Chiral edge states on spheres for lattice domain wall fermions

TL;DR

This paper explores Weyl edge states on spheres in higher dimensions as a way to regularize chiral gauge theories on lattices, demonstrating their potential for discretization without symmetry breaking.

Contribution

It generalizes the construction of Weyl edge states on spheres for any even dimension, showing they describe Weyl fermions with half-integer momenta and can be discretized on a square lattice.

Findings

Edge states on $S^d$ describe Weyl fermions with half-integer momenta.

Theories can be discretized on a square lattice without breaking hypercubic symmetry.

Generalization to any even dimension provides a new approach for lattice chiral gauge theories.

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.