Higher order integrability in generalized holonomy Original Research Article

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 image, the Clifford group for eleven-dimensional spinors. Although previous investigations of generalized holonomy have focused on the curvature image of the generalized image connection image, 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.