Unpaired Weyl fermion on an axion string in a finite lattice

Domain wall fermions use a <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mn>2</a:mn><a:mi>n</a:mi></a:math>-dimensional spacetime defect embedded in (<c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:mn>2</c:mn><c:mi>n</c:mi><c:mo>+</c:mo><c:mn>1</c:mn></c:mrow></c:math>)-dimensional spacetime to realize massless lattice Dirac fermions. Recent work has extended this idea to realize a single unpaired Weyl fermion in a finite lattice. Here, we realize the same using a <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mn>2</e:mn><e:mi>n</e:mi></e:math>-dimensional string defect embedded in (<g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mrow><g:mn>2</g:mn><g:mi>n</g:mi><g:mo>+</g:mo><g:mn>2</g:mn></g:mrow></g:math>)-dimensional spacetime on a finite lattice for <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>n</i:mi><i:mo>=</i:mo><i:mn>1</i:mn></i:math>. This string is a lattice version of the continuum axion string described in Callan-Harvey []. Our results are obtained in a Hamiltonian formulation in Minkowski spacetime. Extending the results to Euclidean spacetime and to <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>n</k:mi><k:mo>&gt;</k:mo><k:mn>1</k:mn></k:math> is straightforward. This work has applications to lattice chiral gauge theories and axion cosmology.