Hyperbolic monopole-type solutions in SU(3) Yang-Mills theory
Abstract
We construct S1-invariant solutions of the SU(3) pure Yang-Mills theory on four-dimensional Euclidean space using the Cho-Faddeev-Niemi decomposition and a harmonic map from S2 into the flag manifold F3=SU(3)/U(1)2. The resulting ansatz reduces the full Yang-Mills equations to coupled radial equations. Solving the coupled equations, we derive two types of solutions: analytic self-dual solutions interpreted as noninteracting clusters of hyperbolic monopoles and non-self-dual numerical solutions that can be interpreted as hyperbolic monopole-antimonopole bound states. In the large-mass limit of the hyperbolic monopole-antimonopole bound states, their normalized action approaches the energy of the corresponding non-Bogomolny SU(3) monopole in flat space.
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BibTeX
@misc{amari2026hyperbolic,
title = {{Hyperbolic monopole-type solutions in $SU(3)$ Yang-Mills theory}},
author = {Yuki Amari},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.15109},
eprint = {2609.15109},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15109},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Hyperbolic monopole-type solutions in SU(3) Yang-Mills theory
AU - Yuki Amari
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.15109
UR - https://arxiv.org/abs/2609.15109
AB - We construct S^1-invariant solutions of the SU(3) pure Yang-Mills theory on four-dimensional Euclidean space using the Cho-Faddeev-Niemi decomposition and a harmonic map from S^2 into the flag manifold F_3=SU(3)/U(1)^2. The resulting ansatz reduces the full Yang-Mills equations to coupled radial equations. Solving the coupled equations, we derive two types of solutions: analytic self-dual solutions interpreted as noninteracting clusters of hyperbolic monopoles and non-self-dual numerical solutions that can be interpreted as hyperbolic monopole-antimonopole bound states. In the large-mass limit of the hyperbolic monopole-antimonopole bound states, their normalized action approaches the energy of the corresponding non-Bogomolny SU(3) monopole in flat space.
ER -