Maximally twisted eleven-dimensional supergravity

TL;DR

This paper performs the maximal twist of eleven-dimensional supergravity, revealing a partially topological theory on manifolds with specific holonomy, and explicitly constructs the twisted theory using BV formalism.

Contribution

It provides an explicit BV complex description and demonstrates the twisted theory as a tensor product of de Rham and Dolbeault complexes on special holonomy manifolds.

Findings

The twisted theory is given by the tensor product of de Rham and Dolbeault complexes.

The twist exists on manifolds with G_2 × SU(2) holonomy.

The construction confirms a conjecture by Costello.

Abstract

We perform the maximal twist of eleven-dimensional supergravity. This twist is partially topological and exists on manifolds of $G_2 \times SU(2)$ 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 $L_\infty$ 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 $G_2$ and $SU(2)$ holonomy manifolds as conjectured by Costello.