Characteristic Cohomology and Observables in Higher Spin Gravity

Alexey Sharapov; Evgeny Skvortsov

RECORD

Characteristic Cohomology and Observables in Higher Spin Gravity

Alexey Sharapov, Evgeny Skvortsov

High Energy Physics - Theory · Submitted 24 Jun 2020

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We give a complete classification of dynamical invariants in $3d$ and $4d$ Higher Spin Gravity models, with some comments on arbitrary $d$.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗

Cite ▾

Claim paper

The compiled record

The paper's own sentences, arranged. 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.

Open the compiled record

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,917 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.21 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.63 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; show every role.

We give a complete classification of dynamical invariants in $3d$ and $4d$ Higher Spin Gravity models, with some comments on arbitrary $d$. These include holographic correlation functions, interaction vertices, on-shell actions, conserved currents, surface charges, and some others. Surprisingly, there are a good many conserved $p$-form currents with various $p$. The last fact, being in tension with `no nontrivial conserved currents in quantum gravity' and similar statements, gives an indication of hidden integrability of the models. Our results rely on a systematic computation of Hochschild, cyclic, and Chevalley--Eilenberg cohomology for the corresponding higher spin algebras. A new invariant in Chern-Simons theory with the Weyl algebra as gauge algebra is also presented.

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 give a complete classification of dynamical invariants in $3d$ and $4d$ Higher Spin Gravity models, with some comments on arbitrary $d$.	contribution 0.88	0.95	0.74	asserted 1.00
s1	These include holographic correlation functions, interaction vertices, on-shell actions, conserved currents, surface charges, and some others.	result 0.81	0.73	0.11	asserted 0.99
s2	Surprisingly, there are a good many conserved $p$-form currents with various $p$.	result 1.00	0.85	0.11	asserted 1.00
s3	The last fact, being in tension with `no nontrivial conserved currents in quantum gravity' and similar statements, gives an indication of hidden integrability of the models.	interpretation 1.00	0.56	0.14	hedged possibility 1.00
s4	Our results rely on a systematic computation of Hochschild, cyclic, and Chevalley--Eilenberg cohomology for the corresponding higher spin algebras.	method 1.00	0.93	0.06	asserted 1.00
s5	A new invariant in Chern-Simons theory with the Weyl algebra as gauge algebra is also presented.	result 0.68	0.93	0.06	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.96.

What was examined, and what was not

sources read

arXiv listing abstract v3

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

The paper

Original abstract

We give a complete classification of dynamical invariants in $3d$ and $4d$ Higher Spin Gravity models, with some comments on arbitrary $d$. These include holographic correlation functions, interaction vertices, on-shell actions, conserved currents, surface charges, and some others. Surprisingly, there are a good many conserved $p$-form currents with various $p$. The last fact, being in tension with `no nontrivial conserved currents in quantum gravity' and similar statements, gives an indication of hidden integrability of the models. Our results rely on a systematic computation of Hochschild, cyclic, and Chevalley--Eilenberg cohomology for the corresponding higher spin algebras. A new invariant in Chern-Simons theory with the Weyl algebra as gauge algebra is also presented.

Human review

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

References

Forward citations

Cited by 2 Pith papers

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

Unfolding the Exotic Supergravity Multiplet
hep-th 2026-08 conditional novelty 7.0 of 10

This paper constructs a Cartan-integrable, superconformally invariant unfolded system of equations that describes the free six-dimensional exotic (4,0) supergravity multiplet.
Chiral Higher Spin Gravity in (A)dS${}_4$ and secrets of Chern-Simons Matter Theories
hep-th 2022-05 conditional novelty 5.0 of 10

A local, Lorentz-covariant chiral higher-spin gravity with cosmological constant is constructed as a Free Differential Algebra, smoothly deforming the authors' flat-space construction.

How the literature uses it

15 arXiv papers cite this in 49 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 · 38 sentences without a confident label

Uses its method or tool 3 papers

One can reduce the integral over the square to the one over the $2d$ simplex $Δ_2={0<u_1<u_2<1}$: [equation] Here, we explicitly see propagators $G(u,v)=1+2(u-v)$ that emerge from Shoikhet-Tsygan-Kontsevich Formality, see [ref] , so that [equation] The integral can be taken to give [ref] ($p_01=x$, $p_02=y$, $p_12=z$ and with $ħ=1$) [equation] In terms of symbols the cocycle condition for $ϕ_1$ reads [equation] Associated to this Hochschild two-cocycle there is also a cyclic cocycle, see [ref] for an explicit formula.

Deformation quantization of the simplest Poisson Orbifold · Deformation via a resolution · 0.88
Therefore, the general strategy and techniques we use can be borrowed from [ref] .

Minimal model of Chiral Higher Spin Gravity · Minimal models · 1.00
It would be interesting to compute the Chevalley-Eilenberg cohomology following the techniques of [ref] , which would give a rigorous answer regarding the number of independent vertices within the covariant approach.

Minimal models of field theories: Chiral Higher Spin Gravity · Vertices · 0.93

Cites it as support 3 papers

The uniqueness of these invariants in the case of Chern–Simons matter theories [ref] implies the three-dimensional bosonization duality [ref] in the large-$N$ limit.

Slightly Broken Higher Spin Symmetry: General Structure of Correlators · Introduction · 0.98
First of all, it can be shown [ref] that the deformed invariants – the $L_∞$-invariants – are unique.

Integrable Models From Non-Commutative Geometry With Applications to 3D Dualities · Slightly-broken higher spin symmetry and three-dimensional bosonization duality · 1.00
The vanishing of the second cohomology group $H^2(gl(𝔄))$ (see [ref] ), however, precludes such a possibility, so that the commutation relations ([ref]) have to survive quantization as they are.

Higher Spin Gravities and Presymplectic AKSZ Models · Higher spin waves and currents · 0.96

Cites it as background 2 papers

It was also known [ref] that the first two `floors' of the $A_∞$-algebra are related to the (Shoikhet–Tsygan–)Kontsevich formality theorem [ref] .

Strong Homotopy Algebras for Chiral Higher Spin Gravity via Stokes Theorem · Introduction and summary · 0.81
It corresponds to $H(Q,Λ^2( 𝒩))$, where the action of $Q$ is understood as Lie derivative $L_Q$ along $Q$ that is defined canonically on $(p,q)$-tensors on $𝒩$, see [ref] for more detail and examples.

Minimal models of field theories: SDYM and SDGR · Conclusions and Discussion · 0.86

What it cites · 121 sentences without a confident label

Uses the method or tool of 1 paper

Formal deformations with $k>3$ are called on occasion irregular. ] To study higher-order deformations it is convenient to rewrite Eqs.([ref]) in the following form: [equation] These equations can be handled effectively by the `step-by-step obstruction' method of homological perturbation theory [ref] , [ref] .

Local BRST cohomology in gauge theories · Homological perturbation theory in action · 1.00

Compares with 2 papers

The zero-form invariants are definitely not new, but they do not a priory coincide with those in [ref] ,[We note that there is a doubly-infinite series of zero-form invariants introduced in [ref] .

Geometry and Observables in Vasiliev's Higher Spin Gravity · Conserved currents and interactions · 0.98
The zero-form invariants are definitely not new, but they do not a priory coincide with those in [ref] ,[We note that there is a doubly-infinite series of zero-form invariants introduced in [ref] .

An Exact Solution of 4D Higher-Spin Gauge Theory · Conserved currents and interactions · 0.98

Cites as support 2 papers

In fact the last two classes coincide [ref] .

A Poincare lemma for sigma models of AKSZ type · Introduction · 0.98
Therefore, the holographic duals face infinitely many fields from the onset and infinitely many derivatives starting from the quartic order [ref] .

Quartic AdS Interactions in Higher-Spin Gravity from Conformal Field Theory · Introduction · 0.98

Cites as background 33 papers

The equivalence classes of conserved currents associated to PDE's were intensively studied in mathematics under the name of characteristic cohomology [ref] , [ref] , [ref] .

Notes on the horizontal cohomology · Q-cohomology vs. characteristic cohomology · 0.94
The equivalence classes of conserved currents associated to PDE's were intensively studied in mathematics under the name of characteristic cohomology [ref] , [ref] , [ref] .

Local BRST cohomology in gauge theories · Q-cohomology vs. characteristic cohomology · 0.94
The study of invariants of higher spin symmetry and of observables in HSGRA was pioneered in [ref] , where several different classes of invariants/observables were discovered, with an important prelude in [ref] .

Geometry and Observables in Vasiliev's Higher Spin Gravity · Introduction · 0.93

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.