2005/09/30 by H. Lü, H. Lu, C.N. Pope +3
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Connection (principal bundle) #Cosmology and Gravitation Theories #Geometry #Holonomy #Mathematical physics #Mathematics #Minkowski space #Noncommutative and Quantum Gravity Theories #Order (exchange) #Physics #Spinor #String (physics) #String theory #Supergravity #Supersymmetry #Theoretical physics #hep-th
paper · pdf · doi:10.1016/j.nuclphysb.2006.01.042
published as Nucl.Phys.B741:17-33,2006 · Latex, 23 pages, clarifying comments and references added
arxiv created 2006/01/04 · openalex publication_date 2006/02/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The notion of \it generalised structure groups and \it generalised holonomy groups has been introduced in supergravity, in order to discuss the spinor rotations generated by commutators of supercovariant derivatives when non-vanishing form fields are included, with their associated gamma-matrix structures that go beyond the usual ΓMN of the Riemannian connection. In this paper we investigate the generalisations to the usual Riemannian structure and holonomy groups that result from the inclusion of higher-order string or M-theory corrections in the supercovariant derivative. Even in the absence of background form fields, these corrections introduce additional terms ΓM1... M6 in the supercovariant connection, and hence they lead to enlarged structure and holonomy groups. In some cases, the corrected equations of motion force form fields to become non-zero too, which can further enlarge the groups. Our investigation focuses on the generalised structure and holonomy groups in the transverse spaces Kn of (Minkowski) × Kn backgrounds for n=6, 7, 8 and 10, and shows how the generalised holonomies allow the continued existence of supersymmetric backgrounds even though the usual Riemannian special holonomy is destroyed by the inclusion of the string or M-theory corrections.