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. Realization of these chiral fermions relies on the
presence of 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. These jumps coincide with phase transitions along a two dimensional
surface passing through the string's core. A one-loop Feynman diagram is used
to demonstrate how anomaly inflow works in this lattice regularized theory.Comment: Typo corrected, new references added and style files change