Unified BRST approach to (partially) massless and massive AdS fields of arbitrary symmetry type
K. B. Alkalaev, Maxim Grigoriev
TL;DR
This work presents a unified BRST framework for bosonic AdS$_d$ fields of arbitrary symmetry type, encompassing massless, partially massless, and massive cases. By formulating the dynamics in ambient space and then lifting to a local fiberBundle/BRST (with a twisted Howe dual $o(d-1,2)$–$sp(2n)$ structure) representation, the authors obtain a first-order, gauge-invariant description whose BRST operator $oldsymbol{ abla}+Q_p$ separates geometric and algebraic constraints. The analysis of the $Q_p$-cohomology identifies a gauge module at negative ghost degree and a Weyl module at zero ghost degree, reproducing unfolded-field content and providing a path to Lagrangian or radial reductions. For generic weights $w$, the gauge symmetry is purely algebraic and the theory reduces to a massive Weyl-type description, while special $w$ values yield (partially) massless sectors with depth $t$, intimately related to the unfolded approach of Vasiliev. Overall, the paper links ambient-space BRST formulations, fibered local realizations, and unfolded dynamics, offering a comprehensive framework for arbitrary mixed-symmetry AdS fields and paving the way for explicit constructions of Lagrangians and interactions.
Abstract
We construct a concise gauge invariant formulation for massless, partially massless, and massive bosonic AdS fields of arbitrary symmetry type at the level of equations of motion. Our formulation admits two equivalent descriptions: in terms of the ambient space and in terms of an appropriate vector bundle, as an explicitly local first-order BRST formalism. The second version is a parent-like formulation that can be used to generate various other formulations via equivalent reductions. In particular, we demonstrate a relation to the unfolded description of massless and partially massless fields.