Dual theories for mixed symmetry fields. Spin-two case: (1,1) versus (2,1) Young symmetry type fields

TL;DR

This paper develops a duality framework for mixed symmetry spin-two fields using the parent Lagrangian method, resulting in a family of dual theories with consistent degrees of freedom, extending the concept beyond p-form fields.

Contribution

It introduces a three-parameter family of dual Lagrangians for massive spin-two fields with mixed symmetry, generalizing duality concepts to non p-form fields.

Findings

Constructed dual Lagrangians with a (2,1) tensor field

Ensured correct degrees of freedom in the massless limit

Extended duality concepts to mixed symmetry tensor fields

Abstract

We show that the parent Lagrangian method gives a natural generalization of the dual theories concept for non p-form fields. Using this generalization we construct here a three-parameter family of Lagrangians that are dual to the Fierz-Pauli description of a free massive spin-two system. The dual field is a three-index tensor T, which dinamically belongs to the (2,1) representation of the Lorentz group. As expected, the massless limit of our Lagrangian, which is parameter independent, has two propagating degrees of freedom per space point.