Exact analytic solutions of static, stable, nonplanar Bogomol’nyi-Prasad-Sommerfield (BPS) domain wall junctions are obtained in extended Abelian-Higgs models in ( D + 1 )-dimensional spacetime. For specific choice of mass parameters, the Lagrangian is invariant under the symmetric group S D + 1 of degree D + 1 spontaneously broken down to S D in vacua, admitting S D + 1 / S D domain wall junctions. In D = 2 , there are three vacua and three domain walls meeting at a junction point, in which the conventional topological charges Y and Z exist for the BPS domain wall junctions and the BPS domain walls, respectively, as known before. In D = 3 , there are four vacua, six domain walls, four junction lines on which three domain walls meet, and one junction point on which all the six domain walls meet. We define a new topological charge X for the junction point in addition to the conventional topological charges Y and Z . In general dimensions, we find that the configuration expressed in the D -dimensional real space is dual to a regular D -simplex in the D -dimensional internal space and that a d -dimensional subsimplex of the regular D -simplex corresponds to a ( D ? d )-dimensional intersection. Topological charges are generalized to the level- d wall charge W d for the d -dimensional subsimplexes.
展开▼
