M-theory moduli spaces and torsion-free structures

Abstract : Motivated by the description of $\mathcal{N}=1$ M-theory compactifications to four-dimensions given by Exceptional Generalized Geometry, we propose a way to geometrize the M-theory fluxes by appropriately relating the compactification space to a higher-dimensional manifold equipped with a torsion-free structure. As a non-trivial example of this proposal, we construct a bijection from the set of $Spin(7)$-structures on an eight-dimensional $S^{1}$-bundle to the set of $G_{2}$-structures on the base space, fully characterizing the $G_{2}$-torsion clases when the total space is equipped with a torsion-free $Spin(7)$-structure. Finally, we elaborate on how the higher-dimensional manifold and its moduli space of torsion-free structures can be used to obtain information about the moduli space of M-theory compactifications.
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Mariana Graña, C. S. Shahbazi. M-theory moduli spaces and torsion-free structures. Journal of High Energy Physics, Springer Verlag (Germany), 2015, 2015 (5), ⟨10.1007/JHEP05(2015)085⟩. ⟨cea-01295188⟩

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