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

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 $n_v$ 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 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.

arXiv commentLaTeX, 31 + 1 pages, no figure. v2: Extended discussion at the end of Section 3, corrected typos and references added

References in corpus (13)

• Consistent couplings between fields with a gauge freedom and deformations of the master equation
• Antibracket, Antifields and Gauge-Theory Quantization
• Local BRST cohomology in the antifield formalism: I. General theorems
• Inconsistency of interacting, multi-graviton theories
• Local BRST cohomology in the antifield formalism: II. Application to Yang-Mills theory
• Pure de Sitter Supergravity
• Higher-Spin Fermionic Gauge Fields and Their Electromagnetic Coupling
• Consistent Interactions between Gauge Fields and Local BRST Cohomology : The Example of Yang-Mills Models
• Gravitational Interactions of Higher-Spin Fermions
• A note on the uniqueness of D=4 N=1 Supergravity
• Conserved currents and gauge invariance in Yang-Mills theory
• Deformations of vector-scalar models
• Gauge-invariant massive BF models

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• Consistent and non-consistent deformations of gravitational theories