Higher-spin algebras and cubic interactions for simple mixed-symmetry fields in AdS spacetime

TL;DR

This paper constructs nonabelian cubic interactions for specific mixed-symmetry higher-spin fields in AdS space, revealing a Clifford algebra structure and a family of compatible higher-spin algebras.

Contribution

It introduces a new class of cubic interactions for mixed-symmetry fields with a Clifford algebra structure and explores the universal enveloping realization of higher-spin algebras.

Findings

Constructed nonabelian cubic interactions for mixed-symmetry fields in AdS.

Identified a Clifford algebra structure underlying the interactions.

Discovered a one-parameter family of higher-spin algebras compatible with unitarity.

Abstract

Nonabelian Fradkin-Vasiliev cubic interactions for dual-graviton-like gauge fields with gravity and themselves are constructed in anti-de Sitter spacetime. The Young diagrams of gauge potentials have shapes of 'tall-hooks', i.e. two columns the second of height one. The underlying nonabelian algebra is a Clifford algebra with the anti-de Sitter signature. We also discuss the universal enveloping realization of higher-spin algebras, showing that there is a one-parameter family of algebras compatible with unitarity, which is reminiscent of 3d deformed oscillators.