Platonic sphalerons

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. 1

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