Bosonic conformal higher--spin fields of any symmetry

TL;DR

This paper develops free Lagrangians for bosonic conformal higher-spin fields of any symmetry in any dimension, introduces their gauge structures, and explores their connections to supersymmetric models and AdS higher-spin theories.

Contribution

It provides a comprehensive construction of conformal higher-spin fields with gauge invariance and establishes links to supersymmetric matrix mechanics and AdS models.

Findings

Derived gauge-invariant field strengths for all symmetry types.

Connected conformal higher-spin fields to supersymmetric vacua.

Demonstrated the equivalence of generalized Weyl tensors in conformal and AdS models.

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 $\sigma_-$ 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.