2024/02/15 by Shoto Aoki, Aoki, Shoto, Hidenori Fukaya +3 · 3 citations
Mathematics · Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #High Energy Physics - Theory (hep-th) #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #Topological Materials and Phenomena
paper · pdf · doi:10.48550/arxiv.2402.09774
openalex publication_date 2024/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.