Yang-Mills solutions on de Sitter space of any dimension

TL;DR

This paper constructs explicit equivariant Yang-Mills solutions on de Sitter spaces of various dimensions for specific gauge groups, analyzing their properties and showing their energy and action characteristics.

Contribution

It provides new explicit solutions for Yang-Mills equations on de Sitter space across multiple dimensions for certain gauge groups, reducing the problem to a Newtonian particle analogy.

Findings

All solutions have finite energy beyond dS4.

Analytic solutions are explicitly displayed.

Solutions exhibit infinite action except in four dimensions.

Abstract

For gauge groups SO$(n{+}1)$, SU$(m{+}1)$ and Sp$(\ell{+}1)$, we construct equivariant Yang-Mills solutions on de Sitter space in $n{+}1$, $2(m{+}1)$ and $4(\ell{+}1)$ 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.