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arXiv · 2106.15640

Maximally twisted eleven-dimensional supergravity

Richard Eager·Fabian Hahner
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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.

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Richard Eager, Fabian Hahner. 2021-06-29. Maximally twisted eleven-dimensional supergravity. https://doi.org/10.1007/s00220-022-04516-5

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