaining why the enlarged constraint set imposes no new conditions would help the reader.
  3. [Section 4, eq. (4.26)] The index-free notation Ψ± = c^{−1/2}ψ± should be made explicit: the ± label refers to the P± projections, not to spacetime indices.
  4. [Appendix B] Given the length of (B.8), a short outline of how it is obtained from (4.1), or a reference to a supplementary file with a symbolic verification, would increase confidence in the result.
  5. [General] The phrase “removing the second-class constraints” (e.g., Section 4) could be sharpened: in the c→0 limit these constraints are not enforced, rather than “removed” from the action.

Circularity Check

0 steps flagged

No circularity: the Carrollian actions are explicit c→0 limits of the Fang–Fronsdal action; the magnetic truncation is a consistency check, not a redefinition.

full rationale

The paper's central claim is that electric and magnetic actions are obtained by taking explicit c→0 limits of the relativistic Fang–Fronsdal action. The electric limit (4.10)–(4.12) is a direct rescaling limit; the magnetic limit (4.13)–(4.21) follows from a redefinition of Lagrange multipliers that isolates the second-class constraints, which are then dropped by rescaling their multipliers with ε>1. The 'minimal magnetic equations' (4.27) are obtained by projecting and taking the limit of the Hamiltonian form (4.24), and the truncation (4.29) is then shown by substitution to reduce the magnetic-action equations (4.28) to exactly those equations. This is a consistency check: each quantity is defined independently (F from the FF gauge symmetry, G from the doubled momentum, and the truncation as an imposed projection), and the matching is the derived conclusion, not an input. The identities (4.17)–(4.20), including F = −(D*)ωΨ and G = 2(D*)Π†, are asserted operatorial facts; if wrong, the matching would fail. That is a correctness risk and an omitted proof, not circularity, because these identities are not assumed by defining the output. Self-citations to [44] and [61] supply the method and the Hamiltonian decomposition; [61] is a parameter-free prior Hamiltonian analysis of the same Fang–Fronsdal actions, and the present paper checks low spins explicitly. No fitted parameter is renamed as a prediction, and no result is equivalent to its input by construction. Therefore the circularity score is 0.

Axiom & Free-Parameter Ledger

0 free parameters · 5 axioms · 0 invented entities

No numbers are fitted to data: the rescalings (e.g., ΨA = √c ψA, ΠA = c^{−1/2} πA, N = c^{−1/2} Ñ, λA = c^ε λ̂ with ε > 1) are powers of c chosen so specific terms survive or vanish in the limit — prescription choices of the established electric/magnetic program, not fitted values. No new physical entities are postulated: the extra spinor fields in the magnetic theory (π, χ, ζ) are conjugate momenta and Lagrange multipliers made independent by removing second-class constraints; they are Hamiltonian field–momentum content, not new physics, and need no independent falsifiable handle. The axioms above are the actual load-bearing background: the [61]-derived Hamiltonian structure, the asserted appendix-B formulas, and the [38] Carroll-invariance criteria.

axioms (5)
  • standard math Gamma-matrix Clifford algebra and Hermiticity conventions (A.1)–(A.7), including (γ0)† = −γ0 and projector properties P±γa = γa P∓.
    Invoked throughout for kinetic terms, constraints, and the P± projections used in the minimal magnetic equations.
  • domain assumption The Hamiltonian decomposition of the arbitrary-spin Fang–Fronsdal action: canonical variables ΨA = (Ψk(s), Ξk(s−2)) with Ξ = Ψ00 − 2γ0γjΨ0j, Lagrange multipliers N, and the algebraic-constraint relations (4.5) expressing temporal components.
    Adapted from [61]; the reader must accept the split and the elimination of trace components. The magnetic action and the truncation inherit this structure.
  • domain assumption The explicit arbitrary-spin symplectic form (B.3)–(B.6) and Hamiltonian (B.8) are correct, and HAB is self-adjoint in the sense of (4.18).
    Asserted in appendix B rather than derived; needed for the magnetic action (4.21), the projected equations (4.27), and the truncation matching.
  • domain assumption The criteria of [38] for Carroll invariance of an action — {H(x), H(x′)} = 0 and scalar behaviour of H under spatial rotations/translations — are valid and sufficient for the gauge systems considered.
    Used to conclude that the magnetic actions (2.20), (3.21), (4.21) are Carroll-invariant (Sections 2–4).
  • ad hoc to paper The truncation conditions (4.29) (and (2.32), (3.36)) define a consistent sub-sector of the magnetic equations of motion.
    The truncation is imposed by hand and is not implementable at the action level (stated in Section 1 for spin 1/2). The paper proves consistency with the equations of motion, which is the relevant content.

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Electric and magnetic Carrollian actions for fermions of arbitrary spin in any spacetime dimension are defined as inequivalent $c \to 0$ limits of the relativistic Fang-Fronsdal actions.

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Reference graph

Works this paper leans on

71 extracted references · 52 linked inside Pith

  1. [1]

    Lévy-Leblond,Une nouvelle limite non-relativiste du groupe de Poincaré,Annales de l’I.H.P

    J.-M. Lévy-Leblond,Une nouvelle limite non-relativiste du groupe de Poincaré,Annales de l’I.H.P. Phys. Theor.3(1965) 1

    1965

  2. [2]

    Sen Gupta,On an Analogue of the Galileo Group,Nuovo Cim.54(1966) 512

    N.D. Sen Gupta,On an Analogue of the Galileo Group,Nuovo Cim.54(1966) 512

    1966

  3. [3]

    Henneaux,Geometry of Zero Signature Space-times,Bull

    M. Henneaux,Geometry of Zero Signature Space-times,Bull. Soc. Math. Belg.31(1979) 47

    1979

  4. [4]

    Duval, G.W

    C. Duval, G.W. Gibbons and P.A. Horvathy,Conformal Carroll groups and BMS symmetry, Class. Quant. Grav.31(2014) 092001 [1402.5894]. – 23 –

    Pith/arXiv arXiv 2014

  5. [5]

    Duval, G.W

    C. Duval, G.W. Gibbons, P.A. Horvathy and P.M. Zhang,Carroll symmetry of plane gravitational waves,Class. Quant. Grav.34(2017) 175003 [1702.08284]

    Pith/arXiv arXiv 2017

  6. [6]

    Donnay and C

    L. Donnay and C. Marteau,Carrollian Physics at the Black Hole Horizon,Class. Quant. Grav.36(2019) 165002 [1903.09654]

    Pith/arXiv arXiv 2019

  7. [7]

    Oling and J.F

    G. Oling and J.F. Pedraza,Mixmasters in Wonderland: Chaotic dynamics from Carroll limits of gravity,SciPost Phys. Core8(2025) 025 [2409.05836]

    Pith/arXiv arXiv 2025

  8. [8]

    Fiorucci, S

    A. Fiorucci, S. Pekar, P. Marios Petropoulos and M. Vilatte,Carrollian-Holographic Derivation of Gravitational Flux-Balance Laws,Phys. Rev. Lett.135(2025) 261602 [2505.00077]

    arXiv 2025

  9. [9]

    Fontanella and O

    A. Fontanella and O. Payne,A Carroll limit of AdS/CFT: A triality with flat space holography?,Phys. Lett. B879(2026) 140669 [2508.10085]

    Pith/arXiv arXiv 2026

  10. [10]

    Casalbuoni, J

    R. Casalbuoni, J. Gomis and D. Hidalgo,Worldline description of fractons,Phys. Rev. D 104(2021) 125013 [2107.09010]

    Pith/arXiv arXiv 2021

  11. [11]

    Peña-Benitez,Fractons, symmetric gauge fields and geometry,Phys

    F. Peña-Benitez,Fractons, symmetric gauge fields and geometry,Phys. Rev. Res.5(2023) 013101 [2107.13884]

    Pith/arXiv arXiv 2023

  12. [12]

    Bidussi, J

    L. Bidussi, J. Hartong, E. Have, J. Musaeus and S. Prohazka,Fractons, dipole symmetries and curved spacetime,SciPost Phys.12(2022) 205 [2111.03668]

    Pith/arXiv arXiv 2022

  13. [13]

    Figueroa-O’Farrill, A

    J. Figueroa-O’Farrill, A. Pérez and S. Prohazka,Carroll/fracton particles and their correspondence,JHEP06(2023) 207 [2305.06730]

    Pith/arXiv arXiv 2023

  14. [14]

    N. Ara, A. Banerjee, R. Basu and B. Krishnan,Flat bands and compact localised states: A Carrollian roadmap,SciPost Phys.19(2025) 046 [2412.18965]

    Pith/arXiv arXiv 2025

  15. [15]

    Bergshoeff, J

    E. Bergshoeff, J. Figueroa-O’Farrill and J. Gomis,A non-lorentzian primer,SciPost Phys. Lect. Notes69(2023) 1 [2206.12177]

    Pith/arXiv arXiv 2023

  16. [16]

    Bagchi, A

    A. Bagchi, A. Banerjee, P. Dhivakar, S. Mondal and A. Shukla,The Carrollian kaleidoscope, Eur. Phys. J. C86(2026) 429 [2506.16164]

    Pith/arXiv arXiv 2026

  17. [17]

    Ciambelli and P

    L. Ciambelli and P. Jai-akson,Foundations of Carrollian geometry,Phys. Rept.1188(2026) 1 [2510.21651]

    Pith/arXiv arXiv 2026

  18. [18]

    Bagchi, R

    A. Bagchi, R. Basu, A. Kakkar and A. Mehra,Flat Holography: Aspects of the dual field theory,JHEP12(2016) 147 [1609.06203]

    Pith/arXiv arXiv 2016

  19. [19]

    Ciambelli, C

    L. Ciambelli, C. Marteau, A.C. Petkou, P.M. Petropoulos and K. Siampos,Flat holography and Carrollian fluids,JHEP07(2018) 165 [1802.06809]

    Pith/arXiv arXiv 2018

  20. [20]

    Donnay, A

    L. Donnay, A. Fiorucci, Y. Herfray and R. Ruzziconi,Carrollian Perspective on Celestial Holography,Phys. Rev. Lett.129(2022) 071602 [2202.04702]

    Pith/arXiv arXiv 2022

  21. [21]

    Bagchi, S

    A. Bagchi, S. Banerjee, R. Basu and S. Dutta,Scattering Amplitudes: Celestial and Carrollian,Phys. Rev. Lett.128(2022) 241601 [2202.08438]

    Pith/arXiv arXiv 2022

  22. [22]

    Nguyen,Lectures on Carrollian holography,Eur

    K. Nguyen,Lectures on Carrollian holography,Eur. Phys. J. C86(2026) 733 [2511.10162]

    Pith/arXiv arXiv 2026

  23. [23]

    Ruzziconi,Carrollian physics and holography,Phys

    R. Ruzziconi,Carrollian physics and holography,Phys. Rept.1182(2026) 1 [2602.02644]

    arXiv 2026

  24. [24]

    Bagchi, R

    A. Bagchi, R. Basu, A. Mehra and P. Nandi,Field Theories on Null Manifolds,JHEP02 (2020) 141 [1912.09388]

    Pith/arXiv arXiv 2020

  25. [25]

    Gupta and N.V

    N. Gupta and N.V. Suryanarayana,Constructing Carrollian CFTs,JHEP03(2021) 194 [2001.03056]. – 24 –

    Pith/arXiv arXiv 2021

  26. [26]

    B. Chen, R. Liu and Y.-f. Zheng,On higher-dimensional Carrollian and Galilean conformal field theories,SciPost Phys.14(2023) 088 [2112.10514]

    Pith/arXiv arXiv 2023

  27. [27]

    Rivera-Betancour and M

    D. Rivera-Betancour and M. Vilatte,Revisiting the Carrollian scalar field,Phys. Rev. D106 (2022) 085004 [2207.01647]

    Pith/arXiv arXiv 2022

  28. [28]

    Baiguera, G

    S. Baiguera, G. Oling, W. Sybesma and B.T. Søgaard,Conformal Carroll scalars with boosts, SciPost Phys.14(2023) 086 [2207.03468]

    Pith/arXiv arXiv 2023

  29. [29]

    de Boer, J

    J. de Boer, J. Hartong, N.A. Obers, W. Sybesma and S. Vandoren,Carroll stories,JHEP09 (2023) 148 [2307.06827]

    Pith/arXiv arXiv 2023

  30. [30]

    Bekaert, A

    X. Bekaert, A. Campoleoni and S. Pekar,Holographic Carrollian conformal scalars,JHEP 05(2024) 242 [2404.02533]

    Pith/arXiv arXiv 2024

  31. [31]

    B. Chen, H. Sun and Y.-f. Zheng,Quantization of Carrollian conformal scalar theories,Phys. Rev. D110(2024) 125010 [2406.17451]

    Pith/arXiv arXiv 2024

  32. [32]

    Cotler, K

    J. Cotler, K. Jensen, S. Prohazka, A. Raz, M. Riegler and J. Salzer,Quantizing Carrollian field theories,JHEP10(2024) 049 [2407.11971]

    Pith/arXiv arXiv 2024

  33. [33]

    Aggarwal, A

    A. Aggarwal, A. Bagchi, S. Detournay, D. Grumiller, M. Riegler and J. Simon,Universal sectors of two-dimensional Carrollian CFTs,JHEP11(2025) 039 [2508.05735]

    arXiv 2025

  34. [34]

    Fredenhagen, S

    S. Fredenhagen, S. Prohazka and R. Tiefenbacher,Carrollian quantum states and flat space holography,2604.22745

    Pith/arXiv arXiv

  35. [35]

    D’Arcy, A

    E. D’Arcy, A. Delfante and S. Fredenhagen,Holographic realization of higher-spin Carrollian free fields,2604.27068

    Pith/arXiv arXiv

  36. [36]

    Duval, G.W

    C. Duval, G.W. Gibbons, P.A. Horvathy and P.M. Zhang,Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time,Class. Quant. Grav.31(2014) 085016 [1402.0657]

    Pith/arXiv arXiv 2014

  37. [37]

    Bagchi, A

    A. Bagchi, A. Mehra and P. Nandi,Field Theories with Conformal Carrollian Symmetry, JHEP05(2019) 108 [1901.10147]

    Pith/arXiv arXiv 2019

  38. [38]

    Henneaux and P

    M. Henneaux and P. Salgado-Rebolledo,Carroll contractions of Lorentz-invariant theories, JHEP11(2021) 180 [2109.06708]

    Pith/arXiv arXiv 2021

  39. [39]

    de Boer, J

    J. de Boer, J. Hartong, N.A. Obers, W. Sybesma and S. Vandoren,Carroll Symmetry, Dark Energy and Inflation,Front. in Phys.10(2022) 810405 [2110.02319]

    Pith/arXiv arXiv 2022

  40. [40]

    Barnich, A

    G. Barnich, A. Gomberoff and H.A. González,Three-dimensional Bondi-Metzner-Sachs invariant two-dimensional field theories as the flat limit of Liouville theory,Phys. Rev. D87 (2013) 124032 [1210.0731]

    Pith/arXiv arXiv 2013

  41. [41]

    O’Connor and S

    J.A. O’Connor and S. Pekar,A note on non-Lorentzian duality symmetries,JHEP03(2025) 084 [2409.12279]

    Pith/arXiv arXiv 2025

  42. [42]

    Le Bellac and J.M

    M. Le Bellac and J.M. Lévy-Leblond,Galilean electromagnetism,Nuovo Cim. B14(1973) 217

    1973

  43. [43]

    Koutrolikos and M

    K. Koutrolikos and M. Najafizadeh,Super-Carrollian and Super-Galilean Field Theories, Phys. Rev. D108(2023) 125014 [2309.16786]

    Pith/arXiv arXiv 2023

  44. [44]

    Bergshoeff, A

    E.A. Bergshoeff, A. Campoleoni, A. Fontanella, L. Mele and J. Rosseel,Carroll fermions, SciPost Phys.16(2024) 153 [2312.00745]

    Pith/arXiv arXiv 2024

  45. [45]

    Bagchi and S

    A. Bagchi and S. Mondal,Carroll fermions, expansions and the lightcone,2604.14301. – 25 –

    Pith/arXiv arXiv

  46. [46]

    Majumdar, A

    S. Majumdar, A. Sharma and S. Singha,Carroll fermions from null reduction: A case of good and bad fermions,2605.05334

    Pith/arXiv arXiv

  47. [47]

    Bagchi, D

    A. Bagchi, D. Grumiller and P. Nandi,Carrollian superconformal theories and super BMS, JHEP05(2022) 044 [2202.01172]

    Pith/arXiv arXiv 2022

  48. [48]

    Banerjee, S

    A. Banerjee, S. Dutta and S. Mondal,Carroll fermions in two dimensions,Phys. Rev. D107 (2023) 125020 [2211.11639]

    Pith/arXiv arXiv 2023

  49. [49]

    Bagchi, A

    A. Bagchi, A. Banerjee, R. Basu, M. Islam and S. Mondal,Magic fermions: Carroll and flat bands,JHEP03(2023) 227 [2211.11640]

    Pith/arXiv arXiv 2023

  50. [50]

    Zorba, I

    U. Zorba, I. Bulunur, O. Kasikci, M. Ozkan, Y. Pang and M.S. Zog,Supersymmetric Carroll Galileons in three dimensions,Phys. Rev. D111(2025) 085008 [2409.15428]

    Pith/arXiv arXiv 2025

  51. [51]

    Ekiz, E.O

    E. Ekiz, E.O. Kahya and U. Zorba,Quantization of Carrollian fermions,Phys. Rev. D111 (2025) 105019 [2502.05645]

    Pith/arXiv arXiv 2025

  52. [52]

    Zheng and B

    Y.-f. Zheng and B. Chen,Structure of Carrollian (conformal) superalgebra,JHEP08(2025) 111 [2503.22160]

    Pith/arXiv arXiv 2025

  53. [53]

    Bruce,The Carrollian Superplane and Supersymmetry,2603.21677

    A.J. Bruce,The Carrollian Superplane and Supersymmetry,2603.21677

    Pith/arXiv arXiv

  54. [54]

    Bulunur, O

    I. Bulunur, O. Ergec, O. Kasikci, M. Ozkan and M.S. Zog,A Twisted Origin for Magnetic Carroll Supersymmetry,2603.28269

    Pith/arXiv arXiv

  55. [55]

    Bagchi, A

    A. Bagchi, A. Lipstein, S. Mondal and A.J. Zhang,Carrollian ABJM: Fermions and Supersymmetry,2604.22582

    Pith/arXiv arXiv

  56. [56]

    Henneaux,Carroll supergravities,2607.08329

    M. Henneaux,Carroll supergravities,2607.08329

    Pith/arXiv arXiv

  57. [57]

    Bergshoeff, A

    E.A. Bergshoeff, A. Campoleoni, A. Fontanella, L. Mele and J. Rosseel,Carroll Fermions, PoSCORFU2023(2024) 235

    2024

  58. [58]

    Grumiller, L

    D. Grumiller, L. Mele and L. Montecchio,Carroll spinors,Mod. Phys. Lett. A(2026) 2540003 [2509.19426]

    arXiv 2026

  59. [59]

    Bergshoeff, J

    E. Bergshoeff, J. Gomis, B. Rollier, J. Rosseel and T. ter Veldhuis,Carroll versus Galilei Gravity,JHEP03(2017) 165 [1701.06156]

    Pith/arXiv arXiv 2017

  60. [60]

    Fang and C

    J. Fang and C. Fronsdal,Massless Fields with Half Integral Spin,Phys. Rev. D18(1978) 3630

    1978

  61. [61]

    Campoleoni, M

    A. Campoleoni, M. Henneaux, S. Hörtner and A. Leonard,Higher-spin charges in Hamiltonian form. II. Fermi fields,JHEP02(2017) 058 [1701.05526]

    Pith/arXiv arXiv 2017

  62. [62]

    Aragone and S

    C. Aragone and S. Deser,Hamiltonian Form for Massless Higher Spin Fermions,Phys. Rev. D21(1980) 352

    1980

  63. [63]

    Borde,HAMILTONIAN FORMALISM FOR THE SPIN 5/2 GAUGE FIELD,Phys

    A. Borde,HAMILTONIAN FORMALISM FOR THE SPIN 5/2 GAUGE FIELD,Phys. Rev. D26(1982) 407

    1982

  64. [64]

    Bunster, M

    C. Bunster, M. Henneaux, S. Hörtner and A. Leonard,Supersymmetric electric-magnetic duality of hypergravity,Phys. Rev. D90(2014) 045029 [1406.3952]

    Pith/arXiv arXiv 2014

  65. [65]

    Aragone and S

    C. Aragone and S. Deser,Higher Spin Vierbein Gauge Fermions and Hypergravities,Nucl. Phys. B170(1980) 329

    1980

  66. [66]

    Vasiliev,Linearized Curvatures for Auxiliary Fields in the De Sitter Space,Nucl

    M.A. Vasiliev,Linearized Curvatures for Auxiliary Fields in the De Sitter Space,Nucl. Phys. B307(1988) 319. – 26 –

    1988

  67. [67]

    Curtright,Massless Field Supermultiplets With Arbitrary Spin,Phys

    T. Curtright,Massless Field Supermultiplets With Arbitrary Spin,Phys. Lett. B85(1979) 219

    1979

  68. [68]

    Kuzenko, A.G

    S.M. Kuzenko, A.G. Sibiryakov and V.V. Postnikov,Massless gauge superfields of higher half integer superspins,JETP Lett.57(1993) 534

    1993

  69. [69]

    Kuzenko and A.G

    S.M. Kuzenko and A.G. Sibiryakov,Massless gauge superfields of higher integer superspins, JETP Lett.57(1993) 539

    1993

  70. [70]

    Singh and C.R

    L.P.S. Singh and C.R. Hagen,Lagrangian formulation for arbitrary spin. 1. The boson case, Phys. Rev. D9(1974) 898

    1974

  71. [71]

    Singh and C.R

    L.P.S. Singh and C.R. Hagen,Lagrangian formulation for arbitrary spin. 2. The fermion case,Phys. Rev. D9(1974) 910. – 27 –

    1974