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.
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ArXiv ePrint: 1802.02966
Senior Research Associate of the F.R.S.-FNRS (Belgium) (Nicolas Boulanger).
Research Fellow of the F.R.S.-FNRS (Belgium) (Lucas Traina).
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Boulanger, N., Julia, B. & Traina, L. Uniqueness of \( \mathcal{N} \) = 2 and 3 pure supergravities in 4D. J. High Energ. Phys. 2018, 97 (2018). https://doi.org/10.1007/JHEP04(2018)097
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DOI: https://doi.org/10.1007/JHEP04(2018)097