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


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.


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


Open Access

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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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