Chiral fermions on lattice axion strings

I discretize axion string configuration coupled to a Dirac fermion, which in the continuum binds a massless chiral fermion in its core when the winding is one. I show that such a configuration can host one or more chiral fermions when regulated on the lattice. To realize these chiral fermions I introduce Wilson-like terms similar to the Wilson term used in lattice domain wall fermions. The number of chiral fermions on the string jumps as the Wilson-like parameter is varied with respect to the other mass scales in the problem. A one-loop Feynman diagram is used to demonstrate how anomaly inflow works in this lattice regularized theory.