On anomalies and gauging of U(1) non-invertible symmetries in 4d QED
On anomalies and gauging of U(1) non-invertible symmetries in 4d QED
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DOI：
10.21468/scipostphys.15.1.002
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发表时间：
2022-11
期刊：
影响因子：
5.5
通讯作者：
A. Karasik
中科院分区：
文献类型：
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作者：
A. Karasik
本文提出了一种将反常轴向U（1）U（1）变换推广到精确不可逆U（1）U（1）对称的方法。我们讨论了耦合的不可逆对称性（动力学或背景）规范场的过程。我们表明，作为测量过程的一部分，施加一定的约束，使测量一致。约束自然地从不可逆U（1）U（1）守恒流的形式出现。在动态规范的情况下，这导致了我们称之为不可逆规范理论的新型规范理论：这些规范理论具有额外的约束，可以消除可能的规范异常。通过与背景规范场的耦合，我们可以讨论不可逆对称性的特胡夫特反常。我们在一个例子中表明，匹配条件成立，但他们实现了一个非常规的方式。即使在对称性未破缺和背景很弱的情况下，打开不可逆规范场的非平凡背景也会改变真空。然后，在新的真空中出现的孤子的异常相匹配。
In this work we propose a way to promote the anomalous axial U(1)U(1) transformations to exact non-invertible U(1)U(1) symmetries. We discuss the procedure of coupling the non-invertible symmetry to a (dynamical or background) gauge field. We show that as part of the gauging procedure, certain constraints are imposed to make the gauging consistent. The constraints emerge naturally from the form of the non-invertible U(1)U(1) conserved current. In the case of dynamical gauging, this results in new type of gauge theories we call non-invertible gauge theories: These are gauge theories with additional constraints that cancel the would-be gauge anomalies. By coupling to background gauge fields, we can discuss ’t-Hooft anomalies of non-invertible symmetries. We show in an example that the matching conditions hold but they are realized in an unconventional way. Turning on non-trivial background for the non-invertible gauge field changes the vacuum even when the symmetry is not broken and the background is very weak. The anomalies are then matched by the appearance of solitons in the new vacuum.