Weyl Action of Two-Column Mixed-Symmetry Field and Its Factorization Around (A)dS Space

TL;DR

This paper explores the Weyl action for two-column mixed-symmetry fields in (A)dS space, demonstrating a unique deformation from flat space, factorization into two-derivative actions, and conditions for unitarity in specific dimensions.

Contribution

It introduces a smooth, unique deformation of flat space Weyl actions to (A)dS space for mixed-symmetry fields, extending factorization patterns known for symmetric higher spin fields.

Findings

The Weyl action can be uniquely deformed to (A)dS space while preserving gauge symmetries.

The action factorizes into two two-derivative gauge-invariant actions with different Young diagram parameters.

Unitarity can be achieved in special dimensions through specific mass deformations.

Abstract

We investigate the four-derivative free Weyl action for two-column mixed-symmetry field that makes use of maximal gauge symmetries. In flat space, the action can be uniquely determined from gauge and Weyl (trace shift) symmetry requirements. We show that there is a smooth and unique deformation of the flat action to (A)dS which keeps the same amount of gauge symmetries. This action admits a factorization into two distinct two-derivative actions having gauge parameters of different Young diagrams. Hence, this factorization pattern naturally extends that of the Weyl actions of symmetric higher spin fields to mixed-symmetry cases. The mass-deformation for these actions can be realized preserving one of the gauge symmetries. Although generically non-unitary, in special dimensions, unitarity is achieved selecting different mass deformations for dS and AdS. We consider particular examples of our construction such as New Massive Gravity in three dimensions, linearized bigravity in four dimensions and their arbitrary dimensional generalizations.