Bosonic conformal higher--spin fields of any symmetry

TL;DR

This work constructs free Lagrangians for bosonic conformal higher-spin fields of arbitrary symmetry in any dimension using a frame-like, unfolded-dynamics framework. Central to the approach is the $oldsymbol{\sigma_-}$-cohomology, which classifies gauge-invariant curvatures, dynamical fields, and gauge symmetries and reveals the Weyl module as the carrier of primary, gauge-invariant data (generalized Weyl tensors). The authors formulate a comprehensive cohomology analysis via a supersymmetric matrix-mechanics interpretation, connect conformal models to their AdS$_d$ counterparts through identical Weyl tensors, and develop explicit Lagrangian constructions for gauge and non-gauge conformal fields, including BF-type systems. The results provide a complete, gauge-invariant, and dimensionally universal framework for bosonic conformal HS fields, with potential applications to unitary HS theories in AdS and to nonlinear extensions within the unfolded dynamics program. These insights pave the way for a systematic exploration of conformal HS models and their relations to AdS theories and two-time/compensator formalisms, with possible extensions to fermionic and sl$_n$/sp$(2M)$-based systems.

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.