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Higher Order Integrability in Generalized Holonomy
Supersymmetric backgrounds in M-theory often involve four-form flux in
addition to pure geometry. In such cases, the classification of supersymmetric
vacua involves the notion of generalized holonomy taking values in SL(32,R),
the Clifford group for eleven-dimensional spinors. Although previous
investigations of generalized holonomy have focused on the curvature
\Rm_{MN}(\Omega) of the generalized SL(32,R) connection \Omega_M, we
demonstrate that this local information is incomplete, and that satisfying the
higher order integrability conditions is an essential feature of generalized
holonomy. We also show that, while this result differs from the case of
ordinary Riemannian holonomy, it is nevertheless compatible with the
Ambrose-Singer holonomy theorem.Comment: 19 pages, Late