Frame-like formulation for free mixed-symmetry bosonic massless higher-spin fields in AdS(d)

TL;DR

This work develops a comprehensive frame-like, gauge-invariant Lagrangian framework for free bosonic higher-spin fields of general mixed symmetry in $AdS_d$, formulated as differential $p$-forms valued in $o(d-1,2)$ modules. A compensator formalism and detailed $o(d-1,2)\to o(d-1,1)$ decomposition organize the field content into physical, auxiliary, and extra components, with a bilinear action built from gauge-invariant curvatures. The authors introduce a fermionic Fock-space reformulation and a $\\mathcal{Q}$-complex to reconstruct the action from field equations under decoupling conditions that exclude unwanted higher-derivative and extra-field contributions; they also demonstrate gauge-symmetry enhancement in the flat limit $\lambda\to0$, ensuring consistency with Minkowski dynamics. The framework generalizes gravity and symmetric HS fields to general mixed-symmetry types and provides a foundation for nonlinear HS theories and potential connections to string theory, including extensions to fermionic and partially massless cases. Overall, the paper offers a principled, algebraically grounded route to frame-like HS dynamics with controlled flat-space limits and a clear path toward unfolded formulations and interactions.

Abstract

In this paper we discuss in detail the frame-like formulation of free bosonic massless higher-spin fields of general symmetry type in AdS(d), announced recently in hep-th/0311164, hep-th/0501108. Properties of gauge invariant and AdS covariant action functionals and their flat limits are carefully analyzed.