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arXiv · 2402.09774

A lattice formulation of Weyl fermions on a single curved surface

Shoto Aoki·Hidenori Fukaya·Naoto Kan
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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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Shoto Aoki, Hidenori Fukaya, Naoto Kan. 2024-02-15. A lattice formulation of Weyl fermions on a single curved surface. https://arxiv.org/abs/2402.09774

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