A construction of Spin(7)-instantons

Abstract

Joyce constructed examples of compact eight-manifolds with holonomy Spin(7), starting with a Calabi-Yau four-orbifold with isolated singular points of a special kind. That construction can be seen as the gluing of ALE Spin(7)-manifolds to each singular point of the Calabi-Yau four-orbifold divided by an anti-holomorphic involution fixing only the singular points. On the other hand, there are higher-dimensional analogues of anti-self-dual instantons in four dimensions on Spin(7)-manifolds, which are called Spin(7)-instantons. They are minimizers of the Yang-Mills action, and the Spin(7)-instanton equation together with a gauge fixing condition forms an elliptic system. In this article, we construct Spin(7)-instantons on the examples of compact Spin(7)-manifolds above, starting with Hermitian-Einstein connections on the Calabi-Yau four-orbifolds and ALE spaces. Under some assumptions on the Hermitian-Einstein connections, we glue them together to obtain Spin(7)-instantons on the compact Spin(7)-manifolds. We also give a simple example of our construction.

37 pages, typos corrected

References in corpus (3)

• Gauge Theory in higher dimensions, II
• On the construction of solutions to the Yang-Mills equations in higher dimensions
• Complex anti-self-dual instantons and Cayley submanifolds

Cited by in corpus (7)

• Orientability of moduli spaces of Spin(7)-instantons and coherent sheaves on Calabi-Yau 4-folds
• Instantons on the exceptional holonomy manifolds of Bryant and Salamon
• On orientations for gauge-theoretic moduli spaces
• Deformations of nearly Kähler instantons
• Spin(7)-instantons, Cayley submanifolds, and Fueter sections
• Deformation Theory of Asymptotically Conical Spin(7)-Instantons
• A topological quantum field theory for $\mathrm{Spin}(7)$-instantons