Geometry and dynamics of higher-spin frame fields

TL;DR

This paper develops a geometric framework for free higher-spin fields in Minkowski and (A)dS spaces, deriving their equations of motion and exploring potential action principles within the frame formalism.

Contribution

It provides a systematic geometric approach to higher-spin fields, including generalized connections, Christoffel symbols, and Einstein equations, extending the understanding of their structure and symmetries.

Findings

Derivation of higher-spin Christoffel symbols from torsion-like constraints.

Proof that higher-derivative Einstein equations reproduce AdS Fronsdal equations.

Discussion on the possibility of a geometrical, invariant action principle for higher-spin fields.

Abstract

We give a systematic account of unconstrained free bosonic higher-spin fields on D-dimensional Minkowski and (Anti-)de Sitter spaces in the frame formalism. The generalized spin connections are determined by solving a chain of torsion-like constraints. Via a generalization of the vielbein postulate these allow to determine higher-spin Christoffel symbols, whose relation to the de Wit--Freedman connections is discussed. We prove that the generalized Einstein equations, despite being of higher-derivative order, give rise to the AdS Fronsdal equations in the compensator formulation. To this end we derive Damour-Deser identities for arbitrary spin on AdS. Finally we discuss the possibility of a geometrical and local action principle, which is manifestly invariant under unconstrained higher-spin symmetries.