On Massive Mixed Symmetry Tensor Fields in Minkowski Space and (A)dS

TL;DR

The paper develops gauge-invariant formulations for massive particles described by mixed-symmetry tensors $\Phi_{[\mu\nu],\alpha}$, $T_{[\mu\nu\alpha],\beta}$, and $R_{[\mu\nu],[\alpha\beta]}$ in Minkowski space and (A)dS, carefully accounting for reducible gauge symmetries via Goldstone fields. It demonstrates that these massive theories admit smooth deformation to (A)dS without introducing new fields and analyses all possible massless and partially massless limits, showing that fully massless limits are absent in (A)dS with these mixed-symmetry fields while partially massless points arise at specific parameter values tied to the cosmological constant. The construction yields explicit gauge-invariant Lagrangians for each tensor sector, reveals the structure of decoupling into subsystems at special points, and provides concrete examples of partially massless theories beyond the familiar spin-2 case, suggesting a path to generalizing to higher-rank mixed-symmetry tensors. This work extends prior symmetric-tensor approaches, clarifies unitarity and representation-theoretic aspects in (A)dS, and offers a framework for exploring more general mixed-symmetry fields in high-energy theory.

Abstract

In this paper we give explicit gauge invariant Lagrangian formulation for massive theories based on mixed symmetry tensors Φ_{[μν],α}, T_{[μνα],β} and R_{[μν],[αβ]} both in Minkowski as well as in (Anti) de Sitter spaces. In particular, we study all possible massless and partially massless limits for such theories in (A)dS.