Choi Yichul, Lam Ho Tat, Shao Shu-Heng
C. N. Yang Institute for Theoretical Physics, Stony Brook University, Stony Brook, New York 11794, USA.
Simons Center for Geometry and Physics, Stony Brook University, Stony Brook, New York 11794, USA.
Phys Rev Lett. 2022 Oct 14;129(16):161601. doi: 10.1103/PhysRevLett.129.161601.
We identify infinitely many noninvertible 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)_{A} axial symmetry because of the Adler-Bell-Jackiw 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 noninvertible fusion algebra. They act invertibly on all local operators as axial rotations, but noninvertibly on the 't Hooft lines. We further generalize our construction to QCD, and show that the coupling π^{0}F∧F in the effective pion Lagrangian is necessary to match these noninvertible 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.
我们发现在无质量极限下的现实世界的量子电动力学（QED）和量子色动力学（QCD）中有无限多个不可逆的广义全局对称性。在QED中，由于阿德勒 - 贝尔 - 贾基夫反常，U(1)_A轴对称性不存在守恒的诺特定流，但对于每个有理角2πp/N，我们构造了一个守恒且规范不变的拓扑对称算符。直观地说，它是轴旋转与耦合到电磁U(1)规范场的分数量子霍尔态的组合。这些守恒对称算符不服从群乘法法则，而是服从一个不可逆的融合代数。它们作为轴旋转对所有局域算符可逆地作用，但对‘t Hooft线不可逆地作用。我们进一步将我们的构造推广到QCD，并表明有效π介子拉格朗日量中的耦合π^0F∧F对于在紫外区域匹配这些不可逆对称性是必要的。因此，现在使用ABJ反常对中性π介子衰变的传统论证被重新表述为广义全局对称性的匹配条件。
