### Abstract

We show that axion models with the domain wall number k in (3+1) dimensions, i.e., periodic scalar field theories admitting k axion domain walls, exhibit an emergent Z_{k} 3-form symmetry for k>1 in addition to a conventional Z_{k} 0-form symmetry. The emergent 3-form symmetry is explicitly shown by establishing a low-energy dual transformation between the scalar field theory and a 3-form gauge theory. We further argue that the emergent 3-form symmetry is spontaneously broken, and the breaking pattern is so-called the type-B spontaneous symmetry breaking. We discuss similar and different points between the phase admitting the domain walls and topologically ordered phases.

Original language | English |
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Article number | 135290 |

Journal | Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics |

Volume | 803 |

DOIs | |

Publication status | Published - 2020 Apr 10 |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics*,

*803*, [135290]. https://doi.org/10.1016/j.physletb.2020.135290