PoS - Proceedings of Science
Volume 318 - Corfu Summer Institute 2017 "Schools and Workshops on Elementary Particle Physics and Gravity" (CORFU2017) - Workshop on Testing Fundamental Physics Principles
Pure Yang-Mills solutions on $dS_4$
T.A. Ivanova, O. Lechtenfeld* and A. Popov
Full text: pdf
Pre-published on: August 22, 2018
Published on: August 24, 2018
We consider pure SU(2) Yang--Mills theory on four-dimensional de Sitter space dS$_4$ and construct smooth and spatially
homogeneous classical Yang--Mills fields. Slicing dS$_4$ as ${\mathbb R}\times S^3$, via an SU(2)-equivariant ansatz
we reduce the Yang--Mills equations to ordinary matrix differential equations and further to Newtonian dynamics
in a particular three-dimensional potential. Its classical trajectories yield spatially homogeneous Yang--Mills solutions
in a very simple explicit form, depending only on de Sitter time with an exponential decay in the past and future.
These configurations have not only finite energy, but their action is also finite and bounded from below.
We present explicit coordinate representations of the simplest examples (for the fundamental SU(2) representation).
Instantons (Yang--Mills solutions on the Wick-rotated $S^4$) and solutions on AdS$_4$ are also briefly discussed.
DOI: https://doi.org/10.22323/1.318.0204
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