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A lattice formulation of Weyl fermions on a single curved surface
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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.
Forward citations
Cited by 2 Pith papers
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Ginsparg-Wilson Hamiltonians with Improved Chiral Symmetry
A tunable family of Ginsparg-Wilson Hamiltonians is constructed in which the chiral charge becomes progressively more quantized as k increases, though locality degrades.
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Lattice Weyl Fermion on a Single Spherical Domain-Wall
On a spherical domain-wall lattice, a monopole background generates an extra center-localized zero mode with opposite chirality, so the low-energy theory is vector-like rather than chiral.
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