Cubic Interaction for Higher Spins in $Ad{S}_{d+1}$ space in the explicit covariant form

Abstract

We present a slightly modified prescription of the radial pullback formalism proposed previously by R. Manvelyan, R. Mkrtchyan and W. Rühl in 2012, where authors investigated possibility to connect the main term of higher spin interaction in flat $d+2$ dimensional space to the main term of interaction in $Ad{S}_{d+1}$ space ignoring all trace and divergent terms but expressed directly through the $AdS$ covariant derivatives and including some curvature corrections. In this paper we succeeded to solve all necessary \emph{recurrence relations} to finalize full radial pullback of the main term of cubic self-interaction for higher spin gauge fields in Fronsdal's formulation from flat to one dimension less $Ad{S}_{d+1}$ space. Nontrivial solutions of recurrence relations lead to the possibility to obtain the full set of $Ad{S}_{d+1}$ dimensional interacting terms with all curvature corrections including trace and divergence terms from any interaction term in $d+2$ dimensional flat space.

arXiv commentLatex, 34 pages. arXiv admin note: text overlap with arXiv:1210.7227; v.2 ref. added, typos corrected

References in corpus (41)

• Nonlinear Equations for Symmetric Massless Higher Spin Fields in $(A)d{S}_d$
• Cubic interaction vertices for massive and massless higher spin fields
• Gauge Invariant Lagrangians for Free and Interacting Higher Spin Fields. A Review of the BRST formulation
• String Lessons for Higher-Spin Interactions
• Cubic interaction vertices for fermionic and bosonic arbitrary spin fields
• On The Uniqueness of Minimal Coupling in Higher-Spin Gauge Theory
• General trilinear interaction for arbitrary even higher spin gauge fields
• Cubic Vertices for Symmetric Higher-Spin Gauge Fields in $(A)d{S}_d$
• Current Exchanges and Unconstrained Higher Spins
• A generating function for the cubic interactions of higher spin fields
• Cubic interactions of massless higher spins in (A)dS: metric-like approach
• Higher-spin Interactions from CFT: The Complete Cubic Couplings
• Spinor-Helicity Three-Point Amplitudes from Local Cubic Interactions
• Constructing the Cubic Interaction Vertex of Higher Spin Gauge Fields
• Elements of Vasiliev theory
• On the Structure of Quartic Vertices for Massless Higher Spin Fields on Minkowski Background
• Consistent couplings between spin-2 and spin-3 massless fields
• Holography, Unfolding and Higher-Spin Theory
• On higher spin interactions with matter
• Constant Curvature Algebras and Higher Spin Action Generating Functions
• On spin 3 interacting with gravity
• Non-abelian cubic vertices for higher-spin fields in anti-de Sitter space
• Spin 3 cubic vertices in a frame-like formalism
• Cubic interactions of Maxwell-like higher spins
• On four-point interactions in massless higher spin theory in flat space
• Direct construction of a cubic selfinteraction for higher spin gauge fields
• On the Non-Local Obstruction to Interacting Higher Spins in Flat Space
• From Higher Spins to Strings: A Primer
• TASI Lectures on the Higher Spin - CFT duality
• Off-shell construction of some trilinear higher spin gauge field interactions
• Cubic interaction vertices for N=1 arbitrary spin massless supermultiplets in flat space
• On Killing tensors and cubic vertices in higher-spin gauge theories
• Solving the Noether procedure for cubic interactions of higher spins in (A)dS
• Cubic interactions of massless bosonic fields in three dimensions II: Parity-odd and Chern-Simons vertices
• Conformal invariant interaction of a scalar field with the higher spin field in AdS_{D}
• Cubic interactions of massless bosonic fields in three dimensions
• Radial Reduction and Cubic Interaction for Higher Spins in (A)dS space
• Investigations into Light-front Quartic Interactions for Massless Fields (I): Non-constructibility of Higher Spin Quartic Amplitudes
• Vertex-Constraints in 3D Higher Spin Theories
• Constraints for Three-Dimensional Higher-Spin Interactions and Conformal Correlators
• Lectures on Higher Spin Holography

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• A note on higher-order vertices of higher-spin fields in flat and (A)dS space
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• Massless higher spin cubic vertices in flat four dimmensional space
• Constructive approach to solution of the conservation condition for conformal higher spin tree-point correlation function with equal spins