Unfolding Mixed-Symmetry Fields in AdS and the BMV Conjecture: I. General Formalism

TL;DR

This paper develops a general formalism for analyzing mixed-symmetry fields in Anti-de Sitter space, focusing on unfolded on-shell dynamics and their relation to the BMV conjecture, with classifications of modules and degrees of freedom.

Contribution

It introduces a comprehensive framework for unfolded on-shell dynamics of mixed-symmetry fields in curved backgrounds, advancing understanding of the BMV conjecture.

Findings

Classification of Lorentz-covariant modules from primary Weyl tensors

Analysis of local degrees of freedom in various gravitational and massive scenarios

Framework applicable to backgrounds with arbitrary cosmological constant

Abstract

We present some generalities of unfolded on-shell dynamics that are useful in analysing the BMV conjecture for mixed-symmetry fields in constantly curved backgrounds. In particular we classify the Lorentz-covariant Harish-Chandra modules generated from primary Weyl tensors of arbitrary mass and shape, and in backgrounds with general values of the cosmological constant. We also discuss the unfolded notion of local degrees of freedom in theories with and without gravity and with and without massive deformation parameters, using the language of Weyl zero-form modules and their duals.