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Higher order integrability in generalized holonomy

AuthorsBatrachenko, A.; Liu, James T.; Varela, Óscar; Wen, W. Y.
KeywordsKilling spinors
Generalized holonomy
Issue Date1-Jan-2007
CitationNuclear Physics B 760(1-2): 89-103 (2007)
AbstractSupersymmetric 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 R-MN(Ω) of the generalized SL(32,R) connection Ω(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.
Description15 pages.-- ISI Article Identifier: 000243546800004.-- ArXiv pre-print available at: http://arxiv.org/abs/hep-th/0412154
Publisher version (URL)http://dx.doi.org/10.1016/j.nuclphysb.2006.10.017
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