Emergent discrete 3-form symmetry and domain walls

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 ${\mathbb{Z}}_k$ 3-form symmetry for $k>1$ in addition to a conventional ${\mathbb{Z}}_k$ 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.

arXiv commentv1: 6 pages; v2: 7 pages, title changed, major results unchanged, references added; v3: 7 pages, published version

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