High Energy Physics - Theory · arXiv:1104.4994 v1 · submitted 26 Apr 2011
Massive Higher Spins from BRST and Tractors
The paper says
“We obtain the higher spin tractor equations of motion conjectured by Gover et al. from a BRST approach and use those methods to prove that they describe massive, partially massless and massless higher spins in conformally flat backgrounds.”
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Abstract
We obtain the higher spin tractor equations of motion conjectured by Gover et al. from a BRST approach and use those methods to prove that they describe massive, partially massless and massless higher spins in conformally flat backgrounds. The tractor description makes invariance under local choices of unit system manifest. In this approach, physical systems are described by conformal, rather than (pseudo-)Riemannian geometry. In particular masses become geometric quantities, namely the weights of tractor fields. Massive systems can therefore be handled in a unified and simple manner mimicking the gauge principle usually employed for massless models. From a holographic viewpoint, these models describe both the bulk and boundary theories in terms of conformal geometry. This is an important advance, because tying the boundary conformal structure to that of the bulk theory gives greater control over a bulk–boundary correspondence.
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How the main claim is stated: asserted 1.00
What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.20 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.60 · mentions code or data availability 0.01
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This table labels the abstract only (arXiv listing abstract v1). The number is the probability the classifier gave the label.
| Sentence | Role | The authors' own work | States the main conclusion | Strength |
|---|---|---|---|---|
| We obtain the higher spin tractor equations of motion conjectured by Gover et al. from a BRST approach and use those methods to prove that they describe massive, partially massless and massless higher spins in conformally flat backgrounds. | contribution 0.95 | 0.95 | 0.82 | asserted 1.00 |
| The tractor description makes invariance under local choices of unit system manifest. | interpretation 0.65 | 0.31 | 0.04 | asserted 1.00 |
| In this approach, physical systems are described by conformal, rather than (pseudo-)Riemannian geometry. | background 0.34 | 0.26 | 0.06 | asserted 1.00 |
| In particular masses become geometric quantities, namely the weights of tractor fields. | interpretation 0.92 | 0.48 | 0.07 | asserted 1.00 |
| Massive systems can therefore be handled in a unified and simple manner mimicking the gauge principle usually employed for massless models. | interpretation 0.90 | 0.64 | 0.15 | asserted 0.97 |
| From a holographic viewpoint, these models describe both the bulk and boundary theories in terms of conformal geometry. | interpretation 0.90 | 0.52 | 0.11 | asserted 0.99 |
| This is an important advance, because tying the boundary conformal structure to that of the bulk theory gives greater control over a bulk--boundary correspondence. | interpretation 1.00 | 0.34 | 0.15 | asserted 1.00 |
What kind of paper the classifier reports this is: theoretical result 0.98 · evidence from proof or derivation 1.00
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,491 input tokens, $0.0002 reported.
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Cited by 15 Pith papers
Reviewed papers on Pith that cite this one. The full citation record
- The Ambient Space Formalism hep-th · Dec 2023
- Type-B Formal Higher Spin Gravity hep-th · Apr 2018
- Gravitational cubic interactions for a simple mixed-symmetry gauge field in AdS and flat backgrounds hep-th · Jul 2011
- Conformal geometry and (super)conformal higher-spin gauge theories hep-th · Feb 2019
- Higher Spin Extension of Fefferman-Graham Construction hep-th · Oct 2017
- Spinning AdS Loop Diagrams: Two Point Functions hep-th · Aug 2017
- Spinning Witten Diagrams hep-th · Feb 2017
- Towards holographic higher-spin interactions: Four-point functions and higher-spin exchange hep-th · Nov 2014
- Higher order singletons, partially massless fields and their boundary values in the ambient approach hep-th · May 2013
- On the cubic interactions of massive and partially-massless higher spins in (A)dS hep-th · Mar 2012
- Spinning Conformal Correlators hep-th · Jul 2011
- Unified BRST approach to (partially) massless and massive AdS fields of arbitrary symmetry type hep-th · May 2011
- Notes on the ambient approach to boundary values of AdS gauge fields hep-th · Jul 2012
- On the Structure of Quartic Vertices for Massless Higher Spin Fields on Minkowski Background hep-th · Mar 2012
- Lectures on Higher Spin Holography hep-th · Jan 2017
How the literature uses it
24 arXiv papers cite this in 40 sentences
Papers citing it · 16 sentences without a confident label
Builds on it 1 paper
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The approach taken in this Section is an extension of that from [ref] to the case of mixed symmetry fields.
Unified BRST approach to (partially) massless and massive AdS fields of arbitrary symmetry type · Massive fields · 0.99
Uses its method or tool 5 papers
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These steps are performed using the combination of various techniques: a version [ref] of the conventional ambient space formalism, parent formulation method which allows to implement ambient construction in the fiber rather than in space-time [ref] , and the approach to boundary values employing both the ambient and the parent techniques [ref] .
Type-B Formal Higher Spin Gravity · Introduction · 1.00
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In order to construct off–shell vertices one can use the BRST charge for massless reducible representations of the $D$–dimensional AdS group [ref] [equation] [equation] For the off–shell description of irreducible massless higher spin modes one can use the corresponding BRST charge [ref] (see also [ref] – [ref] for BRST charges which correspond to various fermionic and bosonic representations of $AdS_D$ group) which has more complicated form and includes more ghost variables than ([ref]).
On the Structure of Quartic Vertices for Massless Higher Spin Fields on Minkowski Background · AdS Deformation · 0.94
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The same methods can be applied in the ambient space (or tractor bundle fibre) [ref] by re-expressing symmetric tractor fields $Φ_M_1⋯M_s$ as [equation] In these terms, the tracefree condition takes the form $∂_U·∂_U Φ(x,U)=0$ .
A Calculus for Higher Spin Interactions · On-shell higher spin tractors · 0.85
Compares with it 1 paper
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In this respect, our approach is analogous to the recently proposed description [ref] of totally symmetric fields.[It is worth mentioning that weight $$ can be also identified to the weight of tractors involved in the description in terms of tractor bundles.
Unified BRST approach to (partially) massless and massive AdS fields of arbitrary symmetry type · Introduction · 0.99
Cites it as support 1 paper
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Further evidence for this, especially in light of the conformal-projective link on Einstein manifolds [ref] , is that these models can also be described by conformally invariant equations coupled to a parallel, conformal, scale tractor [ref] .
Metric projective geometry, BGG detour complexes and partially massless gauge theories · Introduction · 0.98
Cites it as background 13 papers
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For a masive spin $s$ field an ambient formulation is based on essentially the same constrained system (see [ref] for more details) [equation] where $Δ$ is generic (in particular, $Δ≠d/2-ℓ$ with positive integer $ℓ$).
Higher order singletons, partially massless fields and their boundary values in the ambient approach · Massive fields · 0.80
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Since we focus on the TT parts of the cubic interactions, such terms are not relevant for our discussion although they must be taken into account in order to construct the full theory.[ See [ref] for the precise forms of the free action.] The Lagrangian equations are (D^2-M^2) φ^A+ … ≈0 ,
On the cubic interactions of massive and partially-massless higher spins in (A)dS · Free HS fields in (A)dS · 0.90
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The parent formulation of a massive scalar field on $AdS_d+1$ is known [ref] .
Notes on the ambient approach to boundary values of AdS gauge fields · AdS scalar field · 0.90
What it cites · 78 sentences without a confident label
Builds on 1 paper
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To describe an irreducible system in those cases one needs to impose extra irreducibility conditions $(Y.Z)^t Ψ=0$ where $t$ is the depth[This is a straightforward generalization [ref] to the partially massless case of the massless irreducibility condition $Y.ZΨ=0$ from [ref] .], see Section sec:parent-ads as well as the decouplesdiscussion in Section log R.
Unified BRST description of AdS gauge fields · BRST Derivation of On-Shell Massive Higher Spins · 0.99
Compares with 3 papers
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They agree with those of [ref] save for the two constraints involving $Div$ which could not be detected by the spin two example explicitly checked there.
Tractors, Mass and Weyl Invariance · Tractor Equations of Motion · 0.97
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They agree with those of [ref] save for the two constraints involving $Div$ which could not be detected by the spin two example explicitly checked there.
Weyl Invariance and the Origins of Mass · Tractor Equations of Motion · 0.97
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Note, however, that in contrast to the analogous BRST operator considered in [ref] , the operator [ref] is not conformally invariant because it explicitly involves the scale tractor $I$ which breaks manifest $𝔬(d,2)$-invariance down to $𝔬(d-1,2)$.
Manifestly Conformal Descriptions and Higher Symmetries of Bosonic Singletons · Parent BRST Formulation of Tractor Fields · 0.99
Cites as background 30 papers
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In a recent series of works [ref] , it has been pointed out that a certain mathematical calculus coming from conformal geometry called “tractor calculus” [ref] (which can be traced back to ideas of Thomas early last century [ref] , for further details see [ref] ) can be employed to make manifest the local invariance of physical theories under choices of unit systems.
Tractors, Mass and Weyl Invariance · Introduction · 0.87
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In a recent series of works [ref] , it has been pointed out that a certain mathematical calculus coming from conformal geometry called “tractor calculus” [ref] (which can be traced back to ideas of Thomas early last century [ref] , for further details see [ref] ) can be employed to make manifest the local invariance of physical theories under choices of unit systems.
Standard Tractors and the Conformal Ambient Metric Construction · Introduction · 0.87
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In a recent series of works [ref] , it has been pointed out that a certain mathematical calculus coming from conformal geometry called “tractor calculus” [ref] (which can be traced back to ideas of Thomas early last century [ref] , for further details see [ref] ) can be employed to make manifest the local invariance of physical theories under choices of unit systems.
Weyl's Gauge Invariance: Conformal Geometry, Spinors, Supersymmetry, and Interactions · Introduction · 0.87
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