Zero Modes of Massive Fermions Delocalize from Axion Strings

TL;DR

This paper investigates how massive fermion zero modes on axion strings delocalize as the fermion mass increases, affecting the string's properties and interactions, with implications for axion phenomenology.

Contribution

It introduces a detailed analysis of the phase transition of zero modes from localized to delocalized states as fermion mass varies, combining analytic, numerical, and theoretical approaches.

Findings

Zero modes delocalize at a critical fermion mass.

The effective theory breaks down when zero modes delocalize.

Explicit numerical solutions illustrate the phase structure.

Abstract

Massless chiral excitations can arise from the interactions between a fermion and an axion string, propagating along the string and allowing it to superconduct. The properties of these excitations, or zero modes, dictate how the string interacts with light and can thus have important phenomenological consequences. In this paper, we add a nowhere-vanishing Dirac mass for the fermion in the usual model of axion electrodynamics. We find that the zero modes exhibit an interesting phase structure in which they delocalize from the string's core as the mass increases, up until a critical value past which they disappear. We study this structure from an analytic perspective, with explicit numerical solutions, and via anomaly inflow arguments. Finally, we derive the two-dimensional effective theory of the zero mode and its interactions with the four-dimensional gauge field and show how this effective theory breaks down as the zero modes delocalize.