On Higher Spin Symmetries in AdS_{5}

TL;DR

This paper constructs a special embedding of SU(4) in SU(10) to explore higher spin symmetries in AdS_5, proposing a five-dimensional action for massless spin two and three fields with cubic interactions and discussing their relation to existing theories.

Contribution

It introduces a novel embedding of SU(4) in SU(10) incorporating spin two and three symmetries, and proposes a five-dimensional action for these fields with cubic interactions.

Findings

Constructed a special SU(4) in SU(10) embedding including spin 2 and 3.

Proposed a five-dimensional action with cubic interactions for massless spin 2 and 3 fields.

Discussed the connection with existing higher spin theories in AdS_5.

Abstract

A special embedding of the SU(4) algebra in SU(10), including both spin two and spin three symmetry generators, is constructed. A possible five dimensional action for massless spin two and three fields with cubic interaction is constructed. The connection with the previously investigated higher spin theories in $AdS_{5}$ background is discussed. Generalization to the more general case of symmetries, including spins $2,3,\dots s$, is shown.