A Lattice Formulation of Weyl Fermions on a Single Curved Surface
Abstract 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...
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Veröffentlicht in: | Progress of Theoretical and Experimental Physics 2024-04, Vol.2024 (4), p.1 |
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Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | Abstract
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. |
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ISSN: | 2050-3911 2050-3911 |
DOI: | 10.1093/ptep/ptae041 |