A lattice formulation of Weyl fermions on a single curved surface
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914803658784768 |
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| author | Aoki, Shoto Fukaya, Hidenori Kan, Naoto |
| author_facet | Aoki, Shoto Fukaya, Hidenori Kan, Naoto |
| contents | In the standard lattice domain-wall fermion formulation, one needs two flat domain-walls where both of the left- and right-handed massless modes appear. In this work we investigate a single domain-wall system with a nontrivial curved background. Specifically we consider a massive fermion on a $3D$ square lattice, whose domain-wall is a $2D$ sphere. In the free theory, we find that a single Weyl fermion is localized at the wall and it feels gravity through the induced spin connection. With a topologically nontrivial $U(1)$ link gauge field, however, we find a zero mode with the opposite chirality localized at the center where the gauge field is singular. In the latter case, the low-energy effective theory is not chiral but vectorlike. We discuss how to circumvent this obstacle in formulating lattice chiral gauge theory in the single domain-wall fermion system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_09774 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A lattice formulation of Weyl fermions on a single curved surface Aoki, Shoto Fukaya, Hidenori Kan, Naoto High Energy Physics - Lattice Mesoscale and Nanoscale Physics High Energy Physics - Theory In the standard lattice domain-wall fermion formulation, one needs two flat domain-walls where both of the left- and right-handed massless modes appear. In this work we investigate a single domain-wall system with a nontrivial curved background. Specifically we consider a massive fermion on a $3D$ square lattice, whose domain-wall is a $2D$ sphere. In the free theory, we find that a single Weyl fermion is localized at the wall and it feels gravity through the induced spin connection. With a topologically nontrivial $U(1)$ link gauge field, however, we find a zero mode with the opposite chirality localized at the center where the gauge field is singular. In the latter case, the low-energy effective theory is not chiral but vectorlike. We discuss how to circumvent this obstacle in formulating lattice chiral gauge theory in the single domain-wall fermion system. |
| title | A lattice formulation of Weyl fermions on a single curved surface |
| topic | High Energy Physics - Lattice Mesoscale and Nanoscale Physics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2402.09774 |