${\mathrm{G}}_2$-instantons on generalised Kummer constructions

Abstract

In this article we introduce a method to construct ${\mathrm{G}}_2$-instantons on ${\mathrm{G}}_2$-manifolds arising from Joyce's generalised Kummer construction. The method is based on gluing ASD instantons over ALE spaces to flat bundles on ${\mathrm{G}}_2$-orbifolds of the form $T^7/\Gamma$. We use this construction to produce non-trivial examples of ${\mathrm{G}}_2$-instantons.

44 pages; published version

Cited by in corpus (18)

• Supersymmetric Protection and the Swampland
• On Gauge Enhancement and Singular Limits in $G_2$ Compactifications of M-theory
• $G_2$-instantons on twisted connected sums
• Instantons on the exceptional holonomy manifolds of Bryant and Salamon
• On orientations for gauge-theoretic moduli spaces
• Infinitesimal moduli of G2 holonomy manifolds with instanton bundles
• Degenerations of ${\mathbf{C}}^n$ and Calabi-Yau metrics
• $SU(2{)}^2$-invariant $G_2$-instantons
• Deformations of nearly Kähler instantons
• Sigma-model limit of Yang-Mills instantons in higher dimensions
• Marginal deformations of heterotic $G_2$ sigma models
• Gauge theory on Aloff-Wallach spaces
• Instantons on sine-cones over Sasakian manifolds
• Spin(7)-instantons, Cayley submanifolds, and Fueter sections
• Current progress on $G_2$--instantons over twisted connected sums
• Associative submanifolds in Joyce's generalised Kummer constructions
• $G_2$-instantons on resolutions of $G_2$-orbifolds
• New examples of $G_2$-instantons on ${\mathbb{R}}^4\times S^3$