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

authored by

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

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 ℝ³ 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 ℝ³ to 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.

Organisation(s)

Institut für Theoretische Physik
Riemann Center for Geometry and Physics

External Organisation(s)

Joint Institute for Nuclear Research (JINR)

Type

Artikel

Journal

Journal of high energy physics

Volume

2017

ISSN

1126-6708

Publication date

01.11.2017

Publication status

Veröffentlicht

Peer reviewed

Yes

ASJC Scopus Sachgebiete

Kern- und Hochenergiephysik

Electronic version(s)

https://doi.org/10.1007/JHEP11(2017)017 (Access: Offen)