Spin(7)-manifolds in compactifications to four dimensions

Mariana Graña (1) , C. S. Shahbazi (1) , Marco Zambon (2, 3)

1 IPHT - Institut de Physique Théorique - UMR CNRS 3681
2 ICMAT - Instituto de Ciencias Matematicas
3 UAM - Universidad Autónoma de Madrid

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.

Domains: High Energy Physics - Theory [hep-th]

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