Geometric Formulation for Partially Massless Fields

E.D. Skvortsov; M.A. Vasiliev

REVIEW

Geometric Formulation for Partially Massless Fields

E.D. Skvortsov, M.A. Vasiliev

High Energy Physics - Theory · Submitted 15 Jan 2006 · 37 references

Pith's verdict: A clean geometric repackaging of partially massless fields as non-rectangular two-row connections — the construction is general, the proof that it propagates the right spectrum is not yet in this paper.

T0 · AI review

How this review was made: An AI referee (selfhosted/deepseek-v4.1-flash) read the paper on October 29, 2026 and answered a fixed list of questions about it. T0 is the starting level every paper gets. The levels describe how deeply Pith has checked the paper, never the authors.

T0 AI review An AI read the paper and answered a fixed list of questions.
T1 Audit Automatic checks that the references and files the paper relies on exist and match.
T2 Compute The paper's code or calculations re-run with the same results.
T3 Formal statement The claims written out in a formal math language a computer can read.
T4 Proof Those claims proved, and the proof checked by computer.

How Pith checks papers →

· 2 major objections · 8 minor · Ask about this paper · The compiled record · Read the full review →

Challenge this review Comment (0) Read on arXiv ↗

Cite ▾

arXiv IDhep-th/0601095 (version 2)

Pith ID7CHVEHX6, Pith's permanent record of this paper and its review

CitationE.D. Skvortsov, M.A. Vasiliev. "Geometric Formulation for Partially Massless Fields." arXiv:hep-th/0601095 (2006). https://pith.science/paper/7CHVEHX6

Cite this reviewBibTeX for Pith's review of this paper

Claim paper

Why Pith says this

Highlight any text to comment on it.

Editor's note

read the letter

Worth your time if you work on higher-spin or PM fields, but read it as a construction paper, not a completeness paper. The core idea is simple and, once stated, obviously right: massless spin-s is a one-form in the rectangular tableau (s-1, s-1), and partially massless spin-s depth-t is the same thing with the second row shortened to t. Gauge invariance then costs nothing — R = D0 W and D0^2 = 0 do all the work — and the actions are curvature bilinears. That is a real organizing result, and it explains why PM fields kept appearing in Stueckelberg formulations: they were the non-rectangular modules all along. The selection-rule remark in the Discussion (HS algebras must not contain these modules if the AdS theory is to be unitary) is the kind of consequence that makes the identification worth having. The spin-2 and spin-3 examples are worked honestly against Deser-Waldron, including the awkward t=0 case where the action can't be written as a wedge of curvatures and has to be built from the Weyl-like tensor C^{a(s),b} directly (4.23). That is a real structural point, not a fudge, and they say so. The coefficient conditions (4.18) are solved explicitly in (4.19) for general s and t, and the flat-limit argument in Section 4.3 is a boundary condition, not circular fitting — gauge invariance is checked independently of it. Where I'd push back on the stress-test: the general-s action does exist and is gauge invariant for all s, t. What is deferred to [34] is the field-content analysis — the Stueckelberg/auxiliary/dynamical split, the generalized Weyl tensor, and hence the demonstration that no extra degrees of freedom propagate at λ ≠ 0. That is a narrower gap than 'the general claim rests on an unpublished companion', but it is the gap that matters, and the abstract's 'is given' runs ahead of it. The t=1 case is the thinnest: (4.13) is explicitly not applicable, and (4.22) is fixed only by killing the flat-limit divergence — necessary, not shown sufficient at general s. The authors flag the deferral in Section 4.1, so nothing is hidden. Send it out. It will be cited as the reference for the frame-like PM formulation regardless of how [34] lands.

Referee report

Significance

If correct, the result unifies massless (rectangular tableau) and partially massless (non-rectangular tableau) fields under a single geometric scheme, and gives explicit coefficient formulas that can be checked. The paper earns credit for concrete, checkable content: the coefficient formula (4.19) does satisfy the two conditions (4.18), and (4.22) is the m=0 specialization of (4.19); the s=3, t=1 action coefficient ratio a2/a1 = (d-3)/2 in (5.41) agrees with the ratio implied by (4.19); the spin-2 example reproduces the Deser-Waldron gauge transformation (2.13); and the spin-3 example reproduces the Deser-Waldron constraints (5.30)-(5.38). The selection-rule application in the Discussion is a useful, falsifiable consequence if the general-s construction holds.

Major objections (2)

[Section 4.1 and Section 4.3] The general-s, general-t field-content analysis is deferred to reference [34], which is listed as 'in preparation'. Specifically, the classification of fields into Stueckelberg, auxiliary, and dynamical (the paragraph beginning 'By dynamical fields we mean...'), the definitions (4.6)-(4.8), and the identification of the generalized Weyl tensor with the traceless part of R^{a(s-1),b(t)} are all attributed to [34]. Because [34] is unpublished, the paper's claim that the construction describes partially massless fields — rather than merely a family of gauge-invariant curvature bilinears — is independently supported only by the two worked examples (s=2, t=0 in Section 5.1 and s=3, t=1 in Section 5.2). The abstract's unqualified 'is given' should either be scoped accordingly or the general-s analysis should be included here.
[Section 4.2, Eq. (4.21)-(4.22)] For t=1 the extra-field decoupling condition (4.13) is explicitly stated to be 'not applicable', and the coefficient b^{s,1}_{k,0} is fixed solely by requiring the term that diverges in the flat limit λ→0 to vanish. That is a necessary condition for a sensible flat limit, but the paper does not argue that it is sufficient to eliminate extra degrees of freedom at general s for λ≠0. The s=3, t=1 example (Section 5.2) checks the field content explicitly, but no general-s t=1 case is checked, and the reduction of (4.45) to the sum of massless variations is asserted rather than shown term by term. The paper should either supply the sufficiency argument or state clearly that the t=1 general-s spectrum is established only in [34].

Minor objections (8)

[Eq. (4.8)] The coefficients α and β in the definition of φ^{a(t)} are left unspecified, so the definition is incomplete as written.
[Eq. (C.6)] The symbol u in the factor '(d+u+m-2)' is undefined; it appears to be a typo for k or t.
[Section 4.3, Eq. (4.45)] The statement that the remaining variation reduces in the flat limit to that of the sum of massless actions for spins 2 to s is asserted rather than demonstrated; a term-by-term check would strengthen the argument.
[Section 5.1, Eq. (5.16)-(5.19)] The fixing α=a/2, β=a/2, γ=a from the flat limit is stated without derivation, and the equivalence of (5.18) to (4.23) at s=2 should be shown explicitly.
[Section 4.2, Eq. (4.23)] The t=0 action is not of the curvature-bilinear form (4.10), as the paper acknowledges; the abstract's uniform claim 'in terms of gauge connections and linearized curvatures' should note this exception.
[Discussion] The selection-rule claim that a unitary HS theory in AdS_d must be free of PM modules assumes that the HS algebra's module content determines the spectrum; the paper itself notes that dS admits unitary PM fields, so the rule is AdS-specific and should be stated as such.
[Section 1 and Section 6] The paper restricts to P-even actions and integer spins; the fermionic extension is asserted but not demonstrated, and this scope restriction should be stated explicitly.
[Reference [34]] The citation is listed as 'in preparation'; it should be updated, or the results deferred to it should be flagged in the abstract.

How Pith checks papers → · Full audit of this paper →

The paper

The paper claims

Free partially massless fields of any spin and depth in (anti-)de Sitter space can be written as one-form gauge connections carrying a two-row Young tableau, with the first row giving the spin and the second the depth.

The reading

Massless higher-spin fields in (anti-)de Sitter space have a tidy geometric description: a one-form gauge connection whose tangent indices fill a rectangular two-row Young tableau, with a curvature that is automatically gauge invariant. This paper asks whether the partially massless fields — the special tuned-mass cases where a gauge symmetry appears with fewer parameters but more derivatives — fit the same scheme. The authors argue that they do, provided the tableau is allowed to be non-rectangular: the first row has length $s-1$ (spin minus one) and the second row has length $t$ (the depth of partial masslessness), and the massless case is recovered when $t=s-1$. If this holds, partial masslessness stops being a list of separately tuned models and becomes a geometric label on a representation, which in turn constrains which higher-spin algebras can be physically acceptable.

What carries the argument

The load-bearing object is the two-row traceless Young tableau connection: a 1-form $W^{A(s-1),B(t)}$ symmetric within each group of indices, traceless, and vanishing on symmetrization over any $s$ indices. Its curvature $R=D_0 W$ is gauge invariant for free because the $(A)dS_d$ background is described by a flat connection, so the whole gauge structure is inherited rather than constructed. Two conditions do the real work: the extra-field decoupling condition, which demands that variations with respect to connections contracted with fewer than the maximal number of compensators vanish identically, and flat-limit consistency, which requires the action to fall apart into a sum of ordinary massless actions for spins $t+1$ to $s$ as the cosmological constant goes to zero. Together these fix the coefficients $b^{s,t}_{k,m}$ up to one overall normalisation, and the resulting curvature components that survive the constraints are identified as generalized Weyl tensors with tableau shape $(s, t+1)$.

Extended reading notes

Core claim

The central claim is that a free symmetric partially massless field of spin $s$ and depth $t$ in $(A)dS_d$ is described by a 1-form connection $W^{A(s-1),B(t)}$ taking values in the irreducible $o(d-1,2)$ (or $o(d,1)$) module labelled by the two-row traceless Young tableau of row lengths $(s-1,t)$, with gauge transformation $δW = D_0 ξ$ and field strength $R = D_0 W$. Because the background connection is flat, $D_0^2=0$, so the curvature is gauge invariant and obeys a Bianchi identity without any further work. Gauge-invariant actions are then built as bilinears of these curvatures contracted with the compensator and vielbein, and the free coefficients are fixed by requiring that fields carrying too few compensators drop out (an extra-field decoupling condition) and that the flat limit reproduces the known decomposition into massless fields of spins $t+1$ through $s$. The paper checks that the resulting dynamical field transforms with $s-t$ derivatives of a rank-$t$ traceless parameter, matching the gauge laws found by Deser and Waldron and by Zinoviev, and works the scheme through explicitly for $s=2,t=0$ and $s=3,t=1$.

Load-bearing premise

The construction assumes that the extra-field decoupling condition plus flat-limit consistency uniquely fixes the coefficients so that the resulting higher-derivative theory describes exactly the partially massless spectrum with no extra degrees of freedom, for every spin and depth — a claim the paper verifies only for $s=2,t=0$ and $s=3,t=1$, deferring the general classification of dynamical, auxiliary and pure-gauge fields to a companion paper still in preparation.

Editorial extensions

If this is right

Massless and partially massless fields become two cases of one construction, distinguished only by whether the second row of the Young tableau is maximal or shorter.
A higher-spin algebra can be screened for physical acceptability by checking whether its decomposition into $o(d-1,2)$ modules contains the non-rectangular tableaux that would signal non-unitary partially massless gauge fields.
The scheme reproduces, rather than postulates, the Deser–Waldron and Zinoviev gauge transformations with $s-t$ derivatives acting on a rank-$t$ traceless parameter.
The $t=0$ case is genuinely different: no bilinear of two 2-form curvatures can be written, so the action must be built from the generalized Weyl tensor itself, which recovers the known conformal spin-2 and Maxwell cases.

Reading between the lines

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

If the tableau label really is the organising principle, then the classification of which tuned masses admit gauge symmetry should follow from which tableaux appear in the tensor product of the higher-spin algebra with itself — a purely algebraic question rather than a case-by-case tuning of masses.
The same bookkeeping suggests a natural guess for mixed-symmetry partially massless fields: a $p$-form connection whose tableau has at most $p$ cells in its shortest column, which the authors themselves flag as a conjecture left for later work.
The $t=0$ exception is worth watching, since it means the 'curvature bilinear' template is not universal; any extension to fermions or to mixed symmetry will have to say which cases admit a 2-form action and which do not.
Because the general-$s$ field content is asserted rather than derived here, the practical test of the programme is whether the promised companion computation reproduces the correct polarization count for, say, $s=4$, $t=2$ without leftover modes.

Original abstract

The manifestly gauge invariant formulation for free symmetric partially massless fields in $(A)dS_d$ is given in terms of gauge connections and linearized curvatures that take values in the irreducible representations of $(o(d-1,2)) o(d,1)$ described by two-row Young tableaux, in which the lengths of the first and second row are, respectively, associated with spin and depth of partial masslessness.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 1,740 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.19 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.06 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

The manifestly gauge invariant formulation for free symmetric partially massless fields in $(A)dS_d$ is given in terms of gauge connections and linearized curvatures that take values in the irreducible representations of $(o(d-1,2)) o(d,1)$ described by two-row Young tableaux, in which the lengths of the first and second row are, respectively, associated with spin and depth of partial masslessness.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	The manifestly gauge invariant formulation for free symmetric partially massless fields in $(A)dS_d$ is given in terms of gauge connections and linearized curvatures that take values in the irreducible representations of $(o(d-1,2)) o(d,1)$ described by two-row Young tableaux, in which the lengths of the first and second row are, respectively, associated with spin and depth of partial masslessness.	contribution 0.95	0.80	0.81	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.91 · evidence from proof or derivation 0.99.

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

References

Works cited (37)

[34]

E. D. Skvortsov, M. A. Vasiliev, in preparation

View on Pith
[1]

S. Deser and R. I. Nepomechie, Phys. Lett. B 132 (1983) 321; Annals Phys. 154 (1984) 396

View on Pith 1983
[2]

A. Higuchi, YTP-85-22; Nucl. Phys. B 282, 397 (1987); J. Math. Phys. 28, 1553 (1987) [Erratum-ibid. 43, 6385 (2002)]; Class. Quant. Grav. 6, 397 (1989); Nucl. Phys. B 325, 745 (1989)

View on Pith 1987
[3]

I. Bengtsson, J. Math. Phys. 36, 5805 (1995) [arXiv:gr-qc/9411057]

View on Pith Pith review arXiv 1995
[4]

S. Deser and A. Waldron, Phys. Rev. Lett. 87, 031601 (2001) [arXiv:hep-th/0102166]; Nucl. Phys. B 607 (2001) 577 [arXiv:hep-th/0103198]; Phys. Lett. B 508, 347 (2001) [arXiv:hep-th/0103255]; Phys. Lett. B 513, 137 (2001) [arXiv:hep-th/0105181]; Nucl. Phys. B 662 (2003) 379 [arXiv:hep-th/0301068]; “Conformal invariance of partia lly massless higher spins”,...

View on Pith Pith review arXiv 2001
[5]

Y. M. Zinoviev, “On massive high spin particles in (A)dS” , arXiv:hep-th/0108192

View on Pith Pith review arXiv
[6]

I. L. Buchbinder, D. M. Gitman and V. D. Pershin, Phys. Let t. B 492, 161 (2000) [arXiv:hep-th/0006144]

View on Pith Pith review arXiv 2000
[7]

K. Hallowell and A. Waldron, Nucl. Phys. B 724, 453 (2005) [arXiv:hep-th/0505255]

View on Pith Pith review arXiv 2005
[8]

L. Dolan, C. R. Nappi and E. Witten, JHEP 0110, 016 (2001) [arXiv:hep-th/0109096]

View on Pith Pith review arXiv 2001
[9]

N. T. Evans, J. Math. Phys. 8, 170 (1967)

View on Pith 1967
[10]

R.R. Metsaev, Phys. Lett. B 354 (1995) 78; “Arbitrary spin massless bosonic ﬁelds in d-dimensional anti-de Sitter space,” arXiv:hep-t h/9810231

View on Pith 1995
[11]

E. Angelopoulos and M. Laoues, Rev. Math. Phys. 10, 271 (1998) [arXiv:hep-th/9806100]

View on Pith Pith review arXiv 1998
[12]

L. Brink, R. R. Metsaev and M. A. Vasiliev, Nucl. Phys. B 586, 183 (2000) [arXiv:hep-th/0005136]

View on Pith Pith review arXiv 2000
[13]

S. Ferrara and C. Fronsdal, “Conformal ﬁelds in higher d imensions,” arXiv:hep-th/0006009. 40

View on Pith Pith review arXiv
[14]

M. A. Vasiliev, JHEP 0412, 046 (2004) [arXiv:hep-th/0404124]

View on Pith Pith review arXiv 2004
[15]

F. A. Dolan, “Character formulae and partition functio ns in higher dimensional conformal ﬁeld theory,” arXiv:hep-th/0508031

View on Pith Pith review arXiv
[16]

M. A. Vasiliev, Yad. Fiz. 32, 855 (1980)

View on Pith 1980
[17]

M. A. Vasiliev, Fortsch. Phys. 35, 741 (1987) [Yad. Fiz. 45, 1784 (1987)]

View on Pith 1987
[18]

V. E. Lopatin and M. A. Vasiliev, Mod. Phys. Lett. A 3, 257 (1988)

View on Pith 1988
[19]

M. A. Vasiliev, Nucl. Phys. B 616 (2001) 106 [Erratum-ibid. B 652 (2003) 407] [arXiv:hep-th/0106200]

View on Pith Pith review arXiv 2001
[20]

K. B. Alkalaev, O. V. Shaynkman and M. A. Vasiliev, Nucl. Phys. B 692 (2004) 363 [arXiv:hep-th/0311164]

View on Pith Pith review arXiv 2004
[21]

Dirac, P. A. M., Royal Society of London Proceedings Ser ies A, 155, 447, 1936

View on Pith 1936
[22]

M. Fierz and W. Pauli, Proc. Roy. Soc. Lond. A 173 (1939) 211

View on Pith 1939
[23]

L. P. S. Singh and C. R. Hagen, Phys. Rev. D 9 (1974) 898

View on Pith 1974
[24]

M. Bianchi and F. Riccioni, “Massive higher spins and ho lography,” arXiv:hep-th/0601071

View on Pith Pith review arXiv
[25]

I. L. Buchbinder and V. A. Krykhtin, Nucl. Phys. B 727, 537 (2005) [arXiv:hep-th/0505092]

View on Pith Pith review arXiv 2005
[26]

I. L. Buchbinder and V. A. Krykhtin, “BRST approach to hi gher spin ﬁeld theories,” arXiv:hep-th/0511276

View on Pith Pith review arXiv
[27]

C. Fronsdal, Phys. Rev. D 18 (1978) 3624

View on Pith 1978
[28]

I. L. Buchbinder, V. A. Krykhtin and A. Pashnev, Nucl. Ph ys. B 711, 367 (2005) [arXiv:hep-th/0410215]

View on Pith Pith review arXiv 2005
[29]

D. Francia and A. Sagnotti, Phys. Lett. B 543, 303 (2002) [arXiv:hep-th/0207002]; Class. Quant. Grav. 20, S473 (2003) [arXiv:hep-th/0212185]; Phys. Lett. B 624, 93 (2005) [arXiv:hep-th/0507144]

View on Pith Pith review arXiv 2002
[30]

S. W. MacDowell and F. Mansouri, Phys. Rev. Lett. 38, 739 (1977) [Erratum- ibid. 38, 1376 (1977)]. 41

View on Pith 1977
[31]

X. Bekaert, S. Cnockaert, C. Iazeolla and M. A. Vasiliev , “Nonlinear higher spin theories in various dimensions”, arXiv:hep-th/05031 28

View on Pith
[32]

K. S. Stelle and P. C. West, Phys. Rev. D 21 (1980) 1466

View on Pith 1980
[33]

M. A. Vasiliev, ‘Higher spin gauge theories: Star-prod uct and AdS space,” arXiv:hep-th/9910096; Comptes Rendus Physique 5, 1101 (2004) [arXiv:hep-th/0409260]; E. Sezgin and P. Sundell, Nucl. Phys. B 644, 303 (2002) [Erratum-ibid. B 660, 403 (2003)] [arXiv:hep-th/0205131]; D. Sorokin, AIP Conf. Proc. 767, 172 (2005) [arXiv:hep-th/0405069]; N. Bouatta, G. ...

View on Pith Pith review arXiv 2004
[35]

K. B. Alkalaev, O. V. Shaynkman and M. A. Vasiliev, JHEP 0508, 069 (2005) [arXiv:hep-th/0501108]

View on Pith Pith review arXiv 2005
[36]

T. Curtright and P. G. O. Freund, Nucl. Phys. B 172, 413 (1980); T. Curtright, Phys. Lett. B 165, 304 (1985); C. S. Aulakh, I. G. Koh and S. Ouvry, Phys. Lett. B 173, 284 (1986); J. M. F. Labastida and T. R. Morris, Phys. Lett. B 180, 101 (1986). J. M. F. Labastida, Phys. Rev. Lett. 58, 531 (1987); Nucl. Phys. B 322, 185 (1989); M. Dubois-Violette and M. ...

View on Pith arXiv 1980
[37]

Y. M. Zinoviev, “On massive mixed symmetry tensor ﬁelds in Minkowski space and (A)dS,” arXiv:hep-th/0211233; “First order formalism for mixed symmetry tensor ﬁelds,” arXiv:hep-th/0304067; “First order formal ism for massive mixed symmetry tensor ﬁelds in Minkowski and (A)dS spaces,” arXiv :hep-th/0306292. 43

View on Pith Pith review arXiv

Forward citations

Cited by 23 Pith papers

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

A Partially Massless Superconductor
hep-th 2025-07 conditional novelty 8.0 of 10

A covariant Higgs mechanism turns the partially massless graviton into a fully massive spin-2 field by condensing a fractonic matter field with dipole symmetry.
On matter-free Higher Spin Gravities in 3d: (partially)-massless fields and general structure
hep-th 2020-05 conditional novelty 7.0 of 10

All matter-free 3d higher spin gravities with (partially)-massless or conformal fields, under stated assumptions, take the Chern-Simons form, and a new partially-massless class is built from endomorphism algebras of s...
Bosonic conformal higher--spin fields of any symmetry
hep-th 2009-09 conditional novelty 7.0 of 10

A complete classification and explicit free Lagrangians for bosonic conformal higher-spin fields of arbitrary symmetry type in any dimension, derived via a correspondence with supersymmetric matrix mechanics.
BRST-BV approach to fields in Poincare patch of AdS
hep-th 2026-07 conditional novelty 6.5 of 10

A universal BRST-BV Lagrangian for free AdS fields is obtained by solving algebraic defining equations for spin operators, with explicit solutions for totally symmetric integer-spin and continuous-spin fields.
New Conformal Higher Spin Gravities in $3d$
hep-th 2019-09 conditional novelty 6.0 of 10

Taking the Chern-Simons action for the matrix algebra End(V) of any irreducible so(3,2) representation V yields a 3d conformal higher spin gravity with finitely many fields, whose spectrum is read off from the so(3,2)...

Show 18 more citing papers

Shift Symmetries in (Anti) de Sitter Space
hep-th 2018-12 conditional novelty 6.0 of 10

Free (anti) de Sitter fields at a discrete ladder of masses carry polynomial shift symmetries inherited from partially massless fields, and the second rung of that ladder admits a new interacting scalar theory general...
Partially Massless Higher-Spin Theory
hep-th 2016-10 conditional novelty 6.0 of 10

Gauging an enlarged higher-spin algebra yields a theory with an infinite tower of partially massless fields whose four non-gauge masses match the predictions of a dual free fourth-order scalar CFT.
Partially-massless higher-spin algebras and their finite-dimensional truncations
hep-th 2015-08 conditional novelty 6.0 of 10

Partially-massless higher-spin algebras truncate to finite-dimensional algebras identified with the symmetry algebras of one-row Young-diagram representations of so(d+2) when the continuous parameter equals d/2 plus a...
On the uniqueness of higher-spin symmetries in AdS and CFT
hep-th 2013-05 conditional novelty 6.0 of 10

Solving the Jacobi identity for all classified higher-spin bracket products shows the Eastwood-Vasiliev algebra is the unique consistent higher-spin algebra in d=4 and d>6, with a known one-parameter family in 5d.
Higher order singletons, partially massless fields and their boundary values in the ambient approach
hep-th 2013-05 conditional novelty 6.0 of 10

Two order-ℓ singletons tensor-decompose into partially conserved currents of all ranks and odd depths up to 2ℓ-1, supporting a conjectured duality between the O(N) Lifshitz-point model and a partially massless higher-...
Evidence for and Obstructions to Non-Linear Partially Massless Gravity
hep-th 2013-01 accept novelty 6.0 of 10

No non-linear partially massless graviton exists within standard ghost-free massive gravity with an Einstein-Hilbert kinetic term: the required scalar gauge symmetry survives to cubic order in four dimensions but fail...
Non-abelian cubic vertices for higher-spin fields in anti-de Sitter space
hep-th 2012-11 conditional novelty 6.0 of 10

Every non-abelian cubic coupling of totally symmetric higher-spin fields in anti-de Sitter space is counted by the tensor-product multiplicity of two-row Young diagrams, matching the flat-space classification.
Generating functions of (partially-)massless higher-spin cubic interactions
hep-th 2012-11 conditional novelty 6.0 of 10

The authors give closed-form generating functions for all cubic interactions of partially massless higher-spin fields in (anti-)de Sitter space, and show that new couplings appear only when the masses satisfy an integ...
On the cubic interactions of massive and partially-massless higher spins in (A)dS
hep-th 2012-03 accept novelty 6.0 of 10

The traceless-transverse parts of all consistent cubic vertices for massive and partially-massless higher-spin fields in (A)dS are solved as generating functions, with a new condition for partially-massless highest-de...
Higher-spin algebras and cubic interactions for simple mixed-symmetry fields in AdS spacetime
hep-th 2011-07 conditional novelty 6.0 of 10

Cubic interactions of tall-hook mixed-symmetry gauge fields with gravity and themselves in anti-de Sitter space follow from the even Clifford algebra, with all coupling coefficients fixed by consistency.
Frame-Like Action and Unfolded Formulation for Massive Higher-Spin Fields
hep-th 2009-12 conditional novelty 6.0 of 10

The authors derive unfolded equations and a manifestly gauge invariant curvature-based action for symmetric massive bosonic fields of arbitrary spin in any dimension.
Unified BRST description of AdS gauge fields
hep-th 2009-10 accept novelty 6.0 of 10

A single local BRST operator, built from the AdS isometry algebra and its Howe-dual symplectic algebra, describes mixed-symmetry gauge fields on AdS and reduces to known formulations.
Gauge fields in (anti)-de Sitter space and Connections of its symmetry algebra
hep-th 2009-04 conditional novelty 6.0 of 10

Every (partially)-massless gauge field in (anti)-de Sitter space corresponds to a single generalized connection of the (anti)-de Sitter algebra, with the field's Young diagram determining the representation.
Unfolding Mixed-Symmetry Fields in AdS and the BMV Conjecture: I. General Formalism
hep-th 2008-12 conditional novelty 6.0 of 10

The paper classifies the Lorentz-covariant Harish-Chandra modules generated by primary Weyl tensors of arbitrary Young shape and mass in constant-curvature backgrounds, identifying the critical masses at which massles...
On partition function and Weyl anomaly of conformal higher spin fields
hep-th 2013-09 accept novelty 5.0 of 10

The 4D conformal higher-spin partition function factorizes into partially-massless determinants, yielding spin-s Weyl anomaly coefficients whose bosonic a_s matches an independent AdS/CFT result and whose regularized ...
Frame-like gauge invariant formulation for massive high spin particles
hep-th 2008-08 conditional novelty 5.0 of 10

Explicit frame-like Lagrangians and gauge transformations are constructed for massive particles of arbitrary integer and half-integer spin in (A)dS space, with correct massless and partially massless limits.
A Fiber Approach to Harmonic Analysis of Unfolded Higher-Spin Field Equations
hep-th 2008-06 conditional novelty 5.0 of 10

The standard massless particle solutions and the linearized runaway solutions of higher-spin gauge theory combine into a single indecomposable, unitarizable module in Vasiliev's fiber algebra.
Elementary particles with continuous spin
hep-th 2017-08 conditional novelty 3.0 of 10

Continuous-spin particles, massless with an unbounded tower of helicities, now have gauge-invariant free actions on flat and anti-de Sitter space that reduce to Fronsdal's when the spin parameter goes to zero.

How later papers used it

80 later papers cite it

Evidence: some. 61 of the citing papers share no author with it, and 4 of those carry a confident label from Pith's citation classifier.

Pith read 22 of the 167 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

1 later paper by other authors is listed below: 1 built on it.

Builds on it 1 of 7 papers with this label

Generalized to mixed-symmetry cases this paper's results for totally symmetric fields in the framework of unfolding, along with its classification and definition of partially massless fields.

Unfolding Mixed-Symmetry Fields in AdS and the BMV Conjecture: I. General Formalism (2008) · 1.00 · paraphrased: the licence does not allow quoting

How the literature uses it

79 arXiv papers cite this in 166 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 115 sentences without a confident label

Builds on it 7 papers

In this paper we extend the results of [ref] and construct the manifestly $$-covariant description for arbitrary-spin gauge field in $$ in terms of a single connection of the (anti)-de Sitter algebra $𝔤$, which is (de Sitter) or (anti-de Sitter).

Gauge fields in (anti)-de Sitter space and Connections of its symmetry algebra · Field theories in Minkowski and $$, Mixed-Symmetry Fields · 1.00
Our classification and definition of partially massless fields generalizes to the mixed-symmetry cases the results of [ref] for totally symmetric fields in the framework on unfolding.

Unfolding Mixed-Symmetry Fields in AdS and the BMV Conjecture: I. General Formalism · Remarks on metric-like integration · 1.00
The gauge invariant action that describes a unitary theory should satisfy the conditions [equation] which generalize the extra field decoupling condition for massless [ref] and partially massless [ref] fields to the massive case.

Frame-Like Action and Unfolded Formulation for Massive Higher-Spin Fields · Action · 0.97

Compares with it 3 papers

Compared to the approach of [ref] this set provides a non-minimal description of a partially massless field of spin $s$ and depth $t$ that contains additional fields along with constraints that express them algebraically in terms of derivatives of the dynamical fields modulo Stueckelberg degrees of freedom that are gauged away by additional Stueckelberg gauge symmetries.

Frame-Like Action and Unfolded Formulation for Massive Higher-Spin Fields · Massless and partially massless fields · 1.00
The frame-like description is very similar to the partially-massless case [ref] .

On matter-free Higher Spin Gravities in 3d: (partially)-massless fields and general structure · Free fields: metric-like vs. frame-like · 0.87
In this respect, the corresponding conformal fields are analogues of the so-called partially massless fields in $AdS_d$ originally discovered by Deser and Nepomechie in [ref] and investigated further in [ref] .

Bosonic conformal higher--spin fields of any symmetry · Dynamical interpretation · 0.85

Cites it as background 32 papers

The frame-like description of partially-massless fields was developed in [ref] , see also [ref] for the specialization to $4d$ and [ref] for purely massless higher spin fields.[Note that the frame-like description of fields arbitrary mixed-symmetry, both massless and partially-massless, has been worked out, see e.g. [ref] .] The key idea is to consider a (generalized) connection of the (anti-)de Sitter algebra $W^𝕐$, i.e. a one-form that takes values in a finite-dimensional representation $𝕐$ of the algebra that is not necessarily the adjoint one.

Chiral approach to partially-massless fields · Free partially-massless fields, old and new · 0.89
We begin the analysis of possible conformal invariance of $AdS$ gauge fields with the relatively simple, but not so well-known example of totally symmetric partially massless (PM) fields [ref] of maximal depth $t=s$.

Notes on conformal invariance of gauge fields · Maximal-depth partially-massless fields in 4d · 0.90
Lagrangian models for partially massless fields in AdS$_d$ were constructed in [ref] , and in [ref] for the specific case of AdS$_3$. ] with depth $t$ if, in addition to the conditions [ref], the pseudo-mass satisfies [equation] We will refer to $ρ^(±)_(t,n)$ as the depth-$t$ pseudo-mass values.[We note that the $±$ in [ref] coincides the sign of the helicity, since $= ρ^(±)_(t,n)/ |ρ^(±)_(t,n)|=±1$.

Higher-spin Cotton tensors and massive gauge-invariant actions in AdS$_3$ · On-shell massive and partially massless fields · 0.86

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [34]

E. D. Skvortsov, M. A. Vasiliev, in preparation

View on Pith

[2] [1]

S. Deser and R. I. Nepomechie, Phys. Lett. B 132 (1983) 321; Annals Phys. 154 (1984) 396

View on Pith 1983

[3] [2]

A. Higuchi, YTP-85-22; Nucl. Phys. B 282, 397 (1987); J. Math. Phys. 28, 1553 (1987) [Erratum-ibid. 43, 6385 (2002)]; Class. Quant. Grav. 6, 397 (1989); Nucl. Phys. B 325, 745 (1989)

View on Pith 1987

[4] [3]

I. Bengtsson, J. Math. Phys. 36, 5805 (1995) [arXiv:gr-qc/9411057]

View on Pith Pith review arXiv 1995

[5] [4]

S. Deser and A. Waldron, Phys. Rev. Lett. 87, 031601 (2001) [arXiv:hep-th/0102166]; Nucl. Phys. B 607 (2001) 577 [arXiv:hep-th/0103198]; Phys. Lett. B 508, 347 (2001) [arXiv:hep-th/0103255]; Phys. Lett. B 513, 137 (2001) [arXiv:hep-th/0105181]; Nucl. Phys. B 662 (2003) 379 [arXiv:hep-th/0301068]; “Conformal invariance of partia lly massless higher spins”,...

View on Pith Pith review arXiv 2001

[6] [5]

Y. M. Zinoviev, “On massive high spin particles in (A)dS” , arXiv:hep-th/0108192

View on Pith Pith review arXiv

[7] [6]

I. L. Buchbinder, D. M. Gitman and V. D. Pershin, Phys. Let t. B 492, 161 (2000) [arXiv:hep-th/0006144]

View on Pith Pith review arXiv 2000

[8] [7]

K. Hallowell and A. Waldron, Nucl. Phys. B 724, 453 (2005) [arXiv:hep-th/0505255]

View on Pith Pith review arXiv 2005

[9] [8]

L. Dolan, C. R. Nappi and E. Witten, JHEP 0110, 016 (2001) [arXiv:hep-th/0109096]

View on Pith Pith review arXiv 2001

[10] [9]

N. T. Evans, J. Math. Phys. 8, 170 (1967)

View on Pith 1967

[11] [10]

R.R. Metsaev, Phys. Lett. B 354 (1995) 78; “Arbitrary spin massless bosonic ﬁelds in d-dimensional anti-de Sitter space,” arXiv:hep-t h/9810231

View on Pith 1995

[12] [11]

E. Angelopoulos and M. Laoues, Rev. Math. Phys. 10, 271 (1998) [arXiv:hep-th/9806100]

View on Pith Pith review arXiv 1998

[13] [12]

L. Brink, R. R. Metsaev and M. A. Vasiliev, Nucl. Phys. B 586, 183 (2000) [arXiv:hep-th/0005136]

View on Pith Pith review arXiv 2000

[14] [13]

S. Ferrara and C. Fronsdal, “Conformal ﬁelds in higher d imensions,” arXiv:hep-th/0006009. 40

View on Pith Pith review arXiv

[15] [14]

M. A. Vasiliev, JHEP 0412, 046 (2004) [arXiv:hep-th/0404124]

View on Pith Pith review arXiv 2004

[16] [15]

F. A. Dolan, “Character formulae and partition functio ns in higher dimensional conformal ﬁeld theory,” arXiv:hep-th/0508031

View on Pith Pith review arXiv

[17] [16]

M. A. Vasiliev, Yad. Fiz. 32, 855 (1980)

View on Pith 1980

[18] [17]

M. A. Vasiliev, Fortsch. Phys. 35, 741 (1987) [Yad. Fiz. 45, 1784 (1987)]

View on Pith 1987

[19] [18]

V. E. Lopatin and M. A. Vasiliev, Mod. Phys. Lett. A 3, 257 (1988)

View on Pith 1988

[20] [19]

M. A. Vasiliev, Nucl. Phys. B 616 (2001) 106 [Erratum-ibid. B 652 (2003) 407] [arXiv:hep-th/0106200]

View on Pith Pith review arXiv 2001

[21] [20]

K. B. Alkalaev, O. V. Shaynkman and M. A. Vasiliev, Nucl. Phys. B 692 (2004) 363 [arXiv:hep-th/0311164]

View on Pith Pith review arXiv 2004

[22] [21]

Dirac, P. A. M., Royal Society of London Proceedings Ser ies A, 155, 447, 1936

View on Pith 1936

[23] [22]

M. Fierz and W. Pauli, Proc. Roy. Soc. Lond. A 173 (1939) 211

View on Pith 1939

[24] [23]

L. P. S. Singh and C. R. Hagen, Phys. Rev. D 9 (1974) 898

View on Pith 1974

[25] [24]

M. Bianchi and F. Riccioni, “Massive higher spins and ho lography,” arXiv:hep-th/0601071

View on Pith Pith review arXiv

[26] [25]

I. L. Buchbinder and V. A. Krykhtin, Nucl. Phys. B 727, 537 (2005) [arXiv:hep-th/0505092]

View on Pith Pith review arXiv 2005

[27] [26]

I. L. Buchbinder and V. A. Krykhtin, “BRST approach to hi gher spin ﬁeld theories,” arXiv:hep-th/0511276

View on Pith Pith review arXiv

[28] [27]

C. Fronsdal, Phys. Rev. D 18 (1978) 3624

View on Pith 1978

[29] [28]

I. L. Buchbinder, V. A. Krykhtin and A. Pashnev, Nucl. Ph ys. B 711, 367 (2005) [arXiv:hep-th/0410215]

View on Pith Pith review arXiv 2005

[30] [29]

D. Francia and A. Sagnotti, Phys. Lett. B 543, 303 (2002) [arXiv:hep-th/0207002]; Class. Quant. Grav. 20, S473 (2003) [arXiv:hep-th/0212185]; Phys. Lett. B 624, 93 (2005) [arXiv:hep-th/0507144]

View on Pith Pith review arXiv 2002

[31] [30]

S. W. MacDowell and F. Mansouri, Phys. Rev. Lett. 38, 739 (1977) [Erratum- ibid. 38, 1376 (1977)]. 41

View on Pith 1977

[32] [31]

X. Bekaert, S. Cnockaert, C. Iazeolla and M. A. Vasiliev , “Nonlinear higher spin theories in various dimensions”, arXiv:hep-th/05031 28

View on Pith

[33] [32]

K. S. Stelle and P. C. West, Phys. Rev. D 21 (1980) 1466

View on Pith 1980

[34] [33]

M. A. Vasiliev, ‘Higher spin gauge theories: Star-prod uct and AdS space,” arXiv:hep-th/9910096; Comptes Rendus Physique 5, 1101 (2004) [arXiv:hep-th/0409260]; E. Sezgin and P. Sundell, Nucl. Phys. B 644, 303 (2002) [Erratum-ibid. B 660, 403 (2003)] [arXiv:hep-th/0205131]; D. Sorokin, AIP Conf. Proc. 767, 172 (2005) [arXiv:hep-th/0405069]; N. Bouatta, G. ...

View on Pith Pith review arXiv 2004

[35] [35]

K. B. Alkalaev, O. V. Shaynkman and M. A. Vasiliev, JHEP 0508, 069 (2005) [arXiv:hep-th/0501108]

View on Pith Pith review arXiv 2005

[36] [36]

T. Curtright and P. G. O. Freund, Nucl. Phys. B 172, 413 (1980); T. Curtright, Phys. Lett. B 165, 304 (1985); C. S. Aulakh, I. G. Koh and S. Ouvry, Phys. Lett. B 173, 284 (1986); J. M. F. Labastida and T. R. Morris, Phys. Lett. B 180, 101 (1986). J. M. F. Labastida, Phys. Rev. Lett. 58, 531 (1987); Nucl. Phys. B 322, 185 (1989); M. Dubois-Violette and M. ...

View on Pith arXiv 1980

[37] [37]

Y. M. Zinoviev, “On massive mixed symmetry tensor ﬁelds in Minkowski space and (A)dS,” arXiv:hep-th/0211233; “First order formalism for mixed symmetry tensor ﬁelds,” arXiv:hep-th/0304067; “First order formal ism for massive mixed symmetry tensor ﬁelds in Minkowski and (A)dS spaces,” arXiv :hep-th/0306292. 43

View on Pith Pith review arXiv