Abstract

After proving the impossibility of consistent non-minimal coupling of a real Rarita-Schwinger gauge field to electromagnetism, we re-derive the necessity of introducing the graviton in order to couple a complex Rarita-Schwinger gauge field to electromagnetism, with or without a cosmological term, thereby obtaining mathcal{N} = 2 pure supergravity as the only possibility. These results are obtained with the BRST-BV deformation method around the flat and (A)dS backgrounds in 4 dimensions. The same method applied to nv vectors, mathcal{N} real spin-3/2 gauge fields and at most one real spinor field also requires gravity and yields mathcal{N} = 3 pure supergravity as well as mathcal{N} = 1 pure supergravity coupled to a vector supermultiplet, with or without cosmological terms. Independently of the matter content, we finally derive strong necessary quadratic constraints on the possible gaugings for an arbitrary number of spin-1 and spin-3/2 gauge fields, that are relevant for larger supergravities.

Highlights

  • After proving the impossibility of consistent non-minimal coupling of a real Rarita-Schwinger gauge field to electromagnetism, we re-derive the necessity of introducing the graviton in order to couple a complex Rarita-Schwinger gauge field to electromagnetism, with or without a cosmological term, thereby obtaining N = 2 pure supergravity as the only possibility

  • The same method applied to nv vectors, N real spin-3/2 gauge fields and at most one real spinor field requires gravity and yields N = 3 pure supergravity as well as N = 1 pure supergravity coupled to a vector supermultiplet, with or without cosmological terms

  • Starting with two real Rarita-Schwinger gauge fields coupled to Maxwell fields, we see that the introduction of the graviton is necessary in order to ensure consistency at second order in the infinitesimal deformation parameters

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Summary

Cohomological reformulation of the deformation problem

We briefly review the cohomological procedure [7] for perturbative deformation of a Lagrangian gauge theory, exemplifying it on the free theories describing massless spin-s fields.

Cohomological approach
First starting point: free BV functionals in flat background
Second starting point: anti de Sitter background
Deformations around AdS background
General and specific quadratic constraints
Conclusions and perspectives
A Conventions and some Diracology
B Appearance of conserved currents in gaugings
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