Global Structure, Non-Invertible PQ Symmetry, and the DFSZ Domain Wall Problem
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arXiv
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| Format: | Preprint |
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2026
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| author | Choi, Gongjun Hong, Sungwoo Koren, Seth |
| author_facet | Choi, Gongjun Hong, Sungwoo Koren, Seth |
| contents | In recent years it has become increasingly clear that the previously overlooked ``global structure'' of symmetry groups can encode significant theoretical structure and, more importantly, have substantial phenomenological implications. With this in mind we re-examine the DFSZ axion, which suffers from a domain wall problem due to the Standard Model generation structure. We show that global structure $(G_{\text{EW}} \times U(1)_{\text{PQ}})/\mathbb{Z}_2$ acting between the Peccei-Quinn symmetry and the electroweak gauge group plays a crucial role in determining the precise nature of the domain wall problem, which has important implications in both cubic and quartic DFSZ. We then demonstrate that the stability of the domain walls is enforced by a non-invertible chiral symmetry in quark flavor $Z'$ models which have additional global structure $(SU(3)_C \times G_F)/\mathbb{Z}_3$ acting between the color and the gauged quark flavor groups. The strategy of Non-invertible Naturalness then leads us to UV theories that resolve the domain wall problem through small-instanton-induced breaking of non-invertible symmetries. Finally, we sketch potential gravitational wave signatures arising from the annihilation of axion domain walls. Our work illustrates the importance of considerations of global structure in realistic models of particle physics. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_26867 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Global Structure, Non-Invertible PQ Symmetry, and the DFSZ Domain Wall Problem Choi, Gongjun Hong, Sungwoo Koren, Seth High Energy Physics - Phenomenology Cosmology and Nongalactic Astrophysics High Energy Physics - Theory In recent years it has become increasingly clear that the previously overlooked ``global structure'' of symmetry groups can encode significant theoretical structure and, more importantly, have substantial phenomenological implications. With this in mind we re-examine the DFSZ axion, which suffers from a domain wall problem due to the Standard Model generation structure. We show that global structure $(G_{\text{EW}} \times U(1)_{\text{PQ}})/\mathbb{Z}_2$ acting between the Peccei-Quinn symmetry and the electroweak gauge group plays a crucial role in determining the precise nature of the domain wall problem, which has important implications in both cubic and quartic DFSZ. We then demonstrate that the stability of the domain walls is enforced by a non-invertible chiral symmetry in quark flavor $Z'$ models which have additional global structure $(SU(3)_C \times G_F)/\mathbb{Z}_3$ acting between the color and the gauged quark flavor groups. The strategy of Non-invertible Naturalness then leads us to UV theories that resolve the domain wall problem through small-instanton-induced breaking of non-invertible symmetries. Finally, we sketch potential gravitational wave signatures arising from the annihilation of axion domain walls. Our work illustrates the importance of considerations of global structure in realistic models of particle physics. |
| title | Global Structure, Non-Invertible PQ Symmetry, and the DFSZ Domain Wall Problem |
| topic | High Energy Physics - Phenomenology Cosmology and Nongalactic Astrophysics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2603.26867 |