A generalization of Calabi-Yau fourfolds arising from M-theory compactifications

TL;DR

This paper develops a new mathematical framework to analyze flux backgrounds in M-theory compactifications, generalizing Calabi-Yau fourfolds by using differential form relations and Kähler-Atiyah bundles.

Contribution

It introduces a reconstruction theorem linking supersymmetry conditions to differential form relations, generalizing Calabi-Yau fourfold geometry in M-theory compactifications.

Findings

Derived conditions for ${\

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Abstract

Using a reconstruction theorem, we prove that the supersymmetry conditions for a certain class of flux backgrounds are equivalent with a tractable subsystem of relations on differential forms which encodes the full set of contraints arising fom Fierz identities and from the differential and algebraic conditions on the internal part of the supersymmetry generators. The result makes use of the formulation of such problems through K\"{a}hler-Atiyah bundles, which we developed in previous work. Applying this to the most general ${\cal N}=2$ flux compactifications of 11-dimensional supergravity on 8-manifolds, we can extract the conditions constraining such backgrounds and give an overview of the resulting geometry, which generalizes that of Calabi-Yau fourfolds.