发表机构
Dipartimento di Fisica e Astronomia ‘Galileo Galilei’, Università di Padova; INFN, sez. di Padova（帕多瓦大学伽利略·伽利莱物理与天文系; 意大利国家核物理研究所帕多瓦分部）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出一种通用技术，在全纯怪兽 CFT 等多种手征 CFT 中发现新的非可逆对称性与拓扑缺陷，还给出全纯 VOA 自仿射的充分条件并确定对偶缺陷。
AI 中文摘要
二维共形场论（CFT）中非可逆对称性的结构与所保留全纯场的代数、其表示理论及其在 CFT 全手征代数中的嵌入密切相关。遗憾的是，寻找手征代数到另一手征代数的新嵌入是一个困难的数学问题，也是探索新型奇异非可逆对称性范畴的主要障碍之一。在本研究中，我们描述了一种简单通用技术，该技术在该方向上取得了若干新的非平凡结果：（1）对于全纯怪兽 CFT $V^\natural$，我们证明对每个阶为 $N$ 的“Fricke”非异常怪兽元素，parafermion 代数 $\frac{su(2)_N}{u(1)}$ 都可嵌入 $V^\natural$；我们计算了其换位子的特征标，并描述了保留这些子代数的拓扑缺陷。（2）我们给出了全纯顶点算子代数（VOA）$V$ 在（可逆）对称性循环群下自仿射的易验证充分条件，并确定了相关的对偶缺陷。（3）我们在来自 $T^4$ 上杂化弦的 CFT 中发现了若干新的拓扑缺陷。（4）我们证明了 Leech 格 CFT、Schellekens 理论及其他不同中心荷的 CFT 中存在多个 VOA 嵌入和拓扑缺陷，并提出了我们方法的若干推广方向。
英文摘要
The structure of non-invertible symmetries in 2D CFT is closely tied to the algebra of preserved holomorphic fields, its representation theory, and its embedding in the full chiral algebra of the CFT. Unfortunately, finding new embeddings of a chiral algebra into another is a difficult mathematical problem, and one of the major obstacles in the pursue of new and exotic categories of non-invertible symmetries. In this work, we describe a simple general technique that leads to a number of new non-trivial results in this direction: (1) For the holomorphic Monster CFT $V^\natural$, we show that for every `Fricke' non-anomalous Monster element of order $N$, there is an embedding of the parafermion algebra $\frac{su(2)_N}{u(1)}$ in $V^\natural$, we compute the characters of its commutant, and describe the topological defects preserving these subalgebras. (2) We provide an easy-to-check sufficient condition for a holomorphic VOA $V$ to be self-orbifold under a cyclic group of (invertible) symmetries, and determine the associated duality defect. (3) We find several new topological defects in CFTs arising from heterotic strings on $T^4$. (4) We prove a number of VOA embeddings and topological defects in the Leech lattice CFT, in Schellekens theories, and other CFTs of various central charges, and suggest several generalizations of our methods.
Comments37 pages + appendices; v2: minor corrections, clarifications added
