论文标题
$ a \ times b = c $ in $ 2+1 $ d tqft
$a\times b=c$ in $2+1$D TQFT
论文作者
论文摘要
我们研究了Anyon Fusion方程$ A \ Times B = C $对全球属性的含义，$ 2+1 $ d D拓扑量子场理论（TQFTS）。这里$ a $ and $ b $是将融合在一起以提供独特的$ c $的人。众所周知，当$ a $ a和$ b $的至少一个是阿贝利安时，这些方程式描述了该理论的一式对称性的各个方面。当$ a $ and $ b $是非亚洲的，最明显的融合方式是当TQFT可以解决成带有微不足道的互助编织的TQFT的产品，而$ a $ a $ b $则在于不同的因素。更普遍地，我们认为，非阿布莱恩$ a $ a和$ b $的这种融合的外观也可能表明我们在TQFT中的零形式对称性，我们称我们为“ Quasi-Zero Zero形式对称性”（例如，基于最大的Mathieu group，$ m_ $ m_ cumusion，$ m_ {24} $），或者是不合时宜的。我们在各种TQFT环境中研究了这些想法，从（扭曲和无链）离散规格理论到基于连续仪表组和相关coset的Chern-Simons理论。一路上，我们证明了各种有用的定理。
We study the implications of the anyon fusion equation $a\times b=c$ on global properties of $2+1$D topological quantum field theories (TQFTs). Here $a$ and $b$ are anyons that fuse together to give a unique anyon, $c$. As is well known, when at least one of $a$ and $b$ is abelian, such equations describe aspects of the one-form symmetry of the theory. When $a$ and $b$ are non-abelian, the most obvious way such fusions arise is when a TQFT can be resolved into a product of TQFTs with trivial mutual braiding, and $a$ and $b$ lie in separate factors. More generally, we argue that the appearance of such fusions for non-abelian $a$ and $b$ can also be an indication of zero-form symmetries in a TQFT, of what we term "quasi-zero-form symmetries" (as in the case of discrete gauge theories based on the largest Mathieu group, $M_{24}$), or of the existence of non-modular fusion subcategories. We study these ideas in a variety of TQFT settings from (twisted and untwisted) discrete gauge theories to Chern-Simons theories based on continuous gauge groups and related cosets. Along the way, we prove various useful theorems.
