Maximally Twisted Eleven-Dimensional Supergravity

Abstract

AbstractWe perform the maximal twist of eleven-dimensional supergravity. This twist is partially topological and exists on manifolds of $$G_2 \times SU(2)$$ G 2 × S U ( 2 ) holonomy. Our derivation starts with an explicit description of the Batalin–Vilkovisky complex associated to the three-form multiplet in the pure spinor superfield formalism. We then determine the $$L_\infty $$ L ∞ module structure of the supersymmetry algebra on the component fields. We twist the theory by modifying the differential of the Batalin–Vilkovisky complex to incorporate the action of a scalar supercharge. We find that the resulting free twisted theory is given by the tensor product of the de Rham and Dolbeault complexes of the respective $$G_2$$ G 2 and SU(2) holonomy manifolds as conjectured by Costello.