SU(2) 2 -invariant G 2 -instantons.

We initiate the systematic study of G 2 -instantons with SU(2) 2 -symmetry. As well as developing foundational theory, we give existence, non-existence and classification results for these instantons. We particularly focus on R 4 × S 3 with its two explicitly known distinct holonomy G 2 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 G 2 -instantons where "bubbling" and "removable singularity" phenomena occur in the limit.