Constructing the Cubic Interaction Vertex of Higher Spin Gauge Fields

A.C. Petkou; A. Fotopoulos; I.L. Buchbinder; M. Tsulaia

REVIEW

Constructing the Cubic Interaction Vertex of Higher Spin Gauge Fields

I.L. Buchbinder, A. Fotopoulos, A.C. Petkou, M. Tsulaia

High Energy Physics - Theory · Submitted 12 Sep 2006 · 37 references

Pith's verdict: A solid framework paper: the interacting algebra and BRST constraints are real and checkable, but only one of six flat-space equations is solved and nothing is solved on AdS — the title oversells what the body honestly admits.

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arXiv IDhep-th/0609082 (version 2)

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CitationA.C. Petkou, A. Fotopoulos, I.L. Buchbinder, M. Tsulaia. "Constructing the Cubic Interaction Vertex of Higher Spin Gauge Fields." arXiv:hep-th/0609082 (2006). https://pith.science/paper/EABEIKNK

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Editor's note

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What's genuinely new here is the interacting symmetry algebra with triplet-valued indices — Eq. (4.2) in flat space and Eqs. (5.4)-(5.7) on AdS — plus the BRST invariance equations (4.6) and (5.13) that any cubic vertex must satisfy. The AdS algebra is the harder and more valuable piece; the extra D_{μν} commutators are messy and the authors work them out carefully, with a worked example in (5.12) that I could follow. Appendix A is explicit and useful: showing that the diagonal ghost part of a Koh-Ouvry-type vertex is Q̃-exact and removable by field redefinition is a clean, hand-checkable result, and it is the kind of thing people actually reuse. The citation coverage is appropriate for 2006 — Vasiliev, Fradkin-Vasiliev, Metsaev, Francia-Sagnotti, the string-field-theory vertex literature, Koh-Ouvry. Nothing looks padded or missing that should be there. On the stress-test concern: it mostly lands. Only the first of the six flat-space equations is solved, the rest are called 'very similar' and postponed, and no compatibility check between the recursive solution of (4.6a) and (4.6b-f) is performed. The claim that the tower is solvable level by level is asserted, not shown. I'd push back on one part of the concern, though: the solution space is demonstrably nonempty, since the Koh-Ouvry exponential sits in it and the paper verifies it satisfies the constraints. The worry is over-determination, not emptiness. Also note the classifier's 'limitations stated: none found' is wrong — the postponement is stated plainly in Section 4.3 and again in the summary, so this is an acknowledged gap, not a concealed one. One soft spot the stress test missed: using ∑p_i = 0 on AdS (Section 5.2) is justified by 'total derivatives,' which is fine in flat space but needs more care when covariant derivatives don't commute. Minor, but a referee should ask. Who gets value: people working on metric-like higher-spin interactions, and anyone wanting a BRST-based alternative to Vasiliev's frame-like construction. It's a methods paper; the equations are the deliverable, not the vertex. Send it out. Expect the referee to ask for at least the second flat-space equation and an explicit compatibility statement.

Referee report

Major objections (4)

[§4.3, Eqs. (4.6), (4.10)-(4.12)] Only the first of the six equations in (4.6) is solved. The recursive relations (4.12) determine X^2 and X^3 in terms of X^1 subject to (4.11), but no compatibility check against the second through sixth equations is performed, and the text states that the remaining equations 'are very similar' and postpones the analysis. The load-bearing question for the method is whether the tower closes, and a cheap decisive test is available: verify that the Koh-Ouvry exponential (4.25) with coefficients (4.22) and (4.24) satisfies all six equations of (4.6), not merely the first as checked in (4.28)-(4.29). If it fails the others, the claim that the known solution 'emerges as a special case' is wrong; if it passes, the viability of the method is demonstrated at the level the abstract promises.
[§5.2, Eq. (5.13)] The AdS section delivers the deformed algebra and the six constraint equations but no solution, not even the analogue of the flat-space first-equation recursion. The abstract promises construction 'both in flat and in AdS space-times', while §5.2 states only that 'we are content to have a well defined iteration procedure'. In addition, §5.1 asserts that the AdS vertex 'differs from the cubic vertex in flat space-time by terms which are sub-leading as L→∞' without demonstration. Either exhibit the leading-order flat-limit statement explicitly or soften the abstract to match what is delivered.
[§3, p. 9 footnote and Eq. (4.4)] The flat-space vertex requires a length parameter which the paper itself says has 'no obvious candidate'. The expansion (4.4) in powers of l_0 (dimension −2), l_+ and M_+ (dimension −1) is not a controlled derivative expansion without a scale, and the footnote's assertion that each term has length dimension −D after multiplication by an appropriate power of the scale never specifies that scale. State how the expansion is organized (for instance by number of derivatives with the scale held fixed) and whether the flat-space vertex is defined only as a formal series.
[§5.1, Eqs. (5.8)-(5.11)] The deformed AdS algebra is presented 'acting on states' and is claimed to preserve the polynomial form of (3.12)-(3.13), but no Jacobi-identity or nilpotence check is reported. Since the free AdS algebra required compensating terms to restore nilpotence (Eq. 2.22 and the surrounding discussion), a check on a few representative triples, for example [l^{ij}, [l^{kl}, l^{mn,+}]] plus cyclic permutations, would be decisive for the claim that the interacting algebra is consistent and that the projected form is closed.

Minor objections (7)

[Eqs. (2.31), (2.32)] The symbol 'g' appearing in '8 g D − 2 g φ′' and '2/L² g Λ′' is never defined; presumably it denotes the metric trace, but this should be stated.
[§4.1] There is a notation collision between l^{ij}_0 and l^i_0 = l^{ii}_0; the parenthetical '(l^{11}_0, l^{22}_0, l^{33}_0) = (l^1_0, l^2_0, l^3_0)' is easy to misread.
[Eqs. (4.21)-(4.23)] Clarify that l_{k0} and l_{s0} act on the coefficient function multiplying c^{i,+}|−⟩, not on the vacuum |−⟩, on which they vanish; as written the equations appear trivially satisfied.
[§4.3, table (4.12)] The entry for n_2 = 1 gives '−k_1 X^1 − X^3(12) = 0' while the n_3 = 1 entry gives '−k_1 X^1 + X^3(13) = 0'; the relative signs deserve a word of explanation.
[Appendix A] Two field-redefinition schemes, (A.4) and (A.5), are presented; state explicitly which is used in §4.3 (the text says (A.4)) and why the other is mentioned.
[§5.2] Justify that discarding total derivatives via ∑ p_i = 0 is legitimate on AdS when the vertex carries explicit powers of 1/L².
[General] Typographical issues: 'φµ1,µ2,..µ3(x)' in the introduction should read µ_s; 'Langrangian' in §3; 'intersting' in §5.2; 'on has to add' in §6; 'The work of I.L.B was' in the acknowledgments.

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The paper

The paper claims

A systematic recipe for building the three-field interaction vertex of higher-spin gauge fields, in flat space and in anti-de Sitter space.

The reading

Massless higher-spin gauge fields — symmetric tensors of arbitrary rank — have well-understood free Lagrangians, but no one knows how to write down consistent interactions for them in the conventional tensor (Fronsdal) language. This paper proposes a bookkeeping device for the first interacting step, the cubic vertex: take the algebra of operators that generates the free higher-spin gauge symmetry and promote every generator to a matrix carrying indices $i,j=1,2,3$ that label which of the three interacting fields it acts on. Gauge invariance of the cubic action then becomes a single equation, $Q_1|V_1+Q_2|V_2+Q_3|V_3=0$, which expands into an infinite tower of coupled conditions on the coefficients of the vertex. The authors derive those conditions explicitly in flat space and in anti-de Sitter space, solve the first of them recursively, and show that a large part of any solution is pure gauge — removable by field redefinitions — so that the physically meaningful content sits in a BRST cohomology. If the programme closes, it would give, for the first time in this formulation, a controlled order-by-order construction of interacting higher-spin Lagrangians of the kind holography needs.

What carries the argument

The load-bearing device is the index-carrying extension of the free higher-spin constraint algebra, combined with the Becchi-Rouet-Stra-sov-Tyutin (BRST) charge. In the free theory the constraint algebra closes on $l_0$, $l$, $l^+$, $N$ and $M$; the interacting version replaces each generator by a $3$-by-$3$ matrix, so that $[l^{ij}, l^{kl,+}] = -i l^{jl}_0$ and its AdS counterpart with $1/L^2$ corrections encode how a derivative can be moved from one field to another inside the vertex. Because the vertex is taken to be a general polynomial in the oscillators $l^{ij,+}$, $M^{ij,+}$, the momenta $l^{ij}_0$, and the ghost bilinears $c^{i,+}b^{j,+}$, $c^{i,+}b^{j}_0$, the BRST condition becomes a recursion in the oscillator degree $K$ and the total power count $s$. That grading is what makes the otherwise infinite problem solvable level by level, and it is also what makes the field-redefinition ambiguity tractable: the ambiguity is parametrized by a state $|W>$ of ghost number two, and the change it induces is $Q|W>$.

Extended reading notes

Core claim

The central claim is that the free higher-spin symmetry algebra — built from the d'Alembertian $l_0$, the divergence $l$, the symmetrized derivative $l^+$, and the $SO(1,2)$ operators $N$ and $M$ — admits a natural multi-indexed generalization whose generators $l^{ij}$, $l^{ij,+}$, $l^{ij}_0$, $M^{ij}$, $N^{ij}$ carry the labels of the three fields entering a cubic vertex. With this algebra in hand, the requirement that the cubic vertex be annihilated by the sum of the three free BRST charges, $Q_1+Q_2+Q_3$, becomes a concrete, graded set of equations on the coefficients $X^1$ through $X^{10}$ of the vertex's ghost expansion. The authors write these equations down in flat space (their Eq. 4.6) and, with the extra $1/L^2$ terms generated by the AdS commutators, on anti-de Sitter space (Eq. 5.13). They then solve the first equation of the flat system recursively, showing that $X^2$ and $X^3$ are determined by a single unknown matrix $X^1$ subject to one constraint, and they demonstrate that the previously known exponential vertex of Koh and Ouvry appears as a special case. Finally, they show that the part of the vertex built from the diagonal generators is BRST-exact and can be removed by an explicit field redefinition, leaving a shorter vertex.

Load-bearing premise

The construction assumes that the cubic vertex can be taken as an arbitrary polynomial in the oscillator and ghost variables, with no analogue of the string-field-theory overlap conditions, so that BRST invariance alone is the whole story.

Editorial extensions

If this is right

Any cubic vertex for massless higher-spin fields in this formulation can be tested by checking whether it satisfies the tower of equations (4.6) in flat space, or (5.13) in AdS, at each oscillator level.
Because the diagonal-generator part of the vertex is BRST-exact, two vertices that look different may be the same physical interaction written in different field variables, which gives a concrete equivalence criterion for comparing constructions.
In the flat-space case the exponential ansatz of the form $\exp(\Delta_1)$ with the constraint $\tilde Y_i = -\tfrac{1}{2}\epsilon_{ikl}\hat Z^{kl}$ is reproduced as a special case of the general solution, tying the new method to earlier results.
On anti-de Sitter space the interacting vertex necessarily contains positive powers of the AdS radius, so the flat-space vertex is recovered only as the leading term of a $1/L^2$ expansion rather than as a smooth limit.

Reading between the lines

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

If the recursion closes at every level, the resulting vertex would fix the three-point functions of conserved currents in the dual conformal field theory, providing a direct check against known results for spin-one and spin-two currents.
The flat-space construction has no intrinsic length scale, so the vertex is defined only up to an overall dimensionful coupling; tying that coupling to the inverse string tension would connect the construction to the tensionless-string picture the authors mention in passing.
Because the field-redefinition freedom is a BRST cohomology problem, a practical way to compare this vertex with vertices built in the frame-like (Vasiliev) formulation would be to classify both by their cohomology class at fixed oscillator degree.
The AdS algebra closes only up to terms suppressed by $1/L^2$, so one testable structural question is whether requiring the correct flat limit plus the leading curvature correction pins the AdS vertex uniquely.

Original abstract

We propose a method of construction of a cubic interaction in massless Higher Spin gauge theory both in flat and in AdS space-times of arbitrary dimensions. We consider a triplet formulation of the Higher Spin gauge theory and generalize the Higher Spin symmetry algebra of the free model to the corresponding algebra for the case of cubic interaction. The generators of this new algebra carry indexes which label the three Higher Spin fields involved into the cubic interaction. The method is based on the use of oscillator formalism and on the Becchi-Rouet-Stora-Tyutin (BRST) technique. We derive general conditions on the form of cubic interaction vertex and discuss the ambiguities of the vertex which result from field redefinitions. This method can in principle be applied for constructing the Higher Spin interaction vertex at any order. Our results are a first step towards the construction of a Lagrangian for interacting Higher Spin gauge fields that can be holographically studied.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,534 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.27 · states limitation 0.79 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.08 · 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.

We propose a method of construction of a cubic interaction in massless Higher Spin gauge theory both in flat and in AdS space-times of arbitrary dimensions. We consider a triplet formulation of the Higher Spin gauge theory and generalize the Higher Spin symmetry algebra of the free model to the corresponding algebra for the case of cubic interaction. The generators of this new algebra carry indexes which label the three Higher Spin fields involved into the cubic interaction. The method is based on the use of oscillator formalism and on the Becchi-Rouet-Stora-Tyutin (BRST) technique. We derive general conditions on the form of cubic interaction vertex and discuss the ambiguities of the vertex which result from field redefinitions. This method can in principle be applied for constructing the Higher Spin interaction vertex at any order. Our results are a first step towards the construction of a Lagrangian for interacting Higher Spin gauge fields that can be holographically studied.

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	We propose a method of construction of a cubic interaction in massless Higher Spin gauge theory both in flat and in AdS space-times of arbitrary dimensions.	contribution 1.00	0.89	0.38	asserted 0.91
s1	We consider a triplet formulation of the Higher Spin gauge theory and generalize the Higher Spin symmetry algebra of the free model to the corresponding algebra for the case of cubic interaction.	contribution 0.62	0.93	0.09	asserted 1.00
s2	The generators of this new algebra carry indexes which label the three Higher Spin fields involved into the cubic interaction.	contribution 0.66	0.72	0.05	asserted 1.00
s3	The method is based on the use of oscillator formalism and on the Becchi-Rouet-Stora-Tyutin (BRST) technique.	method 1.00	0.62	0.04	asserted 1.00
s4	We derive general conditions on the form of cubic interaction vertex and discuss the ambiguities of the vertex which result from field redefinitions.	result 0.78	0.95	0.16	asserted 1.00
s5	This method can in principle be applied for constructing the Higher Spin interaction vertex at any order.	future work 0.69	0.35	0.12	hedged possibility 0.97
s6	Our results are a first step towards the construction of a Lagrangian for interacting Higher Spin gauge fields that can be holographically studied.	future work 0.67	0.65	0.19	asserted 0.76

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from proof or derivation 1.00.

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A single massless chiral superfield can couple only to half-integer superspin higher spin supermultiplets, and the paper constructs the full tower of conserved supercurrents that generate these cubic interactions.

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Cubic interaction vertices for Maxwell-like higher-spin fields are constructed in flat and (Anti) de Sitter space and shown to be trace-free and simpler than their Fronsdal counterparts.
Off-shell massive N=1 supermultiplets in three dimensions
hep-th 2016-09 conditional novelty 6.0 of 10

Explicit gauge-invariant actions are constructed for off-shell massive higher-spin N=1 supermultiplets in three dimensions, obtained by adding Chern-Simons-like mass terms to massless actions.
4D Higher Spin Gravity with Dynamical Two-Form as a Frobenius--Chern--Simons Gauge Theory
hep-th 2015-05 conditional novelty 6.0 of 10

A Chern-Simons-type action on a nine-dimensional noncommutative manifold yields Vasiliev's extended higher spin gravity equations in a specific two-form background.
Higher-Spin Fermionic Gauge Fields and Their Electromagnetic Coupling
hep-th 2012-06 conditional novelty 6.0 of 10

Using BRST-BV cohomology, the authors show that a massless spin-s fermion (s = n + 1/2) can couple to a photon through only three cubic vertices, with 2n-1, 2n, or 2n+1 derivatives, and that minimal coupling is forbidden.
String Lessons for Higher-Spin Interactions
hep-th 2010-06 conditional novelty 6.0 of 10

A single generating function reproduces every three-point amplitude of the open bosonic string's leading Regge trajectory, and its massless limit organizes all cubic higher-spin couplings under one differential operator.
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.
Geometric Lagrangians for massive higher-spin fields
hep-th 2007-10 conditional novelty 6.0 of 10

Massive higher-spin bosons and fermions can be described by geometric Lagrangians plus a generalized Fierz-Pauli mass term containing all traces of the field, with no auxiliary fields.
On massive spin 2 interactions
hep-th 2006-09 conditional novelty 6.0 of 10

Gauge-invariant linear-order analysis shows massive spin-2 self-interaction exists in any dimension d at least 3 for generic mass, but only in d=4 for the partially massless case, and fixes the structure of matter and...
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The authors solve the recurrence relations that finalize the radial pullback of the main cubic higher spin vertex from flat d+2 space to AdS_{d+1}, trace and divergence corrections included.
Conserved higher spin supercurrents for arbitrary spin massless supermultiplets and higher spin superfield cubic interactions
hep-th 2018-05 conditional novelty 5.0 of 10

A unique real, gauge-invariant, conserved higher-spin supercurrent exists for cubic couplings of a half-integer superspin multiplet to two arbitrary-superspin multiplets, but only when s1 is at least 2Y2.
Light-Front Higher-Spin Theories in Flat Space
hep-th 2016-09 conditional novelty 5.0 of 10

Light-cone quantization admits a complete, parity-violating, non-unitary higher-spin theory in four-dimensional flat space whose four-point amplitude vanishes, and it forces every spin to couple to gravity with equal ...
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hep-th 2012-07 conditional novelty 5.0 of 10

Cubic higher-spin interactions in any constant-curvature background are shown to be in one-to-one correspondence with polynomial solutions of a compact system of linear PDEs.
BRST-BV approach to cubic interaction vertices for massive and massless higher-spin fields
hep-th 2012-05 conditional novelty 5.0 of 10

Explicit BRST-BV generating functions are given for off-shell cubic vertices of massive and massless higher-spin fields, covariantizing earlier light-cone results and restating their spin and derivative restrictions.
Cubic interactions of massless higher spins in (A)dS: metric-like approach
hep-th 2011-10 conditional novelty 5.0 of 10

All parity-invariant cubic interactions of massless higher-spin gauge fields in (A)dS are given in closed form using traceless-transverse constraints and an ambient flat-space embedding.
Higher-Spin Interactions: four-point functions and beyond
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An infinite family of gauge-consistent four-point functions for massless higher-spin fields is built from powers of Yang-Mills four-point amplitudes, at the price of non-local quartic couplings.
On the Tensionless Limit of String theory, Off - Shell Higher Spin Interaction Vertices and BCFW Recursion Relations
hep-th 2010-09 conditional novelty 5.0 of 10

Off-shell cubic and quartic higher-spin vertices are constructed via BRST, and a BCFW consistency test is argued to fail for two candidate couplings, suggesting missing non-local states.
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Working in a frame-like formalism, the author reconstructs explicit cubic Lagrangians and gauge transformations for a massless spin-3 field coupled to spins 2, 1 and 0, and checks that the gauge algebra closes.
On massive spin 2 electromagnetic interactions
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A gauge-invariant construction of electromagnetic interactions for massive spin 2 in (A)dS space yields the charge-mass-cosmological-constant relation e0 = -a0[m^2 - kappa(d-2)](d-3)/(d-2), with smooth massless and fl...
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.
On spin 3 interacting with gravity
hep-th 2008-05 conditional novelty 5.0 of 10

The four-derivative spin-3/spin-2 vertex is recast as Riemann times derivatives of the spin-3 field, and the same structure is shown to restore gauge invariance for massive spin 3 on Ricci-flat backgrounds at linear order.
Higher-Spin Gauge Fields Interacting with Scalars: The Lagrangian Cubic Vertex
hep-th 2007-08 conditional novelty 5.0 of 10

Using a BRST procedure, the authors derive the cubic coupling of a higher-spin triplet to two massive scalars in flat and anti-de Sitter space, giving explicit spin-2 and spin-3 vertices and showing that AdS requires ...
On the Structure of Quartic Vertices for Massless Higher Spin Fields on Minkowski Background
hep-th 2012-03 conditional novelty 4.0 of 10

Quartic vertices exist in closed form for any choice of the cubic vertex function, but the resulting four-point amplitudes fail the Benincasa-Cachazo four-particle consistency test.
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Higher-spin gravity avoids flat-space no-go theorems by making the cosmological constant both an infrared cutoff and a coupling, so minimal spin-two coupling becomes subleading in anti-de Sitter space.
Gauge Invariant Lagrangians for Free and Interacting Higher Spin Fields. A Review of the BRST formulation
hep-th 2008-05 accept novelty 2.0 of 10

The paper reviews how nilpotent BRST charges generate gauge-invariant Lagrangians for higher-spin fields and how cubic interactions are built from BRST-invariant vertices.

How later papers used it

55 later papers cite it

Evidence: some. 31 of the citing papers share no author with it, and 2 of those carry a confident label from Pith's citation classifier.

Pith read 25 of the 86 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. 5 more papers by the same authors are listed: 5 used its method or tool.

Builds on it 1 paper

Extended what was previously considered in the framework of the triplet system in this paper.

Higher-Spin Interactions: four-point functions and beyond (2011) · 0.99 · paraphrased: the licence does not allow quoting

Uses its method or tool 5 of 8 papers with this label · 5 by the same authors

By the same authors

Applied the field redefinition scheme outlined in this paper to eliminate the l_0^i from all three matrix elements and the l^3 dependence from X^1 and X^2.

Higher-Spin Gauge Fields Interacting with Scalars: The Lagrangian Cubic Vertex (2007) (same authors) · 1.00 · paraphrased: the licence does not allow quoting
Followed the covariant BRST formulation of the interacting higher spin fields of this paper.

Current Exchanges for Reducible Higher Spin Multiplets and Gauge Fixing (2009) (same authors) · 0.98 · paraphrased: the licence does not allow quoting
Followed this paper's approach for the construction of off-shell cubic interaction vertices between three bosonic higher spin fields.

Cubic Vertices for N=1 Supersymmetric Massless Higher Spin Fields in Various Dimensions (2021) (same authors) · 1.00 · paraphrased: the licence does not allow quoting
Used the BRST method for interacting higher spin fields, which can be formulated in flat and in AdS spaces.

On the Tensionless Limit of String theory, Off - Shell Higher Spin Interaction Vertices and BCFW Recursion Relations (2010) (same authors) · 0.96 · paraphrased: the licence does not allow quoting
Used a procedure for computing them similar to that for cubic vertices in this paper.

BRST methods for constructing quartic actions for spinning black holes (2026) (same authors) · 0.90 · paraphrased: the licence does not allow quoting

How the literature uses it

55 arXiv papers cite this in 86 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 · 44 sentences without a confident label

Builds on it 1 paper

From this point of view we are going to extend what was previously considered in the framework of the triplet system in [ref] , stressing however the role played by the simpler gauge-fixed system[From now on, with a little abuse of notation, we shall refer to these systems involving transverse and possibly traceless fields as on-shell systems or on-shell gauge-fixed systems or similar circumlocutions.]

Higher-Spin Interactions: four-point functions and beyond · Introduction · 0.99

Uses its method or tool 8 papers

We have applied the general BRST procedure of [ref] to construct the cubic interaction Lagrangian vertex of HS triplets coupled to free massive scalars.

Higher-Spin Gauge Fields Interacting with Scalars: The Lagrangian Cubic Vertex · Summary and Outlook · 0.99
In the present paper we shall follow the covariant BRST formulation of the interacting higher spin fields [ref] (see also [ref] for the earlier work in this direction).

Current Exchanges for Reducible Higher Spin Multiplets and Gauge Fixing · Introduction · 0.98
Below we shall follow the approach of [ref] for the construction of off-shell cubic interaction vertices between three bosonic higher spin fields.

Cubic Vertices for N=1 Supersymmetric Massless Higher Spin Fields in Various Dimensions · Three bosons · 1.00

Cites it as background 27 papers

More details can be found in [ref] , [ref] .

Higher-Spin Gauge Fields Interacting with Scalars: The Lagrangian Cubic Vertex · The BRST approach to the HS cubic vertex · 0.93
The development of the BRST approach for calculating the cubic vertex was initiated by paper [ref] .

General Cubic Interacting Vertex for Massless Integer Higher Spin Fields · Introduction · 0.92
Cubic interactions for reducible higher-spin systems have been investigated using BRST techniques in [ref] , in the so-called triplet formulation [ref] related to the free tensionless limit of string theory and involving additional, unphysical fields.

Cubic interactions of Maxwell-like higher spins · $_ 1,$ · 0.88

Discussion

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