Z-string global gauge anomaly and Lorentz non-invariance

TL;DR

This paper investigates a novel global gauge anomaly in 3+1-dimensional chiral non-Abelian gauge theories linked to Z-string configurations, exploring its relation to other anomalies and potential Lorentz and CPT symmetry violations.

Contribution

It clarifies the connection between the Z-string global gauge anomaly and other known anomalies, and discusses a possible trade-off with Lorentz and CPT invariance violations.

Findings

Identifies a new global gauge anomaly associated with Z-strings.

Establishes a relation between this anomaly and other anomalies in various dimensions.

Suggests a potential link between the anomaly and Lorentz/CPT symmetry breaking.

Abstract

Certain (3+1)-dimensional chiral non-Abelian gauge theories have been shown to exhibit a new type of global gauge anomaly, which in the Hamiltonian formulation is due to the fermion zero-modes of a Z-string-like configuration of the gauge potential and the corresponding spectral flow. Here, we clarify the relation between this Z-string global gauge anomaly and other anomalies in both 3+1 and 2+1 dimensions. We then point out a possible trade-off between the (3+1)-dimensional Z-string global gauge anomaly and the violation of CPT and Lorentz invariance.