标题： 自发破缺的阿贝尔陈-西蒙斯理论 显示英文标题

标题： Spontaneously broken abelian Chern-Simons theories

摘要： 对一种紧致阿贝尔直积规范群 U(1)^k 被自发地破缺为有限循环群的直积 H 的 Chern-Simons (CS) 理论进行了详细分析。该理论的谱特征包括全局 H 电荷、携带由 H 元素标记通量的涡旋以及磁电组合。由于 Aharonov-Bohm 效应，这些粒子表现出拓扑相互作用。在描述此类模型有效长距离物理的离散 H 规范理论中，U(1)^k CS 项的残余被证明是 H 的一个 3 上循环，总结了 U(1)^k CS 项施加于磁涡旋上的非平凡拓扑相互作用。注意到对于有限阿贝尔规范群 H，一般存在三种类型的 3 上循环：一种类型描述了相对于 H 直积中同一循环群携带通量的涡旋之间的拓扑相互作用，另一种类型则导致相对于 H 两个不同循环因子携带通量的涡旋之间的拓扑相互作用，第三种类型则导致相对于 H 三个不同循环因子携带通量的涡旋之间的拓扑相互作用。除了其他内容外，还证明只有前两种类型可以从自发破缺的 U(1)^k CS 理论中获得。以这种方式无法达到的 3 上循环被证明是最有趣的。它们使理论变为非阿贝尔的，并通常导致与具有非阿贝尔有限规范群的平面理论之间的对偶性。特别是，由这样的 3 上循环定义的有限规范群 H = Z_2 x Z_2 x Z_2 的 CS 理论被证明与具有 D_4 二面体群（阶数为 8）的平面离散 D_4 规范理论是对偶的。 显示英文摘要

摘要： A detailed analysis of Chern-Simons (CS) theories in which a compact abelian direct product gauge group U(1)^k is spontaneously broken down to a direct product H of (finite) cyclic groups is presented. The spectrum features global H charges, vortices carrying flux labeled by the elements of H and dyonic combinations. Due to the Aharonov-Bohm effect these particles exhibit toplogical interactions. The remnant of the U(1)^k CS term in the discrete H gauge theory describing the effective long distance physics of such a model is shown to be a 3-cocycle for H summarizing the nontrivial topological interactions cast upon the magnetic vortices by the U(1)^k CS term. It is noted that there are in general three types of 3-cocycles for a finite abelian gauge group H: one type describes topological interactions among vortices carrying flux w.r.t. the same cyclic group in the direct product H, another type gives rise to topological interactions between vortices carrying flux w.r.t. two different cyclic factors of H and a third type leading to topological interactions between vortices carrying flux w.r.t. three different cyclic factors. Among other things, it is demonstrated that only the first two types can be obtained from a spontaneously broken U(1)^k CS theory. The 3-cocycles that can not be reached in this way turn out to be the most interesting. They render the theory nonabelian and in general lead to dualities with planar theories with a nonabelian finite gauge group. In particular, the CS theory with finite gauge group H = Z_2 x Z_2 x Z_2 defined by such a 3-cocycle is shown to be dual to the planar discrete D_4 gauge theory with D_4 the dihedral group of order 8.