Finite-action solutions of Yang-Mills equations on de Sitter dS${}_4$ and anti-de Sitter AdS${}_4$ spaces

Abstract

We consider pure SU(2) Yang-Mills theory on four-dimensional de Sitter dS${}_4$ and anti-de Sitter AdS${}_4$ spaces and construct various solutions to the Yang-Mills equations. On de Sitter space we reduce the Yang-Mills equations via an SU(2)-equivariant ansatz to Newtonian mechanics of a particle moving in ${\mathbb{R}}^3$ under the influence of a quartic potential. Then we describe magnetic and electric-magnetic solutions, both Abelian and non-Abelian, all having finite energy and finite action. A similar reduction on anti-de Sitter space also yields Yang-Mills solutions with finite energy and action. We propose a lower bound for the action on both backgrounds. Employing another metric on AdS${}_4$, the SU(2) Yang-Mills equations are reduced to an analytic continuation of the above particle mechanics from ${\mathbb{R}}^3$ to ${\mathbb{R}}^{2,1}$. We discuss analytical solutions to these equations, which produce infinite-action configurations. After a Euclidean continuation of dS${}_4$ and AdS${}_4$ we also present self-dual (instanton-type) Yang--Mills solutions on these backgrounds.

arXiv comment1+31 pages, 4 figures; v2: some clarifications, published version

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• Exact Multi-Instanton Solutions to Selfdual Yang-Mills Equation on Curved Spaces
• Self-dual instantons and gravitating dyons in non-Abelian ModMax theory
• Generalization of Instanton-Induced Inflation and Dynamical Compactification
• Perturbations to Generalized Kink-like Topological Defects in $AdS$
• Characteristic Lightcone Sources in SO(1,3) Yang-Mills Theory