$$SU(2)^2$$-Invariant Gauge Theory on Asymptotically Conical Calabi–Yau 3-Folds

Abstract

AbstractWe give a complete description of the behaviour of Calabi–Yau instantons and monopoles with an$$SU(2)^2$$SU(2)2-symmetry, on Calabi–Yau 3-folds with asymptotically conical geometry and$$SU(2)^2$$SU(2)2acting with co-homogeneity one. We consider gauge theory on the smoothing and small resolution of the conifold, and on the canonical bundle of$$\mathbb{C}\mathbb{P}^1 \times \mathbb{C}\mathbb{P}^1$$CP1×CP1, 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.