Effective potential and domain-wall evolution of the FN phase

Calculate the anomaly-induced effective potential of the Froggatt–Nielsen phase, determine whether the instanton-induced fermion interaction lifts the degeneracy between Froggatt–Nielsen-related vacua, and analyze the resulting thermal evolution of possible domain walls.

Background

The scalar sector contains a Froggatt–Nielsen phase that is massless at the classical level. Nonperturbative effects may generate an effective potential and thereby affect the degeneracy of vacua related by the Froggatt–Nielsen symmetry. The cosmological consequences, including possible domain-wall formation and evolution, are not resolved by the leading particle-physics analysis.

References

Assessing possible domain walls requires an analysis of the effective potential for the FN phase. In particular, one must determine whether the instanton-induced fermion interaction produces an energy difference between FN-related vacua. We leave the calculation of this potential and of the thermal abundances discussed above, together with an analysis of possible domain-wall evolution, for future work.

— Non-Invertible Froggatt-Nielsen Symmetry  (2610.21688 - Otsuka et al., 15 Oct 2026) in Section 6.3, subsection “Phenomenological consequences”

A detailed analysis of the thermal history and the resulting gravitational-wave signal and dark matter signature is left for future work.

— Froggatt-Nielsen mechanism with non-invertible symmetry  (2610.26761 - Ding et al., 19 Oct 2026) in Appendix, Section “Vacuum structure of the scalar potential compatible with $\mathbb{Z}_2$ gauging of $\mathbb{Z}_N$ (or $U(1)$) symmetry”