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arXiv · 1802.02966

Uniqueness of $\mathcal{N}=2$ and $3$ pure supergravities in 4D

Nicolas Boulanger·Bernard Julia·Lucas Traina
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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 ${\cal N}=2$ 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 $n_{v}$ vectors, ${\cal N}$ real spin-3/2 gauge fields and at most one real spinor field also requires gravity and yields ${\cal N}=3$ pure supergravity as well as ${\cal N}=1$ pure supergravity coupled to a vector supermultiplet, with or without cosmological terms. Independently from 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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Nicolas Boulanger, Bernard Julia, Lucas Traina. 2018-02-08. Uniqueness of $\mathcal{N}=2$ and $3$ pure supergravities in 4D. https://doi.org/10.1007/jhep04(2018)097

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