Intersecting 6-branes from new 7-manifolds with \(G_{2}\) holonomy. (English) Zbl 1226.81157
Summary: We discuss a new family of metrics of 7-manifolds with \(G_{2}\) holonomy, which are \(\mathbb{R}^{3}\) bundles over a quaternionic space. The metrics depend on five parameters and have two abelian isometries. Certain singularities of the \(G_{2}\) manifolds are related to fixed points of these isometries; there are two combinations of Killing vectors that possess co-dimension four fixed points which yield upon compactification only intersecting D6-branes if one also identifies two parameters. Two of the remaining parameters are quantized and we argue that they are related to the number of D6-branes, which appear in three stacks. We perform explicitly the reduction to the type IIA model.
MSC:
81T30 | String and superstring theories; other extended objects (e.g., branes) in quantum field theory |
53C25 | Special Riemannian manifolds (Einstein, Sasakian, etc.) |
53C29 | Issues of holonomy in differential geometry |
81T60 | Supersymmetric field theories in quantum mechanics |
83E30 | String and superstring theories in gravitational theory |
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