Würzburg Seminar on Quantum Field Theory and Gravity

We classify all the possible parity-invariant, non-Abelian couplings involving a partially massless spin-2 field and a pair of massless spin-3/2 fields around anti-de Sitter spacetime AdS_4. We re-derive a non-Abelian vertex found by Yu. M. Zinoviev following a different approach, and make explicit the structure of the non-Abelian gauge algebra, very similar to N=2 supergravity around AdS_4. We show that this vertex is obstructed at higher order in deformation, and that the graviton plus a vector gauge field are required to eliminate most, if not all, of the obstructions. The resulting gauge algebra produces all the structures of the super algebra su(2,2|1), suggesting that the only consistent theory that couples a partially massless spin-2 field with massless gravitini is N=1 pure conformal supergravity expanded around AdS_4.