作为格点规范理论的轴子QED与非可逆对称性
Axion QED as a Lattice Gauge Theory and Non-Invertible Symmetry
AI总结：
本研究利用修正Villain公式研究轴子QED的非可逆对称性，构建格点作用量并引入新自由度得到规范不变磁客体，采用非半空间规范方法计算其在非可逆对称算符下的响应。
摘要：
我们采用修正的Villain公式化方法，研究了轴子量子电动力学（QED）中与手征对称性相关的非可逆对称性。在轴子QED中，已知由于光子场强或轴子“场强”的比安基恒等式被破坏，'t Hooft 环、轴子弦等朴素的磁客体将失去规范不变性。首先，我们在正方晶格上构建了轴子QED的作用量，该作用量比其连续理论中的对应形式更为复杂，随后我们观测到了规范不变性的破缺。接着，我们通过引入局域在磁客体位置上的新自由度，构建了具有规范不变性的磁客体。此外，我们还显式计算了这些磁客体在文献[1]中构建的非可逆对称算符作用下的响应。在该分析中，我们采用了一种不同于所谓半空间规范的方法，后者是研究非可逆对称性的标准方法。
英文摘要：
We investigate the non-invertible symmetry associated with chiral symmetry in axion quantum electrodynamics (QED) using the modified Villain formulation. In axion QED, it is known that naive magnetic objects such as 't Hooft loops and axion strings lose their gauge invariance due to the violation of the Bianchi identity for the field strength of the photon or "field strength" of the axion. First, we construct the action of axion QED on the square lattice, which is more intricate than its counterpart in the continuum theory. We then observe the breaking of gauge invariance. Subsequently, we construct gauge-invariant magnetic objects by introducing new degrees of freedom localized at the positions of the magnetic objects. Furthermore, we explicitly compute the response of the magnetic objects under the action of the non-invertible symmetry operator constructed in Ref. [1]. In this analysis, we employ a method different from the so-called half-space gauging, which is the standard method to study non-invertible symmetries.
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