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.
Highlights
Axion electrodynamics has been extensively studied in many contexts of modern physics from particle physics [1,2,3,4,5,6,7] to condensed matter physics [8,9,10]
Combining the above mentioned two topics together, it may be a natural question whether there are any underlying higher-form symmetries in the axion electrodynamics, and if so, whether they offer fundamental tools to describe the Witten effect and anomalous Hall effect
We study the higher-form symmetries of the massless axion electrodynamics in (3 + 1) dimensions by using a low-energy effective theory described by a massless axion and massless photon with the topological coupling
Summary
Axion electrodynamics has been extensively studied in many contexts of modern physics from particle physics [1,2,3,4,5,6,7] to condensed matter physics [8,9,10] (see, e.g., Refs. [11,12,13,14,15] as a review). Combining the above mentioned two topics together, it may be a natural question whether there are any underlying higher-form symmetries in the axion electrodynamics, and if so, whether they offer fundamental tools to describe the Witten effect and anomalous Hall effect. We study the higher-form symmetries of the massless axion electrodynamics in (3 + 1) dimensions by using a low-energy effective theory described by a massless axion and massless photon with the topological coupling. Where qaE should be an integer as a result of the Dirac quantization condition
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