Abstract
We consider pure SU(2) Yang-Mills theory on four-dimensional de Sitter dS4 and anti-de Sitter AdS4 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 AdS4, 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 dS4 and AdS4 we also present self-dual (instanton-type) Yang-Mills solutions on these backgrounds.
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Ivanova, T.A., Lechtenfeld, O. & Popov, A.D. Finite-action solutions of Yang-Mills equations on de Sitter dS4 and anti-de Sitter AdS4 spaces. J. High Energ. Phys. 2017, 17 (2017). https://doi.org/10.1007/JHEP11(2017)017
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DOI: https://doi.org/10.1007/JHEP11(2017)017