Octonionic Yang-Mills Instanton on Quaternionic Line Bundle of Spin(7) Holonomy

Abstract

The total space of the spinor bundle on the four dimensional sphere S^4 is a quaternionic line bundle that admits a metric of Spin(7) holonomy. We consider octonionic Yang-Mills instanton on this eight dimensional gravitational instanton. This is a higher dimensional generalization of (anti-)self-dual instanton on the Eguchi-Hanson space. We propose an ansatz for Spin(7) Yang-Mills field and derive a system of non-linear ordinary differential equations. The solutions are classified according to the asymptotic behavior at infinity. We give a complete solution, when the gauge group is reduced to a product of SU(2) subalgebras in Spin(7). The existence of more general Spin(7) valued solutions can be seen by making an asymptotic expansion.

A reference added; 22 pages,a final version to appear J.Geom.Phys

References in corpus (5)

• Special Quantum Field Theories In Eight And Other Dimensions
• Higher Dimensional Analogues of Donaldson-Witten Theory
• Chern-Simons and Twisted Supersymmetry in Higher Dimensions
• Octonionic Gravitational Instantons
• Cohomological Yang-Mills Theory in Eight Dimensions

Cited by in corpus (6)

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• Instantons on Special Holonomy Manifolds
• Deformations of nearly Kähler instantons
• Quaternionic Quantization Principle in General Relativity and Supergravity
• Eight Dimensional Noncommutative Instantons and D0-D8 Bound States with B-field
• Partition functions on squashed seven-spheres and holography