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

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.

14 pages

References in corpus (5)

• N=1 and N=2 pure supergravities on a manifold with boundary
• Bundle geometry of the connection space, covariant Hamiltonian formalism, the problem of boundaries in gauge theories, and the dressing field method
• $\mathcal{N}=2$ AdS${}_4$ supergravity, holography and Ward identities
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• Unconventional Supersymmetry via the Dressing Field Method
• Spacetime boundaries do not break diffeomorphism and gauge symmetries
• Toward Manifest Relationality in Transformers via Symmetry Reduction
• Mechanics as a general-relativistic gauge field theory, and Relational Quantization