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

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 canoni-cal bundle of CP1 x 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.