# Spin(7)-manifolds in compactifications to four dimensions

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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 $\mathcal{M}_{8}$ equipped with a particular set of tensors $\mathfrak{S}$ that allow to naturally embed in $\mathcal{M}_{8}$ 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 $\mathcal{M}_{8}$ 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 $\mathcal{M}_{8}$, 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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Journal articles

Cited literature [51 references]

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### Citation

Mariana Graña, C. S. Shahbazi, Marco Zambon. Spin(7)-manifolds in compactifications to four dimensions. Journal of High Energy Physics, Springer Verlag (Germany), 2014, 2014 (11), ⟨10.1007/JHEP11(2014)046⟩. ⟨cea-01295469⟩

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