Higher Order Integrability in Generalized Holonomy

Details Higher Order Integrability in Generalized Holonomy Higher Order Integrability in Generalized Holonomy

2004-12-14

arxiv.org/abs/hep-th/0412154v1

Nucl.Phys. B760 (2007) 89-103

Physics

High Energy Physics

High Energy Physics - Theory

19 pages, Latex

Scientific paper

10.1016/j.nuclphysb.2006.10.017

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.

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