A global anomaly from the Z-string

TL;DR

This paper investigates the spectral flow and Berry phase of fermions in the background of Z-strings in SU(2) Yang-Mills-Higgs theory, revealing a new global gauge anomaly with implications for chiral gauge theories.

Contribution

It demonstrates the existence of a novel global gauge anomaly associated with Z-strings in SU(2) Yang-Mills-Higgs theory, based on spectral flow and Berry phase analysis.

Findings

Spectral flow of Dirac eigenvalues across the Z-string configuration.

Non-vanishing Berry phase around the Z-string.

Identification of a new global gauge anomaly.

Abstract

The response of isodoublet fermions to classical backgrounds of essentially 2-dimensional boson fields in SU(2) Yang-Mills-Higgs theory is investigated. In particular, the spectral flow of Dirac eigenvalues is calculated for a non-contractible sphere of configurations passing through the vacuum and the Z-string (the embedded vortex solution). Also, a non-vanishing Berry phase is established for adiabatic transport "around" the Z-string. These results imply the existence of a new type of global (non-perturbative) gauge anomaly in SU(2) Yang-Mills-Higgs quantum field theory with a single doublet of left-handed fermions. Possible extensions to other chiral gauge field theories are also discussed.