Higher-spin gravity as a theory on a fixed (anti) de Sitter background

TL;DR

This paper reformulates Vasiliev's higher-spin gravity in 3+1 dimensions using a compensator formalism, enabling a fixed (anti) de Sitter background and offering new insights into the theory's structure and holographic implications.

Contribution

It extends Vasiliev's equations to include a spacetime-dependent internal direction, providing a novel perspective on higher-spin gravity on fixed backgrounds.

Findings

Consistent extension of Vasiliev's equations with spacetime-dependent internal directions

Identification of spacetime with the de Sitter space of internal directions

Implications for higher-spin holography and quantization

Abstract

We study Vasiliev's higher-spin gravity in 3+1d. We formulate the theory in the so-called compensator formalism, where the local isometry group SO(4,1) is reduced to the Lorentz group SO(3,1) by a choice of spacelike direction in an internal 4+1d space. We present a consistent extension of Vasiliev's equations that allows this internal direction to become spacetime-dependent. This allows a new point of view on the theory, where spacetime is identified with the de Sitter space of possible internal directions. We thus obtain an interacting theory of higher-spin massless gauge fields on a fixed, maximally symmetric background spacetime. We expect implications for the physical interpretation of higher-spin gravity, for the search for a Lagrangian formulation and/or quantization, as well as for higher-spin holography.