Features of gravity–Yang-Mills hierarchies in d dimensions

Higher-dimensional, direct analogues of the usual d=4 Einstein–Yang-Mills (EYM) systems are studied. They feature single members of both the gravitational and the Yang-Mills hierarchies in d=4p-dimensional spacetimes, both consisting of 2p-form curvature terms only. This enables us to probe the effects of higher order gravitational terms, which in the presence of the usual Einstein term would be masked. Regular and black hole solutions are constructed in 2p+2<=d<=4p, in which dimensions the total mass-energy is finite, generalizing the familiar Bartnik-McKinnon solutions in EYM theory for p=1. In d=4p, this similarity is complete. In the special case of d=2p+1, just beyond the finite energy range of d, exact solutions in closed form are found. Finally, d=2p+1 purely gravitational systems, whose solutions generalize the static d=3 BTZ solutions, are discussed.

©2006 The American Physical Society