Yang-Mills solutions on de Sitter space of any dimension

Abstract

For gauge groups SO(n + 1), SU(m + 1), and Sp(l + 1), we construct equivariant Yang-Mills solutions on de Sitter space in n + 1, 2(m + 1), and 4(l + 1) spacetime dimensions. The latter is conformally mapped to a finite cylinder over a coset space realizing an appropriate unit sphere. The equivariance condition reduces the Yang-Mills system to an analog Newtonian particle in one or two dimensions subject to a time-dependent friction and a particular potential. We analyze some properties of the solutions such as their action and energy and display all analytic ones. Beyond dS(4), all such configurations have finite energy but infinite action.