$SU(2{)}^2$-invariant $G_2$-instantons

Abstract

We initiate the systematic study of $G_2$-instantons with $SU(2{)}^2$-symmetry. As well as developing foundational theory, we give existence, non-existence and classification results for these instantons. We particularly focus on ${\mathbb{R}}^4\times S^3$ with its two explicitly known distinct holonomy $G_2$ metrics, which have different volume growths at infinity, exhibiting the different behaviour of instantons in these settings. We also give an explicit example of sequences of $G_2$-instantons where "bubbling" and "removable singularity" phenomena occur in the limit.

61 pages; v3 minor changes: accepted in Mathematische Annalen

References in corpus (2)

• New G2 holonomy cones and exotic nearly Kaehler structures on the 6-sphere and the product of a pair of 3-spheres
• $G_2$-instantons over twisted connected sums: an example

Cited by in corpus (11)

• Gauge theory on Aloff-Wallach spaces
• $SU(2{)}^2$-invariant gauge theory on asymptotically conical Calabi-Yau 3-folds
• $G_2$-instantons on the spinor bundle of the 3-sphere
• Deformation Theory of Asymptotically Conical Spin(7)-Instantons
• Deformed $G_2$-instantons on ${\mathbb{R}}^4\times S^3$
• Some remarks on strong ${\mathrm{G}}_2$-structures with torsion
• Coclosed $G_2$-structures on $\text{SU}(2{)}^2$-invariant cohomogeneity one manifolds
• $G_2$-instantons on resolutions of $G_2$-orbifolds
• Explicit abelian instantons on $S^1$-invariant Kähler Einstein $6$-manifolds
• New examples of $G_2$-instantons on ${\mathbb{R}}^4\times S^3$
• $G_2$-instantons on the ALC members of the ${\mathbb{B}}_7$ family