(2+1)维拓扑有序中的非可逆规范对称性：弦网模型实现
Noninvertible Gauge Symmetry in (2+1)d Topological Orders: A String-Net Model Realization
AI总结：
本文提出了一种基于弦网模型的研究方法，揭示了(2+1)维拓扑有序中首个非可逆范畴规范对称性，即双Fibonacci拓扑有序的Fibonacci规范对称性。
摘要：
我们发展了一个系统框架，利用弦网模型来理解二维拓扑相中的对称性，包括既保持任意子种类的规范对称性，又置换任意子种类的全局对称性，包括可逆对称性（可由群描述）和非可逆对称性（可由范畴描述）。作为典型例子，我们揭示了首个(2+1)维拓扑有序中的非可逆范畴规范对称性：双Fibonacci拓扑有序的Fibonacci规范对称性，由Fibonacci融合2范畴描述。我们的方法包括两个步骤：首先，建立具有Morita等价输入融合范畴的不同弦网模型之间的对偶性，这些范畴描述相同的拓扑有序；其次，在相同弦网模型内构造对称变换，当双模型具有同构的输入融合范畴时，通过将对偶映射与双模型之间自由度的同构进行复合来实现。
英文摘要：
We develop a systematic framework for understanding symmetries in topological phases in 2+1 dimensions using the string-net model, encompassing both gauge symmetries that preserve anyon species and global symmetries permuting anyon species, including both invertible symmetries describable by groups and noninvertible symmetries described by categories. As an archetypal example, we reveal the first noninvertible categorical gauge symmetry of topological orders in 2+1 dimensions: the Fibonacci gauge symmetry of the doubled Fibonacci topological order, described by the Fibonacci fusion 2-category. Our approach involves two steps: first, establishing duality between different string-net models with Morita equivalent input fusion categories that describe the same topological order; and second, constructing symmetry transformations within the same string-net model when the dual models have isomorphic input fusion categories, achieved by composing duality maps with isomorphisms of degrees of freedom between the dual models.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
