Pith. sign in

REVIEW 2 major objections 4 minor 59 references

Tensor global symmetries and the Stueckelberg mechanism for tensor fields

T0 review · 2 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

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

Pith's one-line read The paper establishes that restoring gauge invariance to massive mixed-symmetry tensor fields forces definite Stueckelberg partner fields, yields conserved mixed-symmetry currents, and produces a 't Hooft anomaly for the graviton in…

desk verdict The paper's central gauge-invariant (2,1) current contains a one-sign error that makes it non-invariant under its own gauge transformations; the construction is promising and likely fixable, but as printed the main claim and the anomaly derivation do not stand. read the letter →

arxiv 2411.16928 v2 pith:HSEVZFK5 submitted 2024-11-25 hep-th gr-qchep-ph

Athanasios Chatzistavrakidis , Arash Ranjbar , Sara Zeko This is my paper · ORCID
classification hep-thgr-qchep-ph
keywords tensorglobalsymmetriesStueckelbergmechanismmixed-symmetryfieldsCurtrightfieldNambu-Goldstonebosons'tHooftanomalylinearizedgravityhigher-form
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

This paper develops a Stueckelberg mechanism for mixed-symmetry tensor fields at the linearized level, showing that a massive tensor field's gauge invariance forces a definite, degree-of-freedom-determined set of shift-symmetric companion fields: a vector and a scalar for the massive graviton, a graviton, a Kalb-Ramond two-form, and a vector for the massive Curtright field, and a Curtright field plus a graviton for a massive $(2,2)$ tensor. For each case the paper constructs a conserved current with the same mixed symmetry, so the resulting gauge theory carries a tensor global symmetry and can be minimally coupled to a background field. It then interprets the graviton and the Kalb-Ramond field as Nambu-Goldstone bosons of spontaneously broken constant symmetric and antisymmetric shift symmetries, and shows by nonminimal coupling that linearized gravity has a 't Hooft anomaly: the electric and magnetic background fields cannot both be gauged. A sympathetic reader would care because this supplies first-derivative, gauge-invariant Noether currents for graviton shift symmetries that earlier constructions lacked, and it ties massive tensor theories into the generalized-global-symmetry framework.

What carries the argument

The central object is the graded-coordinate (Berezin) calculus for mixed-symmetry tensors: a tensor of type $(p,q)$ is encoded as a superfield in two sets of anticommuting variables $\theta^\mu$ and $\tilde\theta^\mu$ under the Deligne sign convention, with de Rham differentials $d$ and $\tilde d$ and a generalized Hodge dual $\star$ mapping $(p,q)$ tensors to $(D-p,D-q)$ tensors. In this notation each massive action takes the compact form $-\frac12\int_B(dT\star dT - T\star T)$, and the Stueckelberg redefinitions become simple gauge-invariant combinations such as (5.8). The paper uses this calculus to perform shift and gauge variations, drop total derivatives, read off conserved mixed-symmetry currents and their double divergences, and derive the anomaly variation (7.13); the degree-of-freedom identity (2.9) is what fixes which Stueckelberg fields must appear before this calculus is applied.

What would settle it

Recompute the gauge variation of $J^{(h)}_{\mu\nu|\rho}+J^{(b)}_{\mu\nu|\rho}-2J^{(a)}_{\mu\nu|\rho}$ using the printed variation (5.26); as written the combination shifts by four times the displayed object, so gauge invariance requires a sign flip in (5.26). A component-level rederivation of (5.11) and (7.13) without the Berezin formalism would settle whether the graded-coordinate sign convention is responsible.

Watch

Extended reading notes

Core claim

The paper's central claim is that the Stueckelberg mechanism for massive mixed-symmetry tensor fields is fixed by degrees of freedom: the identity $|h+b+a|_0 = |T|-|T|_0$ for the $(2,1)$ Curtright case, and its analogues for $(1,1)$ and $(2,2)$, force the companion fields listed above, and these companions transform under constant shift symmetries with parameters of matching symmetry type. With these fields in place, the paper constructs Noether currents of mixed symmetry, such as $J_{\mu\nu|\rho} = J^{(h)}_{\mu\nu|\rho}+J^{(b)}_{\mu\nu|\rho}-2J^{(a)}_{\mu\nu|\rho}$, that are conserved in both index slots and invariant under the full cascade of gauge transformations. It claims that the graviton and the Kalb-Ramond field are Nambu-Goldstone bosons for spontaneously broken symmetric and antisymmetric shift symmetries, and that a nonminimal coupling of the two-derivative magnetic current to a magnetic Curtright background produces the gauge variation (7.13), which is the 't Hooft anomaly of the tensor global symmetry in linearized gravity.

Load-bearing premise

The load-bearing premise is that the graded-coordinate (Berezin) calculus with the Deligne sign convention and generalized Hodge-star rules is error-free, since a sign slip would propagate into every Stueckelberg action, current, and anomaly—and as printed Eqs. (5.26) and (5.27) are not mutually consistent.

Editorial extensions

If this is right

  • The graviton alone cannot be a Stueckelberg field for the constant symmetric shift $\delta h_{\mu\nu}=s_{\mu\nu}$; the massive graviton necessarily brings a vector and a scalar, and only the vector is a candidate Goldstone mode, while the scalar is secondary and decouples in the massless limit.
  • The massive Curtright field forces a graviton, a Kalb-Ramond two-form, and a vector as Stueckelberg partners, with the graviton and the Kalb-Ramond field emerging as Nambu-Goldstone bosons of broken tensor shift symmetries.
  • A conserved, gauge-invariant $(2,1)$ current provides a first-derivative coupling to a Curtright background field, replacing earlier non-gauge-invariant currents of linearized gravity.
  • The same construction works for the massive $(2,2)$ tensor in five dimensions, producing a doubly conserved current built from the linearized Riemann tensor and a graviton as a secondary Stueckelberg field.
  • A 't Hooft anomaly blocks simultaneous gauging of the electric and magnetic background fields in linearized gravity, so the graviton shift symmetry cannot be consistently realized with both duality frames dynamical.

Reading between the lines

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

  • A natural extension is to prove the counting identity for all $p \geq q \geq 1$; the three examples suggest a universal Stueckelberg triple $(p-1,q)$, $(p,q-1)$, $(p-1,q-1)$, generating an infinite ladder of mixed-symmetry gauge theories and conserved currents.
  • The 'secondary' Stueckelberg rule—whoever's shift is gauged by another Stueckelberg field cannot become a Goldstone mode—could be tested in the next cases, such as a massive $(3,1)$ or $(3,2)$ field, where the predicted secondary partner would be a Kalb-Ramond or vector field, respectively.
  • The anomaly is derived from nonminimal couplings; a descent-equation or inflow derivation of an anomaly polynomial, analogous to the $p$-form case, would locate the anomaly more invariantly and could predict which background fields must be frozen in any dual frame.
  • If such tensor global symmetries exist in quantum field theory, their charges should be carried by extended objects whose dimension is fixed by the $(p,q)$ type, suggesting concrete lattice or effective-field-theory realizations of the $(2,1)$ current and a possible handle on subdimensional particles.
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.

Referee Report

2 major / 4 minor

Summary. The paper develops a Stueckelberg mechanism for massive mixed-symmetry tensor fields at the linearized level, working out three cases: the massive Fierz-Pauli graviton, the massive Curtright (2,1) field, and the massive (2,2) field. For each case it identifies the Stueckelberg field content by degree-of-freedom counting, constructs gauge-invariant and conserved currents of mixed symmetry associated with tensor global shift symmetries, and couples these currents to background fields. In the Curtright case the graviton and Kalb-Ramond field are interpreted as Nambu-Goldstone bosons for spontaneously broken symmetric and antisymmetric shift symmetries, and a nonminimal coupling is used to propose a 't Hooft anomaly for linearized gravity. The derivations use a compact graded-coordinate formalism adapted from previous work by the authors, with component expressions given alongside.

Significance. If the central construction were correct, the paper would be a useful extension of generalized global symmetries to mixed-symmetry tensor fields, providing explicit conserved currents and a candidate anomaly in linearized gravity. The degree-of-freedom counting and the structure of the Stueckelberg actions are standard algebraic manipulations, and the paper is self-contained in giving component formulas; there are no fitted parameters and no predictions extracted from numerical fits. However, the main advertised result, the gauge-invariant (2,1) current of Section 5.2, is not gauge invariant under the paper's own variation formulas, and the subsequent minimal coupling and anomaly calculation inherit this problem. The significance of the paper is therefore conditional on repairing the internal inconsistency in the current construction.

major comments (2)
  1. [5.2, Eqs. (5.26)-(5.27) and (7.11)-(7.13)] The central claim that (5.27) is a gauge-invariant, fully conserved (2,1) current is contradicted by the paper's own variation formulas. With the variations stated in (5.26), δJ^(h)=δJ^(b)=−δJ^(a)=X, the combination in (5.27) transforms as δ(J^(h)+J^(b)−2J^(a))=X+X−2(−X)=4X, which is nonzero for generic α. Consequently the minimal coupling in (5.28) is not invariant, and the gauged action (7.11) plus the anomaly variation (7.13) omit the additional contributions that would come from the non-invariant minimal-coupling term. The printed combination J^(h)+J^(b)+2J^(a) would be invariant under (5.26), but even that is not enough by itself because the gauge variation of J^(h) must also be rederived consistently, as noted in the next major comment.
  2. [5.2, Eqs. (5.16)-(5.25)] Equation (5.26) is not what follows from direct substitution of the transformations (5.23)-(5.25) into the component definitions (5.16)-(5.18). Acting on (5.16) with the h-transformation in (5.25) gives, with the standard antisymmetrization convention used consistently throughout, δJ^(h) = 2∂_ρ∂_[μ α_ν] + η_{ρ[μ}∂_{ν]}∂·α − η_{ρ[μ}□α_ν], i.e. the first term has coefficient 2 rather than the coefficient 1 shown in the X of (5.26). This means that a simple sign change in (5.27) is not sufficient on its own; the normalization of δh in (5.25), or of the first term in the definition of J^(h), must also be corrected. The rederivation should be checked against the known equivalent form (5.32) from reference [28], whose normalization does not appear to be demonstrated in the text.
minor comments (4)
  1. [4.2, after Eq. (4.22)] The sentence 'While J^(a)_[μν] is gauge invariant ... the transformation of J^(a)_[μν] does not vanish' appears to contain a typo: the second J^(a)_[μν] should presumably be J^(a)_(μν), since the antisymmetric part is the gauge-invariant field strength and the symmetric part is the one that varies.
  2. [5.2, Eq. (5.32)] The equivalence between the component expression (5.16) and the compact form (5.32) is asserted without derivation; given the normalization issues raised in the major comments, a short verification of the overall factor and index conventions would prevent ambiguity.
  3. [7, Eq. (7.13)] The passage from the first line of (7.13) to the second line changes the derivative structure on the background field T_m; please display the intermediate partial integrations and state the boundary conditions used, since the anomaly expression depends on this step.
  4. [5.1, text after Eq. (5.5)] The statement that the set of Stueckelberg fields is 'completely fixed' by the degree-of-freedom count is stronger than the argument given: the counting exhibits a sufficient collection, but a claim of necessity would require excluding other decompositions of the massive-minus-massless polarization count into three massless fields.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: Stueckelberg actions, currents and the 't Hooft anomaly are algebraic consequences of the stated free actions; the self-cited graded-calculus formalism is a computational tool, not a fitted input.

full rationale

All load-bearing claims are obtained by direct substitution and variation of the displayed free actions, not by fitting or by invoking the paper's own conclusions as premises. Section 2's degree-of-freedom identities (2.4)-(2.9) are representation-theoretic counts that constrain which massless multiplets can serve as Stueckelberg fields; the subsequent Stueckelberg actions (4.13)-(4.14), (5.10)-(5.11) and (6.4)-(6.5) are derived by inserting the explicitly gauge-invariant redefined tensors (4.12), (5.8) and (6.4) into the Fierz-Pauli, Curtright and (2,2) actions and discarding total derivatives, with no free parameters. The currents (4.19)-(4.25), (5.16)-(5.19), (5.27) and (6.9)-(6.11) are Noether currents of the massless Stueckelberg Lagrangians; the fact that their minimal couplings reproduce the Stueckelberg interaction terms is a consistency check, not a fitted input, since both sides are computed from the same unmodified actions. The 't Hooft anomaly (7.13) is a direct gauge variation of the nonminimal coupling (7.9), again an algebraic consequence. The cited graded-coordinate/Hodge-star formalism [44] is self-cited, but it supplies computational identities (e.g. (7.4)) rather than the paper's central results, and its content is independently published. A separate internal-consistency issue appears in (5.26)-(5.27): with deltaJ(h)=deltaJ(b)=-deltaJ(a)=X, the combination (5.27) has variation 4X, so the printed current is not gauge invariant. This is a sign/correctness defect, not circularity, because the claim does not reduce to any fitted parameter or to an unverified self-citation; it would simply make the advertised current wrong as written.

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

The paper posits no new particles or forces; the tensor global symmetries and currents are derived from known fields and actions, so no invented entities are needed. The main axioms are standard counting formulas, the graded-coordinate tool from prior work, and interpretative assumptions about Goldstone bosons and anomaly detection.

assumptions (5)
  • standard math Degree-of-freedom formulas (2.4)-(2.5) for mixed-symmetry tensors
    Used in Section 2 to fix the Stueckelberg field content; these are textbook results from Young-tableau counting.
  • domain assumption Graded-coordinate formalism with Deligne convention (ref. [44])
    The Berezin integration and generalized Hodge star underpin all Stueckelberg action derivations and current calculations; results depend on its sign conventions.
  • domain assumption Stueckelberg fields can be interpreted as Nambu-Goldstone bosons of spontaneously broken shift symmetries
    Standard in generalized-symmetry literature (e.g., [14]); used in Sections 5.2 and 7.
  • domain assumption The anomaly can be detected by nonminimal couplings of background fields to currents
    Section 7 introduces nonminimal couplings L_e, L_m (7.6)-(7.7) to uncover the 't Hooft anomaly; this is a modeling choice, standard in the p-form case but an assumption in this tensor context.
  • domain assumption Unit mass setting
    Mass is set to 1 in all actions, which is a harmless rescaling in the linearized theory.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Tensor global symmetries and the Stueckelberg mechanism for tensor fields." pith.science (2026). https://pith.science/paper/HSEVZFK5

@misc{pith2026241116928,
  author       = {Pith},
  title        = {Pith review of: Tensor global symmetries and the Stueckelberg mechanism for tensor fields},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HSEVZFK5}},
  note         = {Machine review of arXiv:2411.16928}
}
abstract

We investigate the concept of tensor global symmetries, featuring conserved currents of mixed symmetry and higher spin Nambu-Goldstone bosons. We develop a Stueckelberg mechanism for mixed symmetry tensor fields at the linearized level, focusing on the massive graviton, the massive $(2,1)$ Curtright field and the massive $(2,2)$ field. Counting degrees of freedom, we identify the set of fields that necessarily appear in the gauge invariant Stueckelberg action in each case. These fields transform under shift symmetries and they are a vector and a scalar in the first case, a graviton, a Kalb-Ramond field and a vector in the second case and a Curtright field and a graviton in the third case. The analysis results in gauge invariant and fully conserved currents of mixed symmetry for the corresponding gauge theories, which are linked to their tensor global symmetries and they can be minimally coupled to suitable background fields. Viewing the graviton and the Kalb-Ramond field as Nambu-Goldstone bosons for constant symmetric and antisymmetric shift symmetries, we use a nonminimal coupling to uncover a 't Hooft anomaly in linearized gravity.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

59 extracted references · 21 canonical work pages

  1. [44]

    A unified approach to standard and exotic dualizations through graded geometry

    A. Chatzistavrakidis, G. Karagiannis, and P. Schupp, “A unified approach to standard and exotic dualizations through graded geometry,” Commun. Math. Phys. 378 no. 2, (2020) 1157–1201, arXiv:1908.11663 [hep-th]

    work page Pith review arXiv 2020

  2. [28]

    Generalised symmetries in linear gravity,

    C. Hull, M. L. Hutt, and U. Lindstr¨ om, “Generalised symmetries in linear gravity,” arXiv:2409.00178 [hep-th]

    arXiv

  3. [1]

    The notoph and its possible interactions,

    V. I. Ogievetski ˘ ı and I. V. Polubarinov, “The notoph and its possible interactions,” in Supersymmetries and Quantum Symmetries , J. Wess and E. A. Ivanov, eds., pp. 391–396. Springer Berlin Heidelberg, Berlin, Heidelberg, 1999

    work page 1999

  4. [2]

    Classical direct interstring action,

    M. Kalb and P. Ramond, “Classical direct interstring action,” Phys. Rev. D 9 (1974) 2273–2284

    work page 1974

  5. [3]

    Progress Toward a Theory of Supergravity,

    D. Z. Freedman, P. van Nieuwenhuizen, and S. Ferrara, “Progress Toward a Theory of Supergravity,” Phys. Rev. D 13 (1976) 3214–3218

    work page 1976

  6. [4]

    Supergravity Theory in 11 Dimensions,

    E. Cremmer, B. Julia, and J. Scherk, “Supergravity Theory in 11 Dimensions,” Phys. Lett. B 76 (1978) 409–412

    work page 1978

  7. [5]

    Higher gauge theory,

    J. C. Baez and U. Schreiber, “Higher gauge theory,” arXiv:math/0511710 [math.DG]

    arXiv

  8. [6]

    An Invitation to Higher Gauge Theory,

    J. C. Baez and J. Huerta, “An Invitation to Higher Gauge Theory,” Gen. Rel. Grav. 43 (2011) 2335–2392, arXiv:1003.4485 [hep-th]

    arXiv 2011

Show all 59 references
  1. [7]

    Generalized Global Symmetries,

    D. Gaiotto, A. Kapustin, N. Seiberg, and B. Willett, “Generalized Global Symmetries,” JHEP 02 (2015) 172, arXiv:1412.5148 [hep-th]

    2015 arXiv

  2. [8]

    Comments on One-Form Global Symmetries and Their Gauging in 3d and 4d,

    P.-S. Hsin, H. T. Lam, and N. Seiberg, “Comments on One-Form Global Symmetries and Their Gauging in 3d and 4d,” SciPost Phys. 6 no. 3, (2019) 039, arXiv:1812.04716 [hep-th]

    2019 arXiv

  3. [9]

    Field Theories With a Vector Global Symmetry,

    N. Seiberg, “Field Theories With a Vector Global Symmetry,” SciPost Phys. 8 no. 4, (2020) 050, arXiv:1909.10544 [cond-mat.str-el]

    2020 arXiv

  4. [10]

    Exotic Symmetries, Duality, and Fractons in 2+1-Dimensional Quantum Field Theory,

    N. Seiberg and S.-H. Shao, “Exotic Symmetries, Duality, and Fractons in 2+1-Dimensional Quantum Field Theory,” SciPost Phys. 10 no. 2, (2021) 027, arXiv:2003.10466 [cond-mat.str-el]

    2021 arXiv

  5. [11]

    Quantum Glassiness,

    C. Chamon, “Quantum Glassiness,” Phys. Rev. Lett. 94 no. 4, (2005) 040402, arXiv:cond-mat/0404182

    2005 arXiv

  6. [12]

    Fracton Phases of Matter,

    M. Pretko, X. Chen, and Y. You, “Fracton Phases of Matter,” Int. J. Mod. Phys. A 35 no. 06, (2020) 2030003, arXiv:2001.01722 [cond-mat.str-el]

    2020 arXiv

  7. [13]

    Higher Symmetry and Gapped Phases of Gauge Theories,

    A. Kapustin and R. Thorngren, “Higher Symmetry and Gapped Phases of Gauge Theories,” Prog. Math. 324 (2017) 177–202, arXiv:1309.4721 [hep-th]

    2017 arXiv

  8. [14]

    Higher-form symmetries and spontaneous symmetry breaking,

    E. Lake, “Higher-form symmetries and spontaneous symmetry breaking,” arXiv:1802.07747 [hep-th]

    arXiv

  9. [15]

    Exploring 2-Group Global Symmetries,

    C. C´ ordova, T. T. Dumitrescu, and K. Intriligator, “Exploring 2-Group Global Symmetries,” JHEP 02 (2019) 184, arXiv:1802.04790 [hep-th]. – 27 –

    2019 arXiv

  10. [16]

    ICTP lectures on (non-)invertible generalized symmetries,

    S. Schafer-Nameki, “ICTP lectures on (non-)invertible generalized symmetries,” Phys. Rept. 1063 (2024) 1–55, arXiv:2305.18296 [hep-th]

    2024 arXiv

  11. [17]

    What’s Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries,

    S.-H. Shao, “What’s Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries,” arXiv:2308.00747 [hep-th]

    arXiv

  12. [18]

    Notes on generalized global symmetries in QFT,

    E. Sharpe, “Notes on generalized global symmetries in QFT,” Fortsch. Phys. 63 (2015) 659–682, arXiv:1508.04770 [hep-th]

    2015 arXiv

  13. [19]

    Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond,

    C. Cordova, T. T. Dumitrescu, K. Intriligator, and S.-H. Shao, “Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond,” in Snowmass 2021 . 5, 2022. arXiv:2205.09545 [hep-th]

    2021 arXiv

  14. [20]

    On 2-Group Global Symmetries and their Anomalies,

    F. Benini, C. C´ ordova, and P.-S. Hsin, “On 2-Group Global Symmetries and their Anomalies,” JHEP 03 (2019) 118, arXiv:1803.09336 [hep-th]

    2019 arXiv

  15. [21]

    Generalized global symmetries and dissipative magnetohydrodynamics,

    S. Grozdanov, D. M. Hofman, and N. Iqbal, “Generalized global symmetries and dissipative magnetohydrodynamics,” Phys. Rev. D 95 no. 9, (2017) 096003, arXiv:1610.07392 [hep-th]

    2017 arXiv

  16. [22]

    Generalized global symmetries and holography,

    D. M. Hofman and N. Iqbal, “Generalized global symmetries and holography,” SciPost Phys. 4 no. 1, (2018) 005, arXiv:1707.08577 [hep-th]

    2018 arXiv

  17. [23]

    Topological phases with generalized global symmetries,

    B. Yoshida, “Topological phases with generalized global symmetries,” Phys. Rev. B 93 no. 15, (2016) 155131, arXiv:1508.03468 [cond-mat.str-el]

    2016 arXiv

  18. [24]

    Goldstone modes and photonization for higher form symmetries,

    D. M. Hofman and N. Iqbal, “Goldstone modes and photonization for higher form symmetries,” SciPost Phys. 6 no. 1, (2019) 006, arXiv:1802.09512 [hep-th]

    2019 arXiv

  19. [25]

    A symmetry principle for gauge theories with fractons,

    Y. Hirono, M. You, S. Angus, and G. Y. Cho, “A symmetry principle for gauge theories with fractons,” SciPost Phys. 16 no. 2, (2024) 050, arXiv:2207.00854 [cond-mat.str-el]

    2024 arXiv

  20. [26]

    Gravity as a gapless phase and biform symmetries,

    K. Hinterbichler, D. M. Hofman, A. Joyce, and G. Mathys, “Gravity as a gapless phase and biform symmetries,” JHEP 02 (2023) 151, arXiv:2205.12272 [hep-th]

    2023 arXiv

  21. [27]

    Generalized symmetries of the graviton,

    V. Benedetti, H. Casini, and J. M. Magan, “Generalized symmetries of the graviton,” JHEP 05 (2022) 045, arXiv:2111.12089 [hep-th]

    2022 arXiv

  22. [29]

    Generalized symmetry in dynamical gravity,

    C. Cheung, M. Derda, J.-H. Kim, V. Nevoa, I. Rothstein, and N. Shah, “Generalized symmetry in dynamical gravity,” JHEP 10 (2024) 007, arXiv:2403.01837 [hep-th]

    2024 arXiv

  23. [30]

    Theory of Dynamical Affine and Conformal Symmetries as Gravity Theory,

    A. B. Borisov and V. I. Ogievetsky, “Theory of Dynamical Affine and Conformal Symmetries as Gravity Theory,” Teor. Mat. Fiz. 21 (1974) 329–342

    1974

  24. [31]

    Gauge Theories as Theories of Spontaneous Breakdown,

    E. A. Ivanov and V. I. Ogievetsky, “Gauge Theories as Theories of Spontaneous Breakdown,” Lett. Math. Phys. 1 (1976) 309–313

    1976

  25. [32]

    Gauge Fields, Nonlinear Realizations, Supersymmetry,

    E. A. Ivanov, “Gauge Fields, Nonlinear Realizations, Supersymmetry,” Phys. Part. Nucl. 47 no. 4, (2016) 508–539, arXiv:1604.01379 [hep-th]. – 28 –

    2016 arXiv

  26. [33]

    A note on spin s duality,

    N. Boulanger, S. Cnockaert, and M. Henneaux, “A note on spin s duality,” JHEP 06 (2003) 060, arXiv:hep-th/0306023

    2003 arXiv

  27. [34]

    E(11) and M theory,

    P. C. West, “E(11) and M theory,” Class. Quant. Grav. 18 (2001) 4443–4460, arXiv:hep-th/0104081

    2001 arXiv

  28. [35]

    Duality in gravity and higher spin gauge fields,

    C. M. Hull, “Duality in gravity and higher spin gauge fields,” JHEP 09 (2001) 027, arXiv:hep-th/0107149

    2001 arXiv

  29. [36]

    Duality and higher Buscher rules in p-form gauge theory and linearized gravity,

    A. Chatzistavrakidis, G. Karagiannis, and A. Ranjbar, “Duality and higher Buscher rules in p-form gauge theory and linearized gravity,” Fortsch. Phys. 69 no. 3, (2021) 2000135, arXiv:2012.08220 [hep-th]

    2021 arXiv

  30. [37]

    Duality, Generalized Global Symmetries and Jet Space Isometries,

    A. Chatzistavrakidis, G. Karagiannis, and A. Ranjbar, “Duality, Generalized Global Symmetries and Jet Space Isometries,” Universe 8 no. 1, (2021) 10, arXiv:2112.00441 [hep-th]

    2021 arXiv

  31. [38]

    Generalized Gauge Fields,

    T. Curtright, “Generalized Gauge Fields,” Phys. Lett. B 165 (1985) 304–308

    1985

  32. [39]

    On massive mixed symmetry tensor fields in Minkowski space and (A)dS,

    Y. M. Zinoviev, “On massive mixed symmetry tensor fields in Minkowski space and (A)dS,” arXiv:hep-th/0211233

    arXiv

  33. [40]

    Toward frame-like gauge invariant formulation for massive mixed symmetry bosonic fields,

    Y. M. Zinoviev, “Toward frame-like gauge invariant formulation for massive mixed symmetry bosonic fields,” Nucl. Phys. B 812 (2009) 46–63, arXiv:0809.3287 [hep-th]

    2009 arXiv

  34. [41]

    Massive Dual Spin 2 Revisited,

    T. L. Curtright and H. Alshal, “Massive Dual Spin 2 Revisited,” Nucl. Phys. B 948 (2019) 114777, arXiv:1907.11532 [hep-th]

    2019 arXiv

  35. [42]

    Interacting field of spin 2 and the einstein equations,

    V. Ogievetsky and I. Polubarinov, “Interacting field of spin 2 and the einstein equations,” Annals of Physics 35 no. 2, (1965) 167–208. https://www.sciencedirect.com/science/article/pii/0003491665900771

    1965

  36. [43]

    Effective field theory for massive gravitons and gravity in theory space,

    N. Arkani-Hamed, H. Georgi, and M. D. Schwartz, “Effective field theory for massive gravitons and gravity in theory space,” Annals Phys. 305 (2003) 96–118, arXiv:hep-th/0210184

    2003 arXiv

  37. [45]

    Tensor gauge fields in arbitrary representations of GL(D,R): Duality and Poincare lemma,

    X. Bekaert and N. Boulanger, “Tensor gauge fields in arbitrary representations of GL(D,R): Duality and Poincare lemma,” Commun. Math. Phys. 245 (2004) 27–67, arXiv:hep-th/0208058

    2004 arXiv

  38. [46]

    Tensor gauge fields in arbitrary representations of GL(D,R). II. Quadratic actions,

    X. Bekaert and N. Boulanger, “Tensor gauge fields in arbitrary representations of GL(D,R). II. Quadratic actions,” Commun. Math. Phys. 271 (2007) 723–773, arXiv:hep-th/0606198

    2007 arXiv

  39. [47]

    Exotic tensor gauge theory and duality,

    P. de Medeiros and C. Hull, “Exotic tensor gauge theory and duality,” Commun. Math. Phys. 235 (2003) 255–273, arXiv:hep-th/0208155

    2003 arXiv

  40. [48]

    Geometric second order field equations for general tensor gauge fields,

    P. de Medeiros and C. Hull, “Geometric second order field equations for general tensor gauge fields,” JHEP 05 (2003) 019, arXiv:hep-th/0303036. – 29 –

    2003 arXiv

  41. [49]

    Gauge fields and infinite chains of dualities,

    N. Boulanger, P. Sundell, and P. West, “Gauge fields and infinite chains of dualities,” JHEP 09 (2015) 192, arXiv:1502.07909 [hep-th]

    2015 arXiv

  42. [50]

    Massive and massless Yang-Mills and gravitational fields,

    H. van Dam and M. J. G. Veltman, “Massive and massless Yang-Mills and gravitational fields,” Nucl. Phys. B 22 (1970) 397–411

    1970

  43. [51]

    Linearized gravitation theory and the graviton mass,

    V. I. Zakharov, “Linearized gravitation theory and the graviton mass,” JETP Lett. 12 (1970) 312

    1970

  44. [52]

    To the problem of nonvanishing gravitation mass,

    A. I. Vainshtein, “To the problem of nonvanishing gravitation mass,” Phys. Lett. B 39 (1972) 393–394

    1972

  45. [53]

    Covariant theory of asymptotic symmetries, conservation laws and central charges,

    G. Barnich and F. Brandt, “Covariant theory of asymptotic symmetries, conservation laws and central charges,” Nucl. Phys. B 633 (2002) 3–82, arXiv:hep-th/0111246

    2002 arXiv

  46. [54]

    Weinberg, The Quantum Theory of Fields , vol

    S. Weinberg, The Quantum Theory of Fields , vol. 2. Cambridge University Press, 1996

    1996

  47. [55]

    The Riemann-Lovelock Curvature Tensor,

    D. Kastor, “The Riemann-Lovelock Curvature Tensor,” Class. Quant. Grav. 29 (2012) 155007, arXiv:1202.5287 [hep-th]

    2012 arXiv

  48. [56]

    Unfolding E11,

    N. Boulanger, P. P. Cook, J. A. O’Connor, and P. West, “Unfolding E11,” arXiv:2410.21206 [hep-th]

    arXiv

  49. [57]

    Relation between standard and exotic duals of differential forms,

    A. Chatzistavrakidis and G. Karagiannis, “Relation between standard and exotic duals of differential forms,” Phys. Rev. D 100 no. 12, (2019) 121902, arXiv:1911.00419 [hep-th]

    2019 arXiv

  50. [58]

    Gravitational higher-form symmetries and the origin of hidden symmetries in Kaluza-Klein compactifications,

    C. G´ omez-Fayr´ en, T. Ort ´ ın, and M. Zatti, “Gravitational higher-form symmetries and the origin of hidden symmetries in Kaluza-Klein compactifications,” arXiv:2405.16706 [hep-th]

    arXiv

  51. [59]

    Note on non-Abelian two-form gauge fields,

    P.-M. Ho and Y. Matsuo, “Note on non-Abelian two-form gauge fields,” JHEP 09 (2012) 075, arXiv:1206.5643 [hep-th]. – 30 –

    2012 arXiv

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.