Chiral fermions on lattice axion strings

TL;DR

This paper demonstrates how lattice discretization of axion strings can host chiral fermions, with their number changing via phase transitions influenced by Wilson-like terms, illustrating anomaly inflow in a regulated setting.

Contribution

It introduces a lattice regularization of axion strings that supports chiral fermions and explores the role of Wilson-like terms in their emergence and phase transitions.

Findings

Chiral fermions can be realized on lattice axion strings.

The number of chiral fermions jumps with Wilson-like parameter variations.

Anomaly inflow is demonstrated through one-loop Feynman diagrams.

Abstract

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.