Abstract We study higher-form symmetries in a low-energy effective theory of a massless axion coupled with a photon in ( 3 + 1 ) dimensions. It is shown that the higher-form symmetries of this system are accompanied by a semistrict 3-group (2-crossed module) structure, which can be found by the correlation functions of symmetry generators of the higher-form symmetries. We argue that the Witten effect and anomalous Hall effect in the axion electrodynamics can be described in terms of 3-group transformations.

中文翻译：

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轴子电动力学中的高形式对称性和 3 群

摘要 我们研究了无质量轴子与 (3 + 1) 维光子耦合的低能量有效理论中的更高形式的对称性。结果表明，该系统的高级对称性伴随着半严格的3-群（2-交叉模）结构，这可以通过高级对称性的对称生成元的相关函数找到。我们认为轴子电动力学中的 Witten 效应和反常霍尔效应可以用 3 群变换来描述。