Finite energy-action solutions of p1 Yang-Mills equations on p2 Schwarzschild and deSitter backgrounds in dimensions d≥4

Physically relevant gauge and gravitational theories can be seen as special members of hierarchies of more elaborate systems. The Yang-Mills (YM) system is the first member of a hierarchy of Lagrangians which we will index by p(1), and the Einstein-Hilbert (EH) system of general relativity is the first member of another hierarchy which we index by p(2). In this paper, we study the classical equations of the p(1)=1,2 YM hierarchy considered in the background of special geometries (Schwarzschild, deSitter, anti-deSitter) of the p(2)=1,2,3 EH hierarchy. Solutions are obtained in various dimensions and lead to several examples of nonself-dual YM fields. When p(1)=p(2) self-dual solutions exist in addition. Their action is equal to the Chern-Pontryagin charge and can be compared with that of the nonself-dual solutions. (C) 2000 American Institute of Physics. [S0022-2488(00)04008-1].