SU(2)[Formula: see text] -invariant [Formula: see text] -instantons

We initiate the systematic study of [Formula: see text] -instantons with SU(2)[Formula: see text] -symmetry. As well as developing foundational theory, we give existence, non-existence and classification results for these instantons. We particularly focus on [Formula: see text] with its two explicitly known distinct holonomy [Formula: see text] 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 [Formula: see text] -instantons where “bubbling” and “removable singularity” phenomena occur in the limit.