A lattice regularization of Weyl fermions in a gravitational background
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| Format: | Preprint |
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2024
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| _version_ | 1866909106890080256 |
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| author | Aoki, Shoto Fukaya, Hidenori Kan, Naoto |
| author_facet | Aoki, Shoto Fukaya, Hidenori Kan, Naoto |
| contents | We report on a lattice fermion formulation with a curved domain-wall mass term to nonperturbatively describe fermions in a gravitational background. In our previous work in 2022, we showed under the time-reversal symmetry that the edge-localized massless Dirac fermion appears on one and two-dimensional spherical domain-walls and the spin connection is induced on the lattice in a consistent way with continuum theory. In this work, we extend our study to the Shamir type curved domain-wall fermions without the time-reversal symmetry. We find in the free fermion case that a single Weyl fermion appears on the edge, and feels gravity through the induced spin connection. With a topologically nontrivial $U(1)$ gauge potential, however, we find an oppositely chiral zero mode at the center where the gauge field is singular. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_05636 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A lattice regularization of Weyl fermions in a gravitational background Aoki, Shoto Fukaya, Hidenori Kan, Naoto High Energy Physics - Lattice Mesoscale and Nanoscale Physics Strongly Correlated Electrons High Energy Physics - Theory We report on a lattice fermion formulation with a curved domain-wall mass term to nonperturbatively describe fermions in a gravitational background. In our previous work in 2022, we showed under the time-reversal symmetry that the edge-localized massless Dirac fermion appears on one and two-dimensional spherical domain-walls and the spin connection is induced on the lattice in a consistent way with continuum theory. In this work, we extend our study to the Shamir type curved domain-wall fermions without the time-reversal symmetry. We find in the free fermion case that a single Weyl fermion appears on the edge, and feels gravity through the induced spin connection. With a topologically nontrivial $U(1)$ gauge potential, however, we find an oppositely chiral zero mode at the center where the gauge field is singular. |
| title | A lattice regularization of Weyl fermions in a gravitational background |
| topic | High Energy Physics - Lattice Mesoscale and Nanoscale Physics Strongly Correlated Electrons High Energy Physics - Theory |
| url | https://arxiv.org/abs/2401.05636 |