Cohomogeneity One Manifolds of Spin(7) and G2 Holonomy
By M. Cvetič, G. W. Gibbons, Hsueh-I Lu, C. Pope. 2001
171 citations recorded by the source corpus.
In this paper, we look for metrics of cohomogeneity one in D = 8 and D = 7 dimensions with Spin(7) and G2 holonomy respectively. In D = 8, we first consider the case of principal orbits that are S 7 , viewed as an S 3 bundle over S 4 with triaxial squashing of the S 3 fibres. This gives a more general system of first-order equations for Spin(7) holonomy than has been solved previously. Using numerical methods, we establish the existence of new non-singular asymptotically locally conical (ALC) Spin(7) metrics on line bundles over CP 3 , with a non-trivial parameter that characterises the homogeneous squashing of CP 3 . We then consider the case where the principal orbits are the Aloff-Wallach spaces N(k, l) = SU(3)/U(1), where the integers k and l characterise the embedding of U(1). We find new ALC and AC metrics of Spin(7) holonomy, as solutions of the first-order equations that we obtained previously in hep-th/0102185. These include certain explicit ALC metrics for all N(k, l), and numerical and perturbative results for ALC families with AC limits. We then study D = 7 metrics of G2 holonomy, and find new explicit examples, which, however, are singular, where the principal orbits are the flag manifold SU(3)/(U(1) × U(1)). We also obtain numerical results for new non-singular metrics with principal orbits that are S 3 × S 3 . Additional topics include a detailed and explicit discussion of the Einstein metrics
Subfields: Mathematical Physics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/be3b2d11260915a76b55ff459b5c4b3cf85bdcca
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Citations in the corpus
- Orientifolds of K3 and Calabi-Yau manifolds with intersecting D-branes (2002, background): “metric on the cone on CIP(3) with holonomy G2 is known [147,148,149].”
- G-Structures and Wrapped NS5-Branes (2002, background): “Another example is to start with a cohomogeneity one manifold with principal orbits SU( 3)/U (1) × U( 1). Such G2 structures have appeared in [29, 30 ], and solutions have been found for a G2 metric on the R 3 bundle over CP 2 [28].”