G₂-instantons on the ALC members of the B7 family

Using co-homogeneity one symmetries, we construct a two-parameter family of non-abelian G2-instantons on every member of the asymptotically locally conical B7-family of G2-metrics on S3×R4, and classify the resulting solutions. These solutions can be described as perturbations of a one-parameter family of abelian instantons, arising from the Killing vector-field generating the asymptotic circle fibre. Generically, these perturbations decay exponentially to the model, but we find a one-parameter family of instantons with polynomial decay. Moreover, we relate the two-parameter family to a lift of an explicit two-parameter family of anti-self-dual instantons on Taub-NUT R4, fibred over S3 in an adiabatic limit.