Chiral edge states on spheres for lattice domain wall fermions

Abstract: Recently Weyl edge states on manifolds in dimension $d+1$ with a connected $d$-dimensional boundary were proposed as candidates for lattice regularization of chiral gauge theories, for even $d$. The examples considered to date include solid cylinders in any odd dimension, and the 3-ball with boundary $S^2$. Here we consider the general case of a $(d+1)$-dimensional ball for any even $d$ and show that the theory for the edge states on $S^d$ describe a conventional Weyl fermion on a sphere with half-integer momenta. A possible advantage of such theories is that they can be discretized by a square lattice without breaking the underlying discrete hypercubic symmetry.