Abstract We study a model in d = 2 + 1 space-time dimensions with two sectors. One of them, which can be considered as the visible sector, contains just a U ( 1 ) gauge field which acts as a probe for the other (hidden) sector, given by a second U ( 1 ) gauge field and massive scalar and Dirac fermions. Covariant derivatives of these matter fields and a BF gauge mixing term couple the two sectors. Integration over fermion fields leads to an effective theory with Chern-Simons terms that support vortex like solutions in both sectors even if originally there was no symmetry breaking Higgs scalar in the visible sector. We study numerically the solutions which correspond to electrically charged magnetic vortices except for a critical value of the BF coupling constant at which solely purely magnetic vortices exist.

中文翻译：

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d = 3 维模型，具有两个 U(1) 规范场，通过物质场和 BF 相互作用耦合

摘要 我们研究了一个具有两个扇区的 d = 2 + 1 时空维度的模型。其中一个可以被认为是可见扇区，它只包含一个 U ( 1 ) 规范场，它充当另一个（隐藏）扇区的探测器，由第二个 U ( 1 ) 规范场和大量标量和狄拉克给出费米子。这些物质场的协变导数和 BF 规范混合项将两个扇区耦合起来。费米子场上的积分导致了一个有效的理论，其中陈-西蒙斯项支持两个扇区中的涡旋解，即使最初在可见扇区中没有对称性破坏希格斯标量。我们从数值上研究了对应于带电磁涡流的解，除了 BF 耦合常数的临界值，在该值处仅存在纯磁涡流。