Unified BRST description of AdS gauge fields
K. B. Alkalaev, M. Grigoriev
TL;DR
This work presents a unified BRST framework for free bosonic AdS gauge fields with arbitrary mixed symmetry, achieving a local, gauge-invariant description that preserves manifest $o(d-1,2)$ symmetry. By employing a twisted Howe dual realization of $o(d-1,2)$ and $sp(2n)$ and an ambient-space setup, the authors derive a BRST operator that encodes both spacetime isometries and the Howe dual algebra, enabling a coherent reduction to known Minkowski and unfolded formulations. They construct a parent formulation that encompasses ambient, hyperboloid, and unfolded descriptions as reductions, and prove the Brink–Movshev–Vasiliev (BMV) conjecture within this BRST context by showing that the AdS Weyl module decomposes into admissible Poincaré Weyl modules. The framework also accommodates non-unitary and partially-massless cases through $Q_p$-cohomology, offering a robust algebraic handle on spectra and paving the way for studying interactions via higher-spin algebras. This algebraic, BRST-centric perspective is poised to clarify connections to string theory limits and to guide construction of consistent nonlinear theories for mixed-symmetry AdS fields.
Abstract
A concise formulation for mixed-symmetry gauge fields on AdS space is proposed. It is explicitly local, gauge invariant, and has manifest AdS symmetry. Various other known formulations (including the original formulation of Metsaev and the unfolded formulation) can be derived through the appropriate reductions and gauge fixing. As a byproduct, we also identify some new useful formulations of the theory that can be interesting for further developments. The formulation is presented in the BRST terms and extensively uses Howe duality. In particular, the BRST operator is a sum of the term associated to the spacetime isometry algebra and the term associated to the Howe dual symplectic algebra.