$SU(2{)}^2$-invariant gauge theory on asymptotically conical Calabi-Yau 3-folds

Abstract

We give a complete description of the behaviour of Calabi-Yau instantons and monopoles with an $SU(2{)}^2$-symmetry, on Calabi-Yau 3-folds with asymptotically conical geometry and $SU(2{)}^2$ acting with co-homogeneity one. We consider gauge theory on the smoothing and the small resolution of the conifold, and on the canonical bundle of ${\mathbb{CP}}^1\times {\mathbb{CP}}^1$, with their known asymptotically conical co-homogeneity one Calabi-Yau metrics, and find new one-parameter families of invariant instantons. We also entirely classify the relevant moduli-spaces of instantons and monopoles satisfying a natural curvature decay condition, and show that the expected bubbling phenomena occur in these families of instantons.

37 pages, 1 figure. v2: exposition shortened, detailed discussion of the abelian case removed for readability. Version accepted into the Journal of Geometric Analysis

References in corpus (1)

• The asymptotic geometry of ${\mathrm{G}}_2$-monopoles

Cited by in corpus (3)

• $G_2$-instantons on the spinor bundle of the 3-sphere
• Isolated singularities in $G_2$-structures with torsion
• $G_2$-instantons on the ALC members of the ${\mathbb{B}}_7$ family