Platonic Sphalerons
B. Kleihaus, J. Kunz, K. Myklevoll

TL;DR
This paper constructs new sphaleron solutions in Weinberg-Salam theory with discrete symmetries, linking their properties to rational maps and baryon number, and provides explicit examples with various symmetries.
Contribution
It introduces a novel class of sphaleron solutions characterized by discrete symmetries and their relation to rational maps and baryon number in Weinberg-Salam theory.
Findings
Constructed N=3 sphaleron with tetrahedral symmetry
Constructed N=4 sphaleron with cubic symmetry
Constructed N=5 sphaleron with octahedral symmetry
Abstract
We construct sphaleron solutions in Weinberg-Salam theory, which possess only discrete symmetries. Related to rational maps of degree N, these sphalerons carry baryon number Q_B=N/2. The energy density of these sphalerons reflects their discrete symmetries. We present an N=3 sphaleron with tetrahedral energy density, an N=4 sphaleron with cubic energy density, and an N=5 sphaleron with octahedral energy density.
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