Geometry and dynamics of higher-spin frame 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.

30 pages, uses youngtab.sty, v2: minor changes, references added

References in corpus (9)

• Current Exchanges and Unconstrained Higher Spins
• Constructing the Cubic Interaction Vertex of Higher Spin Gauge Fields
• Quartet unconstrained formulation for massless higher spin fields
• On Higher Spins with a Strong Sp(2,R) Condition
• Higher-Spin Gauge Fields Interacting with Scalars: The Lagrangian Cubic Vertex
• Interacting Higher Spins and the High Energy Limit of the Bosonic String
• Higher-spin Chern-Simons theories in odd dimensions
• The Generalized Curvature and Christoffel Symbols for a Higher Spin Potential in AdS_{d+1} Space
• Gauged diffeomorphisms and hidden symmetries in Kaluza-Klein theories

Cited by in corpus (6)

• Gauge Invariant Lagrangians for Free and Interacting Higher Spin Fields. A Review of the BRST formulation
• Unfolding Mixed-Symmetry Fields in AdS and the BMV Conjecture: I. General Formalism
• Higher-Spin Gauge Fields Interacting with Scalars: The Lagrangian Cubic Vertex
• Geometric Lagrangians for massive higher-spin fields
• Shadows, currents and AdS fields
• Generalized Curvature and Ricci Tensors for a Higher Spin Potential and the Trace Anomaly in External Higher Spin Fields in AdS_{4} Space