Abstract
We obtain the complete space of solutions, in the two-dimensional O ( 3 ) nonlinear sigma model, which are foliated by Villarceau circles. In particular, we prove the existence of solitons that admit a foliation by nonparallel circles. This contrasts with the Plateau context, where solitons foliated by nonparallel circles cannot exist. These solitons carry topological charges that are holographically computed via the Gauss–Bonnet formula.
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