Almost Special Holonomy in Type IIA&M Theory
arXiv:hep-th/0203060 · doi:10.1016/S0550-3213(02)00484-4
Abstract
We consider spaces M_7 and M_8 of G_2 holonomy and Spin(7) holonomy in seven and eight dimensions, with a U(1) isometry. For metrics where the length of the associated circle is everywhere finite and non-zero, one can perform a Kaluza-Klein reduction of supersymmetric M-theory solutions (Minkowksi)_4\times M_7 or (Minkowksi)_3\times M_8, to give supersymmetric solutions (Minkowksi)_4\times Y_6 or (Minkowksi)_3\times Y_7 in type IIA string theory with a non-singular dilaton. We study the associated six-dimensional and seven-dimensional spaces Y_6 and Y_7 perturbatively in the regime where the string coupling is weak but still non-zero, for which the metrics remain Ricci-flat but that they no longer have special holonomy, at the linearised level. In fact they have ``almost special holonomy,'' which for the case of Y_6 means almost Kahler, together with a further condition. For Y_7 we are led to introduce the notion of an ``almost G_2 manifold,'' for which the associative 3-form is closed but not co-closed. We obtain explicit classes of non-singular metrics of almost special holonomy, associated with the near Gromov-Hausdorff limits of families of complete non-singular G_2 and Spin(7) metrics.
Latex, 26 pages
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Cited by in corpus (10)
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- Kaehler reduction of metrics with holonomy G_2
- On the geometry of closed G2-structure
- Nontrivial RR two-form field strength and SU(3)-structure
- Supersymmetric Intersecting D6-branes and Fluxes in Massive Type IIA String Theory
- Complete non-compact Spin(7) manifolds from self-dual Einstein 4-orbifolds
- New G2 holonomy metrics, D6 branes with inherent U(1)xU(1) isometry and gamma-deformations
- Constructing Calabi-Yau Metrics From Hyperkahler Spaces
- New G_2 metric, D6-branes and Lattice Universe