论文标题
在（2+1）d拓扑阶段计量u（1）对称性
Gauging U(1) symmetry in (2+1)d topological phases
论文作者
论文摘要
我们研究了（2+1）d中散布系统中全局u（1）对称性的测量。对于一个有限的全局对称组而言，测量过程已被理解，该组导致具有新的距离结构的新相位阶段，可以使用模块化张量类别（MTC）的数学框架来描述代数。考虑到有限组案例中不存在U（1）规格场的动力学，我们对MTC中U（1）的分类描述进行了分类描述。当Ungaig的系统具有非零的HALL电导时，测量理论仍然存在，我们确定了测量理论的完整数据集。另一方面，当霍尔电导消失时，我们认为测量的效果相同，即通过插入$2π$ u（1）通量来凝结特殊的Abelian Anyon。我们将过程应用于SU（2）$ _ K $ MTC，并为$ \ Mathbb {Z} _K $ Parafermion MTC得出完整的MTC数据。我们还讨论了在MTC的原始U（1）对称性后出现的双U（1）对称性。
We study the gauging of a global U(1) symmetry in a gapped system in (2+1)d. The gauging procedure has been well-understood for a finite global symmetry group, which leads to a new gapped phase with emergent gauge structure and can be described algebraically using the mathematical framework of modular tensor category (MTC). We develop a categorical description of U(1) gauging in an MTC, taking into account the dynamics of U(1) gauge field absent in the finite group case. When the ungauged system has a non-zero Hall conductance, the gauged theory remains gapped and we determine the complete set of anyon data for the gauged theory. On the other hand, when the Hall conductance vanishes, we argue that gauging has the same effect of condensing a special Abelian anyon nucleated by inserting $2π$ U(1) flux. We apply our procedure to the SU(2)$_k$ MTCs and derive the full MTC data for the $\mathbb{Z}_k$ parafermion MTCs. We also discuss a dual U(1) symmetry that emerges after the original U(1) symmetry of an MTC is gauged.
