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 small resolution of the conifold, and on the canonical bundle of mathbb{C}mathbb{P}^1 times mathbb{C}mathbb{P}^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.