Platonic self-dual solitons in a (1+1)-dimensional ℂℙ1 model
Abstract
We construct a family of self-dual (1+1)-dimensional ℂℙ1 sigma models whose potentials V are determined from pre-potentials U by Platonic geometry. Using the round metric on 𝕊2≃ℂℙ1 and the generalized self-duality formalism, we build symmetry-invariant pre-potentials U from the unit vertices of each Platonic solid intersecting the unit circumsphere. The regular-lattice sites associated with vertex, face-center, and edge-midpoint directions are critical points of U and degenerate vacua of the scalar potential V. Dual solids share the same regular lattice but generate different pre-potentials, charges, potentials, and metric-gradient flows. Numerical integration reveals distinct self-dual trajectories and energy-density profiles, including multi-peak structures for paths passing near saddle points, while solutions with the same endpoint difference ΔU have the same total energy. The positive maxima of V are also organized into symmetry orbits. This construction provides a geometric prescription for controlling the vacuum structure and self-dual sectors of ℂℙ1 models with a potential.
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BibTeX
@misc{ferreira2026platonic,
title = {{Platonic self-dual solitons in a (1+1)-dimensional $\mathbbCP^1$ model}},
author = {L. A. Ferreira and G. Marcelino},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.12385},
eprint = {2610.12385},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.12385},
}
RIS
TY - UNPB
TI - Platonic self-dual solitons in a (1+1)-dimensional ℂℙ^1 model
AU - L. A. Ferreira
AU - G. Marcelino
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.12385
UR - https://arxiv.org/abs/2610.12385
AB - We construct a family of self-dual (1+1)-dimensional ℂℙ^1 sigma models whose potentials V are determined from pre-potentials U by Platonic geometry. Using the round metric on 𝕊^2≃ℂℙ^1 and the generalized self-duality formalism, we build symmetry-invariant pre-potentials U from the unit vertices of each Platonic solid intersecting the unit circumsphere. The regular-lattice sites associated with vertex, face-center, and edge-midpoint directions are critical points of U and degenerate vacua of the scalar potential V. Dual solids share the same regular lattice but generate different pre-potentials, charges, potentials, and metric-gradient flows. Numerical integration reveals distinct self-dual trajectories and energy-density profiles, including multi-peak structures for paths passing near saddle points, while solutions with the same endpoint difference ΔU have the same total energy. The positive maxima of V are also organized into symmetry orbits. This construction provides a geometric prescription for controlling the vacuum structure and self-dual sectors of ℂℙ^1 models with a potential.
ER -