Radial Reduction and Cubic Interaction for Higher Spins in (A)dS space

Abstract

We present a new version of the radial reduction formalism to obtain a cubic interaction of higher spin gauge fields in $Ad{S}_{d+1}$ space from the corresponding cubic interaction in a flat $d+2$ dimensional background. We modify the radial reduction procedure proposed previously by T. Biswas and W. Siegel in 2002 and applied to the free higher spin Lagrangian by K. Hallowell and A. Waldron in 2005. This modified radial reduction scheme is applied to interacting massless higher spin fields in Fronsdal's formulation, and all results are expressed in a direct $Ad{S}_{d+1}$ invariant way with $AdS$ covariant derivatives. We present a consistent algorithm and define new procedure to obtain all corrections proportional to powers of the cosmological constant, and apply these to the main term of the cubic self-interaction.

Latex, 30 pages,v2 references added

References in corpus (12)

• Nonlinear W(infinity) Algebra as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity
• A generating function for the cubic interactions of higher spin fields
• On the Tensionless Limit of String theory, Off - Shell Higher Spin Interaction Vertices and BCFW Recursion Relations
• BRST-BV approach to cubic interaction vertices for massive and massless higher-spin fields
• Constructing the Cubic Interaction Vertex of Higher Spin Gauge Fields
• Higher-Spin Gauge Fields Interacting with Scalars: The Lagrangian Cubic Vertex
• Higher spin interactions with scalar matter on constant curvature spacetimes: conserved current and cubic coupling generating functions
• (A)dS exchanges and partially-massless higher spins
• Higher Spins and String Interactions
• Ultraviolet behaviour of higher spin gauge field propagators and one loop mass renormalization
• On Killing tensors and cubic vertices in higher-spin gauge theories
• Higher Spins and Current Exchanges

Cited by in corpus (22)

• Generating functions of (partially-)massless higher-spin cubic interactions
• Non-abelian cubic vertices for higher-spin fields in anti-de Sitter space
• Cubic interactions of Maxwell-like higher spins
• Off-shell massive N=1 supermultiplets in three dimensions
• General Lagrangian Formulation for Higher Spin Fields with Arbitrary Index Symmetry. 2. Fermionic fields
• Cubic interactions of massless bosonic fields in three dimensions II: Parity-odd and Chern-Simons vertices
• Looking for partially-massless gravity
• A Calculus for Higher Spin Interactions
• Vertex-Constraints in 3D Higher Spin Theories
• Massless and Massive Higher Spins from Anti-de Sitter Space Waveguide
• Cubic-interaction-induced deformations of higher-spin symmetries
• On special quartic interaction of higher spin gauge fields with scalars and gauge symmetry commutator in the linear approximation
• All spin-2 cubic vertices with two derivatives
• Cubic Interaction for Higher Spins in $Ad{S}_{d+1}$ space in the explicit covariant form
• Restrictions for $n$-Point Vertices in Higher-Spin Theories
• Conformal totally symmetric arbitrary spin fermionic fields
• A note on higher-order vertices of higher-spin fields in flat and (A)dS space
• Massless higher spin cubic vertices in flat four dimmensional space
• On correlation functions of higher-spin currents in arbitrary dimensions $d>3$
• On Gluing CFT Correlators to Higher-Spin Amplitudes in AdS
• Local cubic vertex functions for three massless higher even spin fields on spaces AdS_D: An analytic approach
• Constructive approach to solution of the conservation condition for conformal higher spin tree-point correlation function with equal spins