Formal Higher Spin Gravities

Abstract

We present a complete solution to the problem of Formal Higher Spin Gravities --- formally consistent field equations that gauge a given higher spin algebra and describe free higher spin fields upon linearization. The problem is shown to be equivalent to constructing a certain deformation of the higher spin algebra as an associative algebra. Given this deformation, all interaction vertices are explicitly constructed. All formal solutions of the equations are explicitly described in terms of an auxiliary Lax pair, the deformation parameter playing the role of the spectral one. We also discuss a natural set of observables associated to such theories, including the holographic correlation functions. As an application, we give another form of the Type-B formal Higher Spin Gravity and discuss a number of systems in five dimensions.

30 pages; typos fixed, ref added

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Cited by in corpus (18)

• More on Quantum Chiral Higher Spin Gravity
• Actions for Self-dual Higher Spin Gravities
• More on Chiral Higher Spin Gravity and Convex Geometry
• Leibniz Gauge Theories and Infinity Structures
• Minimal models of field theories: Chiral Higher Spin Gravity
• Minimal model of Chiral Higher Spin Gravity
• Towards higher-spin AdS${}_2$/CFT${}_1$ holography
• Characteristic Cohomology and Observables in Higher Spin Gravity
• Higher Spin Gravities and Presymplectic AKSZ Models
• Metaplectic representation and ordering (in)dependence in Vasiliev's higher spin gravity
• On BF-type higher-spin actions in two dimensions
• Restrictions for $n$-Point Vertices in Higher-Spin Theories
• Higher spin fluctuations on spinless 4D BTZ black hole
• $A_{\infty }$ Algebras from Slightly Broken Higher Spin Symmetries
• Hidden sectors of Chern-Simons Matter theories and Exact Holography
• On deformations of $A_{\infty }$-algebras
• Towards Massless Sector of Tensionless Strings on $Ad{S}_5$
• On tensionless string field theory in AdS${}_3$