Manifestly Conformal Descriptions and Higher Symmetries of Bosonic Singletons

TL;DR

This work develops a manifestly local and conformally invariant description of bosonic singletons by promoting ambient-space coordinates to a fiber over conformal space, with a BRST operator encoding the fiber constraints. The authors identify a subalgebra of higher symmetries given by $\mathfrak{o}(d,2)$-traceless $\mathfrak{osp}(2s|2)$-invariants and argue that, for irreducible singletons, these invariants exhaust all higher symmetries, generalizing Eastwood’s scalar result and relating to higher-spin algebras in AdS. The framework uses Howe duality between $\mathfrak{o}(d,2)$ and the fiber algebras, and offers a BRST-based path from conformal singletons to their AdS higher-spin counterparts, including a potential bulk-boundary interpretation. The approach yields a systematic description of higher symmetries and paves the way for constructing interactions for mixed-symmetry AdS gauge fields associated with singleton spectra, with explicit reduction to Minkowski space and a gauge (non-Lagrangian-to-Lagrangian) discussion for multiforms. Overall, it provides a unified, local, ambient-space formulation of conformal singletons and their symmetry algebras with potential impact on AdS/CFT and higher-spin theory.

Abstract

The usual ambient space approach to conformal fields is based on identifying the d-dimensional conformal space as the Dirac projective hypercone in a flat d+2-dimensional ambient space. In this work, we explicitly concentrate on singletons of any integer spin and propose an approach that allows one to have both locality and conformal symmetry manifest. This is achieved by using the ambient space representation in the fiber rather than in spacetime. This approach allows us to characterize a subalgebra of higher symmetries for any bosonic singleton, which is a candidate higher-spin algebra for mixed symmetry gauge fields on anti de Sitter spacetime. Furthermore, we argue that this algebra actually exhausts all higher symmetries.