Characteristic Cohomology and Observables in Higher Spin Gravity

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.

40 pages + Appendices=74; agrees with the published version, refs and comments added

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Cited by in corpus (12)

• More on Chiral Higher Spin Gravity and Convex Geometry
• Minimal models of field theories: Chiral Higher Spin Gravity
• Minimal model of Chiral Higher Spin Gravity
• Slightly Broken Higher Spin Symmetry: General Structure of Correlators
• Higher Spin Gravities and Presymplectic AKSZ Models
• Metaplectic representation and ordering (in)dependence in Vasiliev's higher spin gravity
• Minimal models of field theories: SDYM and SDGR
• On (spinor)-helicity and bosonization in $Ad{S}_4/CF{T}_3$
• Hidden sectors of Chern-Simons Matter theories and Exact Holography
• Lie and Leibniz Algebras of Lower-Degree Conservation Laws
• On correlation functions as higher-spin invariants
• Deformation quantization of the simplest Poisson Orbifold