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Broken Baby Skyrmions

The baby Skyrme model is a (2+1)-dimensional analogue of the Skyrme model, in which baryons are described by topological solitons. In this paper we introduce a version of the baby Skyrme model in which the global O(3) symmetry is broken to the dihedral group D_N. It is found that the single soliton in this theory is composed of N partons, that are topologically confined. The case N=3 is studied in some detail and multi-soliton solutions are computed. These soliton solutions are related to polyiamonds, which are plane figures composed of equilateral triangles joined by common edges. It is shown that the solitons may be viewed as pieces of a doubly periodic soliton lattice. An alternative model with D_3 symmetry is also introduced, which has an exact explicit soliton lattice solution. Soliton solutions are computed and compared in the two D_3 theories. Some comments are made regarding the extension of these ideas to the Skyrme model.