Journal Article

Finite-action solutions of Yang-Mills equations on de Sitter dS4 and anti-de Sitter AdS4 spaces

Ivanova, Tatiana A., Popov, Alexander D., Lechtenfeld, Olaf

2017

Overview

A bstract 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 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 ℝ 3 to 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.

• Publisher: Springer Berlin Heidelberg,Springer Nature B.V,SpringerOpen
• Subject: Classical and Quantum Gravitation / Classical Theories of Gravity / Confinement / Differential and Algebraic Geometry / Elementary Particles / High energy physics / Mathematical analysis / Mechanics (physics) / Physics / Physics and Astronomy / Quantum Field Theories / Quantum Field Theory / Quantum Physics / Regular Article - Theoretical Physics / Relativity Theory / Solitons Monopoles and Instantons / String Theory / Yang-Mills theory