论文标题
（2+1）D对称性拓扑状态和精确（3+1）D构建体中的绝对异常
Absolute anomalies in (2+1)D symmetry-enriched topological states and exact (3+1)D constructions
论文作者
论文摘要
（2+1）d拓扑阶的物质阶段中对称分数的某些模式可能是异常的，这意味着它们具有纯粹在纯粹（2+1）d中实现的障碍。在本文中，我们演示了如何计算完全普遍性的玻色子的对称式拓扑（集合）状态的异常。我们演示了如何在全球对称组$ g $的任何统一模块化张量类别（UMTC）和对称分数类别中，一个人可以根据$ g $ symmetry-propticted topological（SPT）状态定义A（3+1）d拓扑上不变的路径积分。我们为该系统提供了一个准确的解决哈密顿量，并明确证明了A（2+1）d $ g $对称的表面终止，该终止托管给定的UMTC和对称分数化类别所描述的解谐和的Anyon激发。我们提出了一般可以用于计算异常指标的混凝土算法。我们的方法适用于一般对称群，包括任何人 - 佩尔玛和反对对称性。除了提供一种计算异常的一般方法外，我们的结果还通过明确的结构表明，任何UMTC的每个对称分数化类别都可以在A（3+1）D SPT状态的表面上实现。作为副产品，该结构还提供了一种明确查看定义对称性分数的代数数据的方式，这是在一般可解决模型的背景下出现的。对于单一的定向对称性，我们的结果也可以被视为提供了一种方法来计算$ \ Mathcal {h}^4（g，u（1））$阻塞在$ g $ ch $ crowsed braided braided Tensor类别中产生的障碍物，而这些类别没有一般的方法可以迄今为止提供一般方法。
Certain patterns of symmetry fractionalization in (2+1)D topologically ordered phases of matter can be anomalous, which means that they possess an obstruction to being realized in purely (2+1)D. In this paper we demonstrate how to compute the anomaly for symmetry-enriched topological (SET) states of bosons in complete generality. We demonstrate how, given any unitary modular tensor category (UMTC) and symmetry fractionalization class for a global symmetry group $G$, one can define a (3+1)D topologically invariant path integral in terms of a state sum for a $G$ symmetry-protected topological (SPT) state. We present an exactly solvable Hamiltonian for the system and demonstrate explicitly a (2+1)D $G$ symmetric surface termination that hosts deconfined anyon excitations described by the given UMTC and symmetry fractionalization class. We present concrete algorithms that can be used to compute anomaly indicators in general. Our approach applies to general symmetry groups, including anyon-permuting and anti-unitary symmetries. In addition to providing a general way to compute the anomaly, our result also shows, by explicit construction, that every symmetry fractionalization class for any UMTC can be realized at the surface of a (3+1)D SPT state. As a byproduct, this construction also provides a way of explicitly seeing how the algebraic data that defines symmetry fractionalization in general arises in the context of exactly solvable models. In the case of unitary orientation-preserving symmetries, our results can also be viewed as providing a method to compute the $\mathcal{H}^4(G, U(1))$ obstruction that arises in the theory of $G$-crossed braided tensor categories, for which no general method has been presented to date.
