Curved domain-wall fermions

TL;DR

This paper explores fermion systems with curved domain-wall mass terms on a lattice, revealing edge states that experience gravity-like effects and recover symmetry in the continuum limit.

Contribution

It introduces curved domain-wall fermions on a lattice and demonstrates their edge states' gravitational interactions and symmetry restoration in the continuum.

Findings

Edge modes feel gravity via induced Spin or Spin^c connections.

Good agreement with continuum theory predictions.

Rotational symmetry is recovered in the continuum limit.

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.