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

References in corpus (4)

• AdS_4/CFT_3 Construction from Collective Fields
• Unfolding Mixed-Symmetry Fields in AdS and the BMV Conjecture: I. General Formalism
• A Fiber Approach to Harmonic Analysis of Unfolded Higher-Spin Field Equations
• A Note on (Non)-Locality in Holographic Higher Spin Theories

Cited by in corpus (6)

• Actions for Self-dual Higher Spin Gravities
• 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
• Metaplectic representation and ordering (in)dependence in Vasiliev's higher spin gravity
• Hidden sectors of Chern-Simons Matter theories and Exact Holography