Solutions to Yang-Mills Equations on Four-Dimensional de Sitter Space

authored by

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

Abstract

We consider pure SU(2) Yang-Mills theory on four-dimensional de Sitter space dS4 and construct a smooth and spatially homogeneous magnetic solution to the Yang-Mills equations. Slicing dS4 as R×S3, via an SU(2)-equivariant ansatz, we reduce the Yang-Mills equations to ordinary matrix differential equations and further to Newtonian dynamics in a double-well potential. Its local maximum yields a Yang-Mills solution whose color-magnetic field at time τR is given by Ba=-12Ia/(R2cosh2τ), where Ia for a=1, 2, 3 are the SU(2) generators and R is the de Sitter radius. At any moment, this spatially homogeneous configuration has finite energy, but its action is also finite and of the value -12j(j+1)(2j+1)π3 in a spin-j representation. Similarly, the double-well bounce produces a family of homogeneous finite-action electric-magnetic solutions with the same energy. There is a continuum of other solutions whose energy and action extend down to zero.

Organisation(s)

Institut für Theoretische Physik
Riemann Center for Geometry and Physics

External Organisation(s)

Joint Institute for Nuclear Research (JINR)

Type

Artikel

Journal

Physical review letters

Volume

119

ISSN

0031-9007

Publication date

11.08.2017

Publication status

Veröffentlicht

Peer reviewed

Yes

ASJC Scopus Sachgebiete

Physik und Astronomie (insg.)

Electronic version(s)

https://doi.org/10.1103/PhysRevLett.119.061601 (Access: Unbekannt)