Yang-Mills instantons on cones and sine-cones over nearly Kähler manifolds

Details Yang-Mills instantons on cones and sine-cones over nearly Kähler manifolds Yang-Mills instantons on cones and sine-cones over nearly Kähler manifolds

2011-08-19

arxiv.org/abs/1108.3951v1

Physics

High Energy Physics

High Energy Physics - Theory

1+21 pages

Scientific paper

We present a unified eight-dimensional approach to instanton equations on several seven-dimensional manifolds associated to a six-dimensional homogeneous nearly K\"ahler manifold. The cone over the sine-cone on a nearly K\"ahler manifold has holonomy group Spin(7) and can be foliated by submanifolds with either holonomy group G_2, a nearly parallel G_2-structure or a cocalibrated G_2-structure. We show that there is a G_2-instanton on each of these seven-dimensional manifolds which gives rise to a Spin(7)-instanton in eight dimensions. The well-known octonionic instantons on R^7 and R^8 are contained in our construction as the special cases of an instanton on the cone and on the cone over the sine-cone, both over the six-sphere, respectively.

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