Abstract
We describe off-shell \( \mathcal{N}=1 \) M-theory compactifications down to four dimensions in terms of eight-dimensional manifolds equipped with a topological Spin(7)-structure. Motivated by the exceptionally generalized geometry formulation of M-theory compactifications, we consider an eight-dimensional manifold \( {\mathrm{\mathcal{M}}}_8 \) equipped with a particular set of tensors \( \mathfrak{S} \) that allow to naturally embed in \( {\mathrm{\mathcal{M}}}_8 \) a family of G 2-structure seven-dimensional manifolds as the leaves of a codimension-one foliation. Under a different set of assumptions, \( \mathfrak{S} \) allows to make \( {\mathrm{\mathcal{M}}}_8 \) into a principal S 1 bundle, which is equipped with a topological Spin(7)-structure if the base is equipped with a topological G 2-structure. We also show that \( \mathfrak{S} \) can be naturally used to describe regular as well as a singular elliptic fibrations on \( {\mathrm{\mathcal{M}}}_8 \), which may be relevant for F-theory applications, and prove several mathematical results concerning the relation between topological G 2-structures in seven dimensions and topological Spin(7)-structures in eight dimensions.
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Graña, M., Shahbazi, C.S. & Zambon, M. Spin(7)-manifolds in compactifications to four dimensions. J. High Energ. Phys. 2014, 46 (2014). https://doi.org/10.1007/JHEP11(2014)046
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DOI: https://doi.org/10.1007/JHEP11(2014)046