Counterpart of the Weyl tensor for Rarita-Schwinger type fields

TL;DR

This paper constructs a modified, unconstrained field strength for Rarita-Schwinger fields in higher dimensions, linking it to the supercovariant Weyl tensor in supergravity, with on-shell equivalence to standard field strengths.

Contribution

It introduces a new modified field strength for Rarita-Schwinger fields that is not constrained by equations, connecting it to supergravity's supercovariant Weyl tensor.

Findings

Modified field strength is unconstrained and related to the Weyl tensor.

On-shell, the modified and standard field strengths coincide.

Results extend to derivatives of Dirac spinor fields.

Abstract

In dimensions larger than 3 a modified field strength for Rarita-Schwinger type fields is constructed whose components are not constrained by the field equations. In supergravity theories the result provides a modified (supercovariant) gravitino field strength related by supersymmetry to the (supercovariantized) Weyl tensor. In various cases, such as for free Rarita-Schwinger type gauge fields and for gravitino fields in several supergravity theories, the modified field strength coincides on-shell with the usual field strength. A corresponding result for first order derivatives of Dirac type spinor fields is also presented.