论文标题
关于连续的2类对称性和阳米尔斯理论
On Continuous 2-Category Symmetries and Yang-Mills Theory
论文作者
论文摘要
我们研究了4D量规理论$ u（1）^{n-1} \ rtimes s_n $，通过测量0型对称$ s_n $从$ u（1）^{n-1} $理论获得。我们表明，该理论具有全球连续的2类对称性，其结构特别丰富，以$ n> 2 $。这个示例使我们能够在较高的测量过程与本地融合和全局融合之间的差异之间建立连接，事实证明，这是较高类别对称性的关键特征。通过研究本地和扩展运营商的范围，我们发现了与4D $ SU（N）$ Yang-Mills理论的规格不变运算符的映射。我们理论的不可转化对称性的最大类似组的子类别是$ \ mathbb {z} _n^{（1）} $ 1形式的对称性，以与杨 - 米尔斯理论的中心对称性相同。 Supported by a path-integral argument, we propose that the $U(1)^{N-1}\rtimes S_N$ gauge theory has a relation with the ultraviolet limit of $SU(N)$ Yang-Mills theory in which all Gukov-Witten operators become topological, and form a continuous non-invertible 2-category symmetry, broken down to the center symmetry by the RG flow.
We study a 4d gauge theory $U(1)^{N-1}\rtimes S_N$ obtained from a $U(1)^{N-1}$ theory by gauging a 0-form symmetry $S_N$. We show that this theory has a global continuous 2-category symmetry, whose structure is particularly rich for $N>2$. This example allows us to draw a connection between the higher gauging procedure and the difference between local and global fusion, which turns out to be a key feature of higher category symmetries. By studying the spectrum of local and extended operators, we find a mapping with gauge invariant operators of 4d $SU(N)$ Yang-Mills theory. The largest group-like subcategory of the non-invertible symmetries of our theory is a $\mathbb{Z}_N^{(1)}$ 1-form symmetry, acting on the Wilson lines in the same way as the center symmetry of Yang-Mills theory does. Supported by a path-integral argument, we propose that the $U(1)^{N-1}\rtimes S_N$ gauge theory has a relation with the ultraviolet limit of $SU(N)$ Yang-Mills theory in which all Gukov-Witten operators become topological, and form a continuous non-invertible 2-category symmetry, broken down to the center symmetry by the RG flow.
