Abstract
We consider spaces of “virtual” constrained generalized Killing spinors, i.e. spaces of Majorana spinors which correspond to “off-shell” s-extended supersymmetry in compactifications of eleven-dimensional supergravity based on eight-manifolds M. Such spaces naturally induce two stratifications of M, called the chirality and stabilizer stratification. For the case s = 2, we describe the former using the canonical Whitney stratification of a three-dimensional semi-algebraic set \( \mathrm{\mathcal{R}} \). We also show that the stabilizer stratification coincides with the rank stratification of a cosmooth generalized distribution \( {\mathcal{D}}_0 \) and describe it explicitly using the Whitney stratification of a four-dimensional semi-algebraic set \( \mathfrak{P} \). The stabilizer groups along the strata are isomorphic with SU(2), SU(3), G2 or SU(4), where SU(2) corresponds to the open stratum, which is generically non-empty. We also determine the rank stratification of a larger generalized distribution \( \mathcal{D} \) which turns out to be integrable in the case of compactifications down to AdS3.
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Babalic, E.M., Lazaroiu, C.I. The landscape of G-structures in eight-manifold compactifications of M-theory. J. High Energ. Phys. 2015, 7 (2015). https://doi.org/10.1007/JHEP11(2015)007
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DOI: https://doi.org/10.1007/JHEP11(2015)007