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
Summary
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.
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