Chiral edge states on spheres for lattice domain wall fermions

Recently Weyl edge states on manifolds in dimension <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>d</a:mi><a:mo>+</a:mo><a:mn>1</a:mn></a:math> with a connected <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>d</c:mi></c:math>-dimensional boundary were proposed as candidates for lattice regularization of chiral gauge theories, for even <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>d</e:mi></e:math>. The examples considered to date include solid cylinders in any odd dimension, and the 3 ball with boundary <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msup><g:mi>S</g:mi><g:mn>2</g:mn></g:msup></g:math>. Here we consider the general case of a (<i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mrow><i:mi>d</i:mi><i:mo>+</i:mo><i:mn>1</i:mn></i:mrow></i:math>)-dimensional ball for any even <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>d</k:mi></k:math> and show that the theory for the edge states on <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msup><m:mi>S</m:mi><m:mi>d</m:mi></m:msup></m:math> 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.