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Higher-Rank Fields and Currents
High Energy Physics - Theory · Submitted 23 Dec 2013
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim $Sp(2M)$ invariant field equations in the space ${\cal M}_M$ with symmetric matrix coordinates are classified.
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The abstract, sentence by sentence
$Sp(2M)$ invariant field equations in the space ${\cal M}_M$ with symmetric matrix coordinates are classified. Analogous results are obtained for Minkowski-like subspaces of ${\cal M}_M$ which include usual $4d$ Minkowski space as a particular case. The constructed equations are associated with the tensor products of the Fock (singleton) representation of $Sp(2M)$ of any rank ${\mathbf{r }}$. The infinite set of higher-spin conserved currents multilinear in rank-one fields in ${\cal M}_M$ is found. The associated conserved charges are supported by $({\mathbf{r }} M-\frac{{\mathbf{r }} ({\mathbf{r }} -1)}{2})-$dimensional differential forms in ${\cal M}_M$, that are closed by virtue of the rank-$2{\mathbf{r }}$ field equations. The cohomology groups $H^p(\sigma^{\mathbf{r }}_-)$ with all $p$ and ${\mathbf{r }}$, which determine the form of appropriate gauge fields and their field equations, are found both for ${\cal M}_M$ and for its Minkowski-like subspace.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | $Sp(2M)$ invariant field equations in the space ${\cal M}_M$ with symmetric matrix coordinates are classified. | contribution 0.57 | 0.87 | 0.27 | asserted 1.00 |
| s1 | Analogous results are obtained for Minkowski-like subspaces of ${\cal M}_M$ which include usual $4d$ Minkowski space as a particular case. | result 0.81 | 0.85 | 0.08 | asserted 1.00 |
| s2 | The constructed equations are associated with the tensor products of the Fock (singleton) representation of $Sp(2M)$ of any rank ${\mathbf{r }}$. | result 0.59 | 0.71 | 0.15 | asserted 1.00 |
| s3 | The infinite set of higher-spin conserved currents multilinear in rank-one fields in ${\cal M}_M$ is found. | result 0.98 | 0.93 | 0.24 | asserted 1.00 |
| s4 | The associated conserved charges are supported by $({\mathbf{r }} M-\frac{{\mathbf{r }} ({\mathbf{r }} -1)}{2})-$dimensional differential forms in ${\cal M}_M$, that are closed by virtue of the rank-$2{\mathbf{r }}$ field equations. | result 1.00 | 0.89 | 0.19 | asserted 1.00 |
| s5 | The cohomology groups $H^p(\sigma^{\mathbf{r }}_-)$ with all $p$ and ${\mathbf{r }}$, which determine the form of appropriate gauge fields and their field equations, are found both for ${\cal M}_M$ and for its Minkowski-like subspace. | result 0.94 | 0.93 | 0.26 | asserted 1.00 |
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The paper
Original abstract
$Sp(2M)$ invariant field equations in the space ${\cal M}_M$ with symmetric matrix coordinates are classified. Analogous results are obtained for Minkowski-like subspaces of ${\cal M}_M$ which include usual $4d$ Minkowski space as a particular case. The constructed equations are associated with the tensor products of the Fock (singleton) representation of $Sp(2M)$ of any rank ${\mathbf{r }}$. The infinite set of higher-spin conserved currents multilinear in rank-one fields in ${\cal M}_M$ is found. The associated conserved charges are supported by $({\mathbf{r }} M-\frac{{\mathbf{r }} ({\mathbf{r }} -1)}{2})-$dimensional differential forms in ${\cal M}_M$, that are closed by virtue of the rank-$2{\mathbf{r }}$ field equations. The cohomology groups $H^p(\sigma^{\mathbf{r }}_-)$ with all $p$ and ${\mathbf{r }}$, which determine the form of appropriate gauge fields and their field equations, are found both for ${\cal M}_M$ and for its Minkowski-like subspace.
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How the literature uses it
10 arXiv papers cite this in 30 sentences
Papers citing it · 23 sentences without a confident label
Uses its method or tool 1 paper
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In Section [ref] we derive MHV amplitudes in the framework of generalized Minkowski space [ref] where polylocal products of HS fields live.
Scattering amplitudes as multi-particle higher-spin charges in the correspondence space · Introduction · 0.82
Compares with it 1 paper
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In case of $λ_+ = 4$, for which the corresponding $𝔰𝔬(3,2)$ module survives a unitary truncation, we are left with [equation] which coincides with the analysis of [ref] .
The $\sigma_-$ Cohomology Analysis for Coxeter HS $B_2$ model · $H^1(σ_-)$ · 0.98
Cites it as background 4 papers
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However, in the context of $B_2$ CHS, the relevant results are those concerning $H(σ_-)$ in the standard $4d$ theory of HS [ref] , partially massless systems [ref] , as well as $σ_-$ analysis of $𝔰𝔭(2M)$ invariant equations in spaces with matrix coordinates [ref] , which include usual $4d$ Minkowski space as a particular case.
The $\sigma_-$ Cohomology Analysis for Coxeter HS $B_2$ model · Introduction · 0.89
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The first well-known examples of this type projectors are the Behrends-Fronsdal (BF) spin operators $Θ^(j)$, constructed in papers [ref] , [ref] , devoted to the fundamentals of the theory of higher spin fields (about this theory see, e.g., papers [ref] , [ref] , [ref] , [ref] , [ref] , [ref] and references therein).
D-dimensional spin projection operators for arbitrary type of symmetry via Brauer algebra idempotents · Introduction · 0.97
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This formulation, which was originally put forward by Fronsdal as an alternative to the Kaluza–Klein theory [ref] , has been extensively developed by several authors [ref] .
Higher Spins in Hyper-Superspace · Introduction · 0.99
What it cites · 5 sentences without a confident label
Builds on 1 paper
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Our analysis generalizes those of [ref] , where the case of rank-2 was considered, and of [ref] , where conformal field equations in Minkowski space of any dimension were obtained.
Bosonic conformal higher--spin fields of any symmetry · Details of $σ_-$–cohomology analysis · 0.99
Uses the method or tool of 1 paper
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To show that this list of solutions is complete, analogously to [ref] , one can use the semi-positive definiteness of $Δ^$.
Bosonic conformal higher--spin fields of any symmetry · Details of $σ_-$–cohomology analysis · 0.95
Cites as background 12 papers
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We expect that results of the present paper may have applications in the context of $AdS/CFT$ holography [ref] and especially, higher-spin holography (see, e.g., [ref] and references therein) because, as was emphasized in [ref] , the duality between fields in higher dimensions and currents in lower dimensions to large extent amounts in the language of this paper to the duality between lower-rank fields in $_M$ with higher $M$ and higher-rank fields in $_M$ with lower $M$.
Higher Spin Gauge Theory and Holography: The Three-Point Functions · Introduction · 0.81
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We expect that results of the present paper may have applications in the context of $AdS/CFT$ holography [ref] and especially, higher-spin holography (see, e.g., [ref] and references therein) because, as was emphasized in [ref] , the duality between fields in higher dimensions and currents in lower dimensions to large extent amounts in the language of this paper to the duality between lower-rank fields in $_M$ with higher $M$ and higher-rank fields in $_M$ with lower $M$.
Unfolded Equations for Current Interactions of 4d Massless Fields as a Free System in Mixed Dimensions · Introduction · 0.81
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We expect that results of the present paper may have applications in the context of $AdS/CFT$ holography [ref] and especially, higher-spin holography (see, e.g., [ref] and references therein) because, as was emphasized in [ref] , the duality between fields in higher dimensions and currents in lower dimensions to large extent amounts in the language of this paper to the duality between lower-rank fields in $_M$ with higher $M$ and higher-rank fields in $_M$ with lower $M$.
Constraining conformal field theories with a higher spin symmetry · Introduction · 0.81
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