Unfolding Mixed-Symmetry Fields in AdS and the BMV Conjecture: II. Oscillator Realization

TL;DR

This paper develops a unified oscillator-based formalism to describe mixed-symmetry tensor fields in AdS spaces, providing explicit unfolded equations and analyzing massless limits in relation to the BMV conjecture.

Contribution

It introduces a novel oscillator realization of unfolded equations for arbitrary tensor fields in AdS, connecting massless and massive representations within a unified framework.

Findings

Derived unfolded equations for tensor fields of arbitrary shape and mass in AdS.

Explicitly connected the formalism to the BMV conjecture and flat limit behavior.

Identified and disentangled frame-like potentials in massless cases.

Abstract

Following the general formalism presented in arXiv:0812.3615 -- referred to as Paper I -- we derive the unfolded equations of motion for tensor fields of arbitrary shape and mass in constantly curved backgrounds by radial reduction of Skvortsov's equations in one higher dimension. The complete unfolded system is embedded into a single master field, valued in a tensorial Schur module realized equivalently via either bosonic (symmetric basis) or fermionic (anti-symmetric basis) vector oscillators. At critical masses the reduced Weyl zero-form modules become indecomposable. We explicitly project the latter onto the submodules carrying Metsaev's massless representations. The remainder of the reduced system contains a set of Stueckelberg fields and dynamical potentials that leads to a smooth flat limit in accordance with the Brink--Metsaev--Vasiliev (BMV) conjecture. In the unitary massless cases in AdS, we identify the Alkalaev--Shaynkman--Vasiliev frame-like potentials and explicitly disentangle their unfolded field equations.