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.

Figure 1

The one-loop Feynman diagram for the Goldstone-Wilczek current.

Figure 2

The light red, green, and yellow regions indicate the values of the parameters of the crossed domain wall, $m_1$ and $m_2$, for which there exist chiral edge states. The net chirality for the relevant parameters is also indicated inside the colored regions. In the region outside of the colored boxes, there are no chiral edge states confined to the defect.