SU(2) 2 -invariant G2 -instantons

Abstract

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× 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 also give an explicit example of sequences of G2-instantons where “bubbling” and “removable singularity” phenomena occur in the limit.