Platonic Sphalerons
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 QB=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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