Monopoles on the Bryant-Salamon G2-manifolds

JOURNAL OF GEOMETRY AND PHYSICS

卷:86

Article

Oliveira, Goncalo

关键词: G(2) manifold;    Monopoles;    Gauge theory;   

DOI  :  10.1016/j.geomphys.2014.10.005

来源: Elsevier

【 摘 要 】

G(2)-monopoles are solutions to gauge theoretical equations on noncompact 7-manifolds of G(2) holonomy. We shall study this equation on the 3 Bryant-Salamon manifolds. We construct examples of G(2)-monopoles on two of these manifolds, namely the total space of the bundle of anti-self-dual two forms over the S-4 and CP2. These are the first nontrivial examples of G(2)-monopoles. Associated with each monopole there is a parameter m is an element of R+, known as the mass of the monopole. We prove that under a symmetry assumption, for each given m is an element of R+ there is a unique monopole with mass m. We also find explicit irreducible G(2)-instantons on Lambda(2)(-)(S-4) and on Lambda(2)(-)(CP2). The third Bryant-Salamon G(2)-metric lives on the spinor bundle over the 3-sphere. In this case we produce a vanishing theorem for monopoles. (C) 2014 Elsevier By. All rights reserved.

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