论文标题
标准模型中的不可逆转全局对称性
Non-invertible Global Symmetries in the Standard Model
论文作者
论文摘要
我们在无限限制中确定了QED和QCD中QED中的许多不可糊化的通用全局对称性。在QED中，虽然由于ABJ异常，$ U（1）_ \ text {a} $轴向对称性没有任何保守的Noether电流，但对于每个有理角$2πp/n $，我们构建了一个保守的和规范的式拓扑对称对称性运算符。从直觉上讲，它是轴向旋转的组成和一个与电磁$ u（1）$量规场耦合的分数量子厅状态。这些保守的对称算子不遵守群体乘法定律，而是在TQFT系数上的不可变形融合代数。它们在所有本地运算符上作为轴向旋转而反而作用，但并非在't Hooft Lines上。这些不可变形的对称性导致选择规则，这些规则与QED中的散射幅度一致。我们将我们的构造进一步概括为QCD，并证明在有效的pion lagrangian中，$π^0 f \ wedge f $是匹配紫外线中这些不可脱离的对称性的必要条件。因此，现在使用ABJ异常的中性触发衰减的常规论证是作为广义全局对称性的匹配条件重新塑造的。
We identify infinitely many non-invertible generalized global symmetries in QED and QCD for the real world in the massless limit. In QED, while there is no conserved Noether current for the $U(1)_\text{A}$ axial symmetry because of the ABJ anomaly, for every rational angle $2πp/N$, we construct a conserved and gauge-invariant topological symmetry operator. Intuitively, it is a composition of the axial rotation and a fractional quantum Hall state coupled to the electromagnetic $U(1)$ gauge field. These conserved symmetry operators do not obey a group multiplication law, but a non-invertible fusion algebra over TQFT coefficients. They act invertibly on all local operators as axial rotations, but non-invertibly on the 't Hooft lines. These non-invertible symmetries lead to selection rules, which are consistent with the scattering amplitudes in QED. We further generalize our construction to QCD, and show that the coupling $π^0 F\wedge F$ in the effective pion Lagrangian is necessary to match these non-invertible symmetries in the UV. Therefore, the conventional argument for the neutral pion decay using the ABJ anomaly is now rephrased as a matching condition of a generalized global symmetry.
