论文标题
较高的测量和不可凝聚的凝结缺陷
Higher Gauging and Non-invertible Condensation Defects
论文作者
论文摘要
我们讨论了在时空中较高的编成歧管上测量离散的更高形式对称性引起的可逆和不可延缓的拓扑凝结缺陷，我们将其定义为较高的测量值。如果可以在SpaceTime中的Codimension-$ p $歧管上进行测量，则称为$ p $对称性。我们专注于一般2+1d QFT中的1仪表1形式对称性，并在时空中的表面上衡量它们。确定了可逆的和不可凝的冷凝表面的通用融合规则。在2+1d TQFT的特殊情况下，每个（可逆和不可粘）0形式的全局对称性，包括$ \ Mathbb {Z} _2 $ the $ \ mathbb {z} _2 $ aguge理论的电磁对称性，从高级级别上实现。我们进一步计算了仅生存在表面上的表面，批量线和线之间的融合规则，从而确定了基础融合2类别的一些最基本数据。我们强调，这些不可依赖的融合规则中的融合“系数”通常不是数字，而是1+1D TQFT。最后，我们讨论了非客观2+1D QFT中的不可变形对称性的示例，例如自由$ u（1）$ MAXWELL理论和QED。
We discuss invertible and non-invertible topological condensation defects arising from gauging a discrete higher-form symmetry on a higher codimensional manifold in spacetime, which we define as higher gauging. A $q$-form symmetry is called $p$-gaugeable if it can be gauged on a codimension-$p$ manifold in spacetime. We focus on 1-gaugeable 1-form symmetries in general 2+1d QFT, and gauge them on a surface in spacetime. The universal fusion rules of the resulting invertible and non-invertible condensation surfaces are determined. In the special case of 2+1d TQFT, every (invertible and non-invertible) 0-form global symmetry, including the $\mathbb{Z}_2$ electromagnetic symmetry of the $\mathbb{Z}_2$ gauge theory, is realized from higher gauging. We further compute the fusion rules between the surfaces, the bulk lines, and lines that only live on the surfaces, determining some of the most basic data for the underlying fusion 2-category. We emphasize that the fusion "coefficients" in these non-invertible fusion rules are generally not numbers, but rather 1+1d TQFTs. Finally, we discuss examples of non-invertible symmetries in non-topological 2+1d QFTs such as the free $U(1)$ Maxwell theory and QED.
