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

TL;DR

The paper constructs nonabelian Fradkin–Vasiliev cubic interactions for simple mixed-symmetry gauge fields in $AdS$ spacetime, focusing on tall-hook representations with two columns and the second column of height one. The underlying nonabelian algebra is identified as a Clifford algebra associated with the $AdS$ signature. It also develops a universal enveloping realization of higher-spin algebras, demonstrating a one-parameter family of algebras compatible with unitarity, reminiscent of $3d$ deformed oscillators. These results extend the higher-spin interaction program beyond totally symmetric fields and reveal algebraic structures that govern consistent couplings in $AdS$.

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.