论文标题
量子场理论中的拓扑对称性
Topological symmetry in quantum field theory
论文作者
论文摘要
我们介绍了量子场理论中内部拓扑对称性的框架，包括“非可逆对称性”和“分类对称性”。这导致了拓扑缺陷的演算，从而充分利用了拓扑领域理论中发达的定理和技术的优势。我们的讨论集中在有限的对称性上，我们给出了对其他对称性的概括。我们处理商和商缺陷（通常称为“测量”和“凝结缺陷”），有限的电磁二元性以及二元性缺陷等主题。我们包括有关有限同源理论的附录，该附录通常用于编码有限的对称性，并使用代数拓扑方法对哪种计算进行计算。在整个过程中，我们强调了详细的技术治疗方法的博览会和例子。
We introduce a framework for internal topological symmetries in quantum field theory, including "noninvertible symmetries" and "categorical symmetries". This leads to a calculus of topological defects which takes full advantage of well-developed theorems and techniques in topological field theory. Our discussion focuses on finite symmetries, and we give indications for a generalization to other symmetries. We treat quotients and quotient defects (often called "gauging" and "condensation defects"), finite electromagnetic duality, and duality defects, among other topics. We include an appendix on finite homotopy theories, which are often used to encode finite symmetries and for which computations can be carried out using methods of algebraic topology. Throughout we emphasize exposition and examples over a detailed technical treatment.
