Monopoles on the Bryant–Salamon G2G2-manifolds

G2G2-monopoles are solutions to gauge theoretical equations on noncompact 77-manifolds of G2G2 holonomy. We shall study this equation on the 33 Bryant–Salamon manifolds. We construct examples of G2G2-monopoles on two of these manifolds, namely the total space of the bundle of anti-self-dual two forms over the S4S4 and CP2CP2. These are the first nontrivial examples of G2G2-monopoles.Associated with each monopole there is a parameter m∈R+m∈R+, known as the mass of the monopole. We prove that under a symmetry assumption, for each given m∈R+m∈R+ there is a unique monopole with mass mm. We also find explicit irreducible G2G2-instantons on Λ−2(S4) and on Λ−2(CP2).The third Bryant–Salamon G2G2-metric lives on the spinor bundle over the 33-sphere. In this case we produce a vanishing theorem for monopoles.