Instantons on the exceptional holonomy manifolds of Bryant and Salamon

We give a construction of G2G2 and Spin(7)Spin(7) instantons on exceptional holonomy manifolds constructed by Bryant and Salamon, by using an ansatz of spherical symmetry coming from the manifolds being the total spaces of rank-4 vector bundles. In the G2G2 case, we show that, in the asymptotically conical model, the connections are asymptotic to Hermitian Yang–Mills connections on the nearly Kähler S3×S3S3×S3.