Twisted eleven-dimensional supergravity

TL;DR

This paper constructs a novel interacting holomorphic/topological theory in eleven dimensions, aligning with twisted supergravity, and explores its symmetry algebra and potential holographic implications.

Contribution

It introduces a new fully interacting twisted eleven-dimensional supergravity model based on Calabi-Yau fivefolds and analyzes its symmetry structure and holographic prospects.

Findings

The model matches the holomorphic twist of 11D supergravity multiplet.

The symmetry algebra is an $L_$ extension of $E(5,10)$.

Potential for a holomorphic twisted holography framework.

Abstract

We construct a fully interacting holomorphic/topological theory in eleven dimensions that is defined on products of Calabi-Yau fivefolds with real one-manifolds. The theory describes a particular deformation of the cotangent bundle to the moduli space of Calabi-Yau structures on the fivefold. Its field content matches the holomorphic (or minimal) twist of the eleven-dimensional supergravity multiplet recently computed by the second two authors, and we offer numerous consistency checks showing that the interactions correctly describe interacting twisted eleven-dimensional supergravity at the perturbative level. We prove that the global symmetry algebra of our model on flat space is an $L_\infty$ central extension of the infinite-dimensional simple exceptional super Lie algebra $E(5,10)$, following a recent suggestion of Cederwall in the context of the relevant pure spinor model. Twists of superconformal algebras map to the fields of our model on the complement of a stack of M2 or M5 branes, laying the groundwork for a fully holomorphic version of twisted holography in this context.