On special quartic interaction of higher spin gauge fields with scalars and gauge symmetry commutator in the linear approximation

Abstract

Local quartic interaction of higher-spin gauge field with a scalar field is considered. In this special case, the nontrivial task of construction of interacting Lagrangian for the higher spin field in physical gauge was solved using the full power of Noether's procedure. As a result, the linear on-field gauge transformation is obtained and the corresponding commutator of transformation is analyzed. To understand the closure of this algebra the right-hand side of this commutator is classified in respect to gauge transformations coming from cubic interactions with different higher spin symmetric tensor fields and with mixed symmetry tensor fields transformations.

arXiv commentv.3 accepted for publication in Nucl.Phys.B

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• Actions for Self-dual Higher Spin Gravities
• Carrollian and Galilean conformal higher-spin algebras in any dimensions
• Interacting massive and massless arbitrary spin fields in 4d flat space
• $\mathcal{N}=2$ higher spins: superfield equations of motion, the hypermultiplet supercurrents, and the component structure
• Mixed-symmetry continuous-spin fields in flat and AdS spaces
• On interactions of massless spin 3 and scalar fields
• Quintic vertices of spin 3, vector and scalar fields
• Higher-Spin Gauge Models in the BRST-antifield Formalism