Instantons on the exceptional holonomy manifolds of Bryant and Salamon

Abstract

We give a construction of \(G_2\) and \(Spin(7)\) 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 \(G_2\) case, we show that, in the asymptotically conical model, the connections are asymptotic to Hermitian Yang-Mills connections on the nearly K\"ahler \(S^3\times S^3\).