High Energy Physics - Theory · arXiv:1808.04320 v1 · submitted 13 Aug 2018
On the structure of the conformal higher-spin wave operators
The paper says
“By employing parent formulation technique in combination with tractor description of GJMS operators we find a manifestly factorized form of the CHS wave operators for symmetric fields of arbitrary integer spin s and gauge invariance of arbitrary order t ≤ s.”
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Abstract
We study conformal higher spin (CHS) fields on constant curvature backgrounds. By employing parent formulation technique in combination with tractor description of GJMS operators we find a manifestly factorized form of the CHS wave operators for symmetric fields of arbitrary integer spin s and gauge invariance of arbitrary order t ≤ s. In the case of the usual Fradkin-Tseytlin fields t = 1 this gives a systematic derivation of the factorization formulas known in the literature while for t > 1 the explicit formulas were not known. We also relate the gauge invariance of the CHS fields to the partially-fixed gauge invariance of the factors and show that the factors can be identified with (partially gauge-fixed) wave operators for (partially)-massless or special massive fields. As a byproduct, we establish a detailed relationship with the tractor approach and, in particular, derive the tractor form of the CHS equations and gauge symmetries.
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abstract compiled · 2026-09-23 · no language-model review
How the main claim is stated: asserted 1.00
What the abstract itself states, as probabilities: claims first 0.16 · states limitation 0.26 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.11 · compares with prior results 0.93 · mentions code or data availability 0.02
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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 study conformal higher spin (CHS) fields on constant curvature backgrounds. | background 0.55 | 0.89 | 0.03 | asserted 0.90 |
| By employing parent formulation technique in combination with tractor description of GJMS operators we find a manifestly factorized form of the CHS wave operators for symmetric fields of arbitrary integer spin $s$ and gauge invariance of arbitrary order $t\leq s$. | contribution 0.48 | 0.96 | 0.81 | asserted 1.00 |
| In the case of the usual Fradkin-Tseytlin fields $t=1$ this gives a systematic derivation of the factorization formulas known in the literature while for $t>1$ the explicit formulas were not known. | gap 0.64 | 0.53 | 0.18 | asserted 1.00 |
| We also relate the gauge invariance of the CHS fields to the partially-fixed gauge invariance of the factors and show that the factors can be identified with (partially gauge-fixed) wave operators for (partially)-massless or special massive fields. | result 0.79 | 0.94 | 0.24 | asserted 1.00 |
| As a byproduct, we establish a detailed relationship with the tractor approach and, in particular, derive the tractor form of the CHS equations and gauge symmetries. | result 0.62 | 0.96 | 0.10 | asserted 1.00 |
What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,440 input tokens.
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Cited by 2 Pith papers
Reviewed papers on Pith that cite this one. The full citation record
- The Ambient Space Formalism hep-th · Dec 2023
- Conformal geometry and (super)conformal higher-spin gauge theories hep-th · Feb 2019
How the literature uses it
12 arXiv papers cite this in 18 sentences
Papers citing it · 11 sentences without a confident label
Uses its method or tool 1 paper
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A crucial technical tool employed in [ref] is the parent formulation approach which allows to perform the ambient construction in the fiber of a suitable fiber bundle rather than in the space-time.
Conformal Lagrangians from the (formal) near boundary analysis of AdS gauge fields · Conformal fields as boundary values · 0.99
Cites it as support 1 paper
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This conjecture was supported by the explicit construction of the second-derivative gauge invariant Lagrangian for arbitrary spin conformal $(A)dS$ field in Ref. [ref] (see also Refs. [ref] ).
Conformal Yang-Mills field in (A)dS space · Introduction · 0.97
Cites it as background 4 papers
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The latter describe conformal spin-$s$ fields of depth $t>1$, which have been studied for more than thirty years [ref] .
Generalised conformal higher-spin fields in curved backgrounds · Introduction · 0.96
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We use this technology to solve the kinematical constraints obeyed by correlators in such CFTs.[Other uses of the ambient space in physics include (but are not limited to) higher spin theories and holographic anomalies [ref] .]
An embedding formalism for CFTs in general states on curved backgrounds · Introduction · 0.96
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In this paper we will use the ambient space to provide solutions of [ref] for $n >1$ with prescribed leading singularity at coincident points, as dictated by physics.[Previous uses of the ambient space and related notions in physics include higher spin theories, holographic anomalies and Weyl-covariant theories [ref] .] This will be done by building a set of Weyl covariant functions of the insertion points $x_i$, as geometric objects in $d+2$ dimensional ambient space.
The Ambient Space Formalism · Introduction · 0.94
What it cites · 58 sentences without a confident label
Uses the method or tool of 3 papers
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It is based on reformulating the system [ref] in the so-called parent form [ref] in which the ambient construction is realized in the formal version of the ambient space rather than in the space-time.
Manifestly Conformal Descriptions and Higher Symmetries of Bosonic Singletons · Tractors in parent formulation · 1.00
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It is based on reformulating the system [ref] in the so-called parent form [ref] in which the ambient construction is realized in the formal version of the ambient space rather than in the space-time.
Parent form for higher spin fields on anti-de Sitter space · Tractors in parent formulation · 1.00
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Constructing the factorized form requires introducing the so-called scale tractor [ref] and a new ingredient – operators $B_k$, $k=1,2,…$.
Laplacian operators and Q-curvature on conformally Einstein manifolds · Introduction · 0.85
Compares with 4 papers
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In the special case $w=s-2$ we get the result obtained by Nutma and Taronna [ref] : [equation] Note that although the formulas coincide in our derivation we assumed that $ϕ$ is traceless.
On conformal higher spin wave operators · Explicit form of the factors · 0.99
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It is also worth mentioning that if one drops the equivalence relation in [ref], takes $V$ such that $V^2=-1$, and takes as $Φ$ a field on $AdS_n+1$ rather than $n$-dimensional conformal space, the above system is precisely the one from [ref] see also [ref] , which describes partially-massless fields on $AdS_n+1$.
Unified BRST approach to (partially) massless and massive AdS fields of arbitrary symmetry type · Manifestly $o(n, 2)$-invariant description of CHS fields · 0.89
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It is also worth mentioning that if one drops the equivalence relation in [ref], takes $V$ such that $V^2=-1$, and takes as $Φ$ a field on $AdS_n+1$ rather than $n$-dimensional conformal space, the above system is precisely the one from [ref] see also [ref] , which describes partially-massless fields on $AdS_n+1$.
Parent form for higher spin fields on anti-de Sitter space · Manifestly $o(n, 2)$-invariant description of CHS fields · 0.89
Cites as background 16 papers
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These were originally proposed [ref] for scalar densities and later extended to generic tractors [ref] using the Feffermann-Graham construction which reduces to the above ambient space approach in the conformally flat case.
Conformally invariant powers of the Laplacian, Q-curvature, and tractor calculus · GJMS operators · 0.83
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These were originally proposed [ref] for scalar densities and later extended to generic tractors [ref] using the Feffermann-Graham construction which reduces to the above ambient space approach in the conformally flat case.
Laplacian operators and Q-curvature on conformally Einstein manifolds · GJMS operators · 0.83
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As far as the structure of CHS operators on constant curvature background is concerned in addition to manifestly-factorized form [ref] it is also worth mentioning a suggestive ordinary derivative Lagrangian formulations proposed in [ref] .
Arbitrary spin conformal fields in (A)dS · Introduction · 0.83
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