4D Higher Spin Gravity with Dynamical Two-Form as a Frobenius--Chern--Simons Gauge Theory

Abstract

We provide an off-shell formulation of four-dimensional higher spin gravity based on a covariant Hamiltonian action on an open nine-dimensional Poisson manifold whose boundary consists of the direct product of spacetime and a noncommutative twistor space of S^2 x S^2 topology. The fundamental field is a superconnection consisting of even and odd differential forms valued in the odd and even sectors of a 3-graded associative algebra given by the direct product of an eight-dimensional Frobenius algebra and a higher spin algebra extended by inner Klein operators. The superconnection consists of two one-forms gauging the one-sided actions of the higher spin algebra, two bi-fundamental real forms given by the Weyl zero-form and a new dynamical two-form, an additional set of forms providing a maximal duality extension, and, finally, the Lagrange multipliers required for the covariant Hamiltonian action. In a particular two-form background, the model yields Vasiliev's recently proposed extended higher spin gravity equations, whose interaction terms are accounted for by de Rham closed globally defined forms arising in the dynamical two-form.

50 pages; v2: 44 pages. Higher spin algebra extended to include inner Klein operators. Appendix A dropped. Trace operation modified and Z_2 projection on the base manifold removed. Comparison with Vasiliev's theory is made precise. Perturbation expansion in holomorphic gauge removed for an expanded treatment in a separate publication. The presentation is somewhat reorganized

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• Characteristic Cohomology and Observables in Higher Spin Gravity
• An Action for Matter Coupled Higher Spin Gravity in Three Dimensions
• 2D sigma models and differential Poisson algebras
• Higher Spin Gravities and Presymplectic AKSZ Models
• Quantum field theories of arbitrary-spin massive multiplets and Palatini quantum gravity
• Action principles for higher and fractional spin gravities
• One Loop Tests of Supersymmetric Higher Spin $Ad{S}_4/CF{T}_3$
• Off-shell higher-spin fields in $Ad{S}_4$ and external currents
• Differential Poisson Sigma Models with Extended Supersymmetry
• All-Order Quartic Couplings in Highly Symmetric D-brane-Anti-D-brane Systems
• Induced Action for Conformal Higher Spins from Worldline Path Integrals
• On boundary conditions and spacetime/fibre duality in Vasiliev's higher-spin gravity
• Bosonic Higher Spin Gravity in any Dimension with Dynamical Two-Form