Bosonic conformal higher-spin fields of any symmetry

Abstract

Free Lagrangians are found both for gauge and non-gauge bosonic conformal fields of any symmetry type and in any space–time dimension. Conformal gauge fields of various types, their gauge transformations and gauge invariant field strengths (generalized Weyl tensors), which are derived by the σ − cohomology technics in the frame-like formulation, are shown to correspond to supersymmetric vacua of certain supersymmetric matrix mechanics. The correspondence between conformal and AdS d higher-spin models, that turn out to have identical generalized Weyl tensors, is discussed.