论文标题
（3+1）d的拓扑阶段d仪表模型中的差异边界和类似弦的激发
Gapped boundaries and string-like excitations in (3+1)d gauge models of topological phases
论文作者
论文摘要
我们研究了（3+1）Dijkgraaf-witten理论的晶格哈密顿的实现，并具有宽大的边界。除了散装环状激发外，汉密尔顿还产生了散装的敌对弦乐激发，这些激发在边界上终止。使用管代数方法，我们对这种激发进行了分类并得出相应的表示理论。通过尺寸还原参数，我们将此管代数与描述（2+1）d边界点的激发在两个间隙边界之间的接口处的激发相关。众所周知，这种类似点的激发被编码为输入融合类别的模块类别的生物。利用此对应关系，我们定义了一个生物学，该生物是在缝隙边界上编码类似字符串的激发，表明它是组毕业2个矢量空间的输入生物学中心的一个子生物。在此过程中，我们解释了（3+1）d中的间隙边界如何在此输入bicategory上通过所谓的伪代核心对象标记。
We study lattice Hamiltonian realisations of (3+1)d Dijkgraaf-Witten theory with gapped boundaries. In addition to the bulk loop-like excitations, the Hamiltonian yields bulk dyonic string-like excitations that terminate at gapped boundaries. Using a tube algebra approach, we classify such excitations and derive the corresponding representation theory. Via a dimensional reduction argument, we relate this tube algebra to that describing (2+1)d boundary point-like excitations at interfaces between two gapped boundaries. Such point-like excitations are well known to be encoded into a bicategory of module categories over the input fusion category. Exploiting this correspondence, we define a bicategory that encodes the string-like excitations ending at gapped boundaries, showing that it is a sub-bicategory of the centre of the input bicategory of group-graded 2-vector spaces. In the process, we explain how gapped boundaries in (3+1)d can be labelled by so-called pseudo-algebra objects over this input bicategory.
