Anomalous Discrete Flavor Symmetry and Domain Wall Problem

TL;DR

This paper explores how making discrete flavor symmetries anomalous under QCD can address the cosmological domain wall problem, but finds that in most models, the anomaly only partially resolves the issue.

Contribution

It investigates the impact of QCD anomalies on discrete flavor symmetries and their effectiveness in solving the domain wall problem in flavor models.

Findings

QCD anomaly can partially lift vacuum degeneracy

Most known models still have residual degenerate vacua

Addressing the domain wall problem requires additional mechanisms

Abstract

Discrete flavor symmetry is often introduced for explaining quark/lepton masses and mixings. However, its spontaneous breaking leads to the appearance of domain walls, which is problematic for cosmology. We consider a possibility that the discrete flavor symmetry is anomalous under the color SU(3) so that it splits the energy levels of degenerate discrete vacua as a solution to the domain wall problem. We find that in most known models of flavor symmetry, the QCD anomaly effect can only partially remove the degeneracy and there still remain degenerate vacua.