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Curved domain-wall fermions
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abstract
We consider fermion systems on a square lattice with a mass term having a curved domain-wall. Similarly to the conventional flat domain-wall fermions, massless and chiral edge states appear on the wall. In the cases of $S^1$ and $S^2$ domain-walls embedded into flat hypercubic lattices, we find that these edge modes feel gravity through the induced Spin or Spin$^c$ connections. The gravitational effect is encoded in the Dirac eigenvalue spectrum as a gap from zero. In the standard continuum extrapolation of the square lattice, we find a good agreement with the analytic prediction in the continuum theory. We also find that the rotational symmetry of the edge modes is automatically recovered in the continuum limit.
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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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