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Journal of High Energy Physics

, 2017:17 | Cite as

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

  • Tatiana A. Ivanova
  • Olaf Lechtenfeld
  • Alexander D. Popov
Open Access
Regular Article - Theoretical Physics

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.

Keywords

Solitons Monopoles and Instantons Differential and Algebraic Geometry Classical Theories of Gravity Confinement 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2017

Authors and Affiliations

  • Tatiana A. Ivanova
    • 1
  • Olaf Lechtenfeld
    • 2
  • Alexander D. Popov
    • 2
  1. 1.Bogoliubov Laboratory of Theoretical Physics, JINRDubnaRussia
  2. 2.Institut für Theoretische Physik and Riemann Center for Geometry and PhysicsLeibniz Universität HannoverHannoverGermany

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