Maximally twisted eleven-dimensional supergravity

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.

arXiv comment40 pages, 10 tables

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Cited by in corpus (9)

• Perspectives on the pure spinor superfield formalism
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• Holomorphic boundary conditions for topological field theories via branes in twisted supergravity
• The Derived Pure Spinor Formalism as an Equivalence of Categories
• Six-dimensional supermultiplets from bundles on projective spaces
• Exploring Felix Klein's contested modernism
• Twisting BFSS & IKKT
• Holomorphic field theories and higher algebra