Manifestly Conformal Descriptions and Higher Symmetries of Bosonic Singletons

TL;DR

This paper introduces a novel ambient space approach for bosonic singletons that makes conformal symmetry manifest and characterizes a comprehensive higher symmetry algebra, relevant for higher-spin theories in AdS space.

Contribution

It proposes a new ambient space representation in the fiber to explicitly realize locality and conformal symmetry for singletons, and identifies the full higher symmetry algebra.

Findings

Characterizes a subalgebra of higher symmetries for bosonic singletons.

Proposes this algebra as a candidate for higher-spin symmetry algebra in AdS.

Argues that this algebra exhausts all higher symmetries.

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.