M-theory on non-K\"ahler manifolds

TL;DR

This paper explores M-theory compactifications on a broader class of internal manifolds, specifically locally conformally K"ahler manifolds, which generalize Calabi-Yau spaces while preserving supersymmetry.

Contribution

It demonstrates that supersymmetric M-theory compactifications can occur on locally conformally K"ahler manifolds, expanding the known geometric frameworks beyond Calabi-Yau manifolds.

Findings

Supersymmetric M-theory compactifications are compatible with locally conformally K"ahler manifolds.

These manifolds locally admit a Calabi-Yau structure.

The class of internal manifolds for M-theory compactification is broader than previously known.

Abstract

We show that supersymmetric M-theory compactifications to three-dimensional Minkowski space-time preserving $\mathcal{N}=2$ supersymmetry allow for a class of internal manifolds more general than the Calabi-Yau one, namely the class of locally conformally K\"ahler manifolds which locally carry a preferred Calabi-Yau structure.