Eleven-dimensional supergravity as a Calabi–Yau twofold

Abstract We construct a generalization of Poisson–Chern–Simons theory, defined on any supermanifold equipped with an appropriate filtration of the tangent bundle. Our construction recovers interacting eleven-dimensional supergravity in Cederwall’s formulation, as well as all possible twists of the theory, and does so in a uniform and geometric fashion. Among other things, this proves that Costello’s description of the maximal twist is the twist of eleven-dimensional supergravity in its pure spinor description. It also provides a pure spinor lift of the interactions in the minimally twisted theory. Our techniques enhance the BV formulation of the interactions of each theory to a homotopy Poisson structure by defining a compatible graded-commutative product; this suggests interpretations in terms of deformations of geometric structures on superspace, and provides some concrete evidence for a first-quantized origin of the theories.