Einstein manifolds, Abelian instantons, bundle reduction and the cosmological constant

The antiself-dual projection of the spin connections of certain four-dimens ional Einstein manifolds can be Abelian in nature. These configurations sig nify bundle reductions. By a theorem of Kobayashi and Nomizu such a process is predicated on the existence of a covariantly constant field. It turns o ut that even without fundamental Higgs fields and other physical matter, gr avitational self-interactions can generate this mechanism if the cosmologic al constant is non-vanishing. This paper identifies the order parameter, an d clarifies how these Abelian instanton solutions are associated with a Hig gs triplet which causes the bundle reduction from the SO(3) gauge group to U(1).