First Order Formalism for Massive Mixed Symmetry Tensor Fields in Minkowski and (A)dS Spaces

TL;DR

The paper develops a gauge-invariant, first-order framework for massive mixed-symmetry tensor fields in Minkowski and (A)dS spaces by augmenting massless sectors with carefully chosen Goldstone pairs and systematically adding low-derivative and mass-like terms. It derives precise parameter relations that ensure invariance under extended gauge symmetries and reveals how (A)dS cosmological constant and field content control massless and partially massless limits. For each of the studied tensors—$h_\mu{}^a$, $\Phi_{[\mu\nu],\alpha}$, and $R_{[\mu\nu],[\alpha\beta]}$—the authors identify when a true massless limit exists and characterize partially massless branches, including explicit mass scales such as $m^2 = - \kappa (d-2)/2$, $m^2 = \frac{3}{8}\kappa (d-3)$, and $m^2 = \frac{\kappa (d-4)}{8}$. They also show how AdS and dS backgrounds yield decoupled subsystems or alternative partially massless realizations, enriching the understanding of high-spin gauge theories in curved backgrounds. Overall, the work extends first-order, gauge-invariant descriptions to massive mixed-symmetry fields and clarifies the structure of partially massless limits in (A)dS spaces.

Abstract

In this paper we extend our recent results (hep-th/0304067) on the first order formulation for the massless mixed symmetry tensor fields to the case of massive fields both in Minkowski as well as in (Anti) de Sitter spaces (including all possible massless and partially massless limits). Main physical results are essentially the same as in hep-th/0211233.