Dressing fields for supersymmetry: The cases of the Rarita-Schwinger and gravitino fields

TL;DR

This paper applies the dressing field method to supersymmetric theories, showing that gauge-fixing conditions for Rarita-Schwinger and gravitino fields can be understood as symmetry reduction, leading to relational variable formulations.

Contribution

It introduces the dressing field method into supersymmetry, providing a novel perspective on gauge fixing and field interpretation in supergravity.

Findings

Gauge-fixing conditions are instances of the dressing field method.

Rarita-Schwinger and gravitino fields can be viewed as relational variables.

First application of dressing field method to supersymmetric theories.

Abstract

In this paper we argue that the gauge-fixing conditions typically used to extract the (off-shell) degrees of freedom of the Rarita-Schwinger spinor-vector and gravitino, respectively in rigid supersymmetric field theory and supergravity, are actually instances of the dressing field method of symmetry reduction. Since the latter has a natural relation interpretation, solving the ``gauge-fixing condition" -- or, better, ``dressing functional constraints" -- actually realises the Rarita-Schwinger spinor-vector and the gravitino fields as (non-local) relational variables. To the best of our knowledge, this is the first application of the dressing field method to supersymmetric theories.