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.

arXiv comment40 pages + Appendices=74; agrees with the published version, refs and comments added

References in corpus (58)

• Deformation quantization of Poisson manifolds, I
• Generalized Global Symmetries
• AdS Dual of the Critical O(N) Vector Model
• Nonlinear Equations for Symmetric Massless Higher Spin Fields in $(A)d{S}_d$
• The Geometry of the Master Equation and Topological Quantum Field Theory
• Introduction to sh Lie algebras for physicists
• Local BRST cohomology in gauge theories
• Massless Higher Spins and Holography
• Nonlinear W(infinity) Algebra as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity
• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Chern-Simons Theory with Vector Fermion Matter
• Nonlinear higher spin theories in various dimensions
• Holography in 4D (Super) Higher Spin Theories and a Test via Cubic Scalar Couplings
• Higher-Spin Gauge Interactions for Massive Matter Fields in 3D AdS Space-Time
• Stringy gravity, interacting tensionless strings and massless higher spins
• Minimal Model Holography
• Baryons, monopoles and dualities in Chern-Simons-matter theories
• Constraints on symmetry from holography
• Conformal Higher Spin Theory
• Light-Front Higher-Spin Theories in Flat Space
• Holography of the N=1 Higher-Spin Theory on AdS4
• Quartic AdS Interactions in Higher-Spin Gravity from Conformal Field Theory
• Diffeomorphism-invariant observables and their nonlocal algebra
• Effective action in a higher-spin background
• On the uniqueness of higher-spin symmetries in AdS and CFT
• Exact higher-spin symmetry in CFT: all correlators in unbroken Vasiliev theory
• Higher order singletons, partially massless fields and their boundary values in the ambient approach
• Semiclassical approximation in Batalin-Vilkovisky formalism
• Higher Spin Symmetry and N=4 SYM
• Quantum Chiral Higher Spin Gravity
• Higher-Spin Gauge Theories and Bulk Locality
• Higher Spin Interactions in Four Dimensions: Vasiliev vs. Fronsdal
• Elements of Vasiliev theory
• An Exact Solution of 4D Higher-Spin Gauge Theory
• Chiral Higher Spin Theories and Self-Duality
• More on Quantum Chiral Higher Spin Gravity
• Novel supermultiplets of SU(2,2|4) and the AdS_5/CFT_4 duality
• A Fiber Approach to Harmonic Analysis of Unfolded Higher-Spin Field Equations
• Brane Partons and Singleton Strings
• Higher Spin Gravity Amplitudes From Zero-form Charges
• On matter-free Higher Spin Gravities in 3d: (partially)-massless fields and general structure
• Geometry and Observables in Vasiliev's Higher Spin Gravity
• Exact higher-spin symmetry in CFT: free fermion correlators from Vasiliev Theory
• A Poincare lemma for sigma models of AKSZ type
• A minimal BV action for Vasiliev's four-dimensional higher spin gravity
• Minimal unitary representation of SU(2,2) and its deformations as massless conformal fields and their supersymmetric extensions
• Surface charges and dynamical Killing tensors for higher spin gauge fields in constant curvature spaces
• Formal Higher Spin Gravities
• Higher Spins and Matter Interacting in Dimension Three
• Type-B Formal Higher Spin Gravity
• Formal Higher-Spin Theories and Kontsevich-Shoikhet-Tsygan Formality
• 4D Higher Spin Gravity with Dynamical Two-Form as a Frobenius--Chern--Simons Gauge Theory
• Higher-spin gravity as a theory on a fixed (anti) de Sitter background
• Hochschild cohomology of the Weyl algebra and Vasiliev's equations
• Supertrace and superquadratic Lie structure on the Weyl algebra, with applications to formal inverse Weyl transform
• Currents on Grassmann algebras
• Hypergravity in five dimensions
• Towards Massless Sector of Tensionless Strings on $Ad{S}_5$

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