SU(2)² -invariant G₂ -instantons

We initiate the systematic study of G₂-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 R⁴ x S³ with its two explicitly known distinct holonomy G₂ metrics, which have different volume growths at infinity, exhibiting the different behaviour of instantons in these settings. We alsogive an explicit example of sequences of G₂-instantons where “bubbling” and “removable singularity” phenomena occur in the limit.