On the Frame-Like Formulation of Mixed-Symmetry Massless Fields in (A)dS(d)

TL;DR

The work addresses covariant Lagrangian descriptions of mixed-symmetry massless fields in $(A)dS_d$ using a frame-like, $p$-form formalism. It develops a geometric framework where each field is a $p$-form valued in an $AdS_d$ representation obtained by cutting the shortest column and adding the longest row of the Young tableau, and builds manifestly gauge-invariant curvatures and actions. The paper provides explicit constructions and actions for the three-cell hook, four-cell window, and arbitrary two-row rectangular tableaux, analyzes their equations of motion, Weyl tensors, and flat-space limits, and discusses the unfolded structure via $\sigma_-$ cohomology. This approach clarifies higher-spin gauge symmetry structures, connects to known results (BMV, Metsaev, Zinoviev, Labastida) and offers a systematic path toward nonlinear, unfolded higher-spin dynamics in $(A)dS_d$ with a consistent Minkowski limit.

Abstract

The frame-like covariant Lagrangian formulation of bosonic and fermionic mixed-symmetry type higher spin massless fields propagating on the AdS(d) background is proposed. Higher spin fields are described in terms of gauge p-forms which carry tangent indices representing certain traceless tensor or gamma transversal spinor-tensor representations of the AdS(d) algebra o(d-1,2) (or o(d,1) for bosonic fields in dS(d)). Manifestly gauge invariant Abelian higher spin field strengths are introduced for the general case. We describe the general framework and demonstrate how it works for the mixed-symmetry type fields associated with the three-cell "hook" and arbitrary two-row rectangular tableaux. The manifestly gauge invariant actions for these fields are presented in a simple form. The flat limit is also analyzed.