Non-Invertible Froggatt-Nielsen Symmetry
Abstract
We investigate non-invertible completions of anomalous flavor symmetries and their application to Dirac neutrino masses. We formulate symmetry defects dressed by topological quantum field theories for flavor symmetries including finite non-Abelian flavor transformations with rational anomaly characters and modular flavor symmetries with the rational part of modular anomaly cocycles, for gauge sectors with the required exact higher-form symmetry. As a concrete example, we construct a Froggatt-Nielsen (FN) model in which an order-four subgroup ℤ4FN⊂ U(1)FN is completed into a non-invertible defect through its mixed anomaly with an intermediate hidden U(1)H gauge sector in the infrared monopole-decoupling limit. The non-invertible FN symmetry can be explicitly broken at the energy scale where monopoles become dynamical. This breaking from the infrared viewpoint can be realized in an ultraviolet hidden SU(2)H theory as instanton effects, where a constrained instanton with topological charge one generates a fermion mixing term that violates FN charge by one unit. Its coefficient contains the nonperturbative factor ζH∼exp[−8π2/gH2(vH)]. When independent FN-breaking terms are subleading, integrating out the heavy fermions gives (Yν)ij∝ζHεℓi+nj in a rotated basis for the right-handed neutrinos, to leading order in the instanton-induced fermion mixing. The nonperturbative factor provides the exponential suppression of the neutrino Yukawa couplings, while the FN charges determine the powers of ε. For the chosen FN charges and generic order-one coefficients, m2/m3∼ε, favoring normal ordering. An independent ℤ8D gauge symmetry forbids Majorana masses. The same FN charge assignment reproduces the leading quark and charged-lepton Yukawa hierarchies.
Related
- Froggatt-Nielsen mechanism with non-invertible symmetry
- How natural are Froggatt-Nielsen Models?
- Probing the Geometry of Viable Froggatt-Nielsen-like Flavor Textures
- Lightest-mass suppression and weaker Majorana cancellation in Froggatt--Nielsen textures
- Symmetry-permuting entanglers for non-invertible symmetry-protected topological phases
BibTeX
@misc{otsuka2026noninvertible,
title = {{Non-Invertible Froggatt-Nielsen Symmetry}},
author = {Hajime Otsuka and Ryo Yokokura},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.21688},
eprint = {2610.21688},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.21688},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Non-Invertible Froggatt-Nielsen Symmetry
AU - Hajime Otsuka
AU - Ryo Yokokura
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.21688
UR - https://arxiv.org/abs/2610.21688
AB - We investigate non-invertible completions of anomalous flavor symmetries and their application to Dirac neutrino masses. We formulate symmetry defects dressed by topological quantum field theories for flavor symmetries including finite non-Abelian flavor transformations with rational anomaly characters and modular flavor symmetries with the rational part of modular anomaly cocycles, for gauge sectors with the required exact higher-form symmetry. As a concrete example, we construct a Froggatt-Nielsen (FN) model in which an order-four subgroup ℤ_4^FN⊂ U(1)_FN is completed into a non-invertible defect through its mixed anomaly with an intermediate hidden U(1)_H gauge sector in the infrared monopole-decoupling limit. The non-invertible FN symmetry can be explicitly broken at the energy scale where monopoles become dynamical. This breaking from the infrared viewpoint can be realized in an ultraviolet hidden SU(2)_H theory as instanton effects, where a constrained instanton with topological charge one generates a fermion mixing term that violates FN charge by one unit. Its coefficient contains the nonperturbative factor ζ_H∼exp[−8π^2/g_H^2(v_H)]. When independent FN-breaking terms are subleading, integrating out the heavy fermions gives (Y_ν)_ij∝ζ_Hε^ℓ_i+n_j in a rotated basis for the right-handed neutrinos, to leading order in the instanton-induced fermion mixing. The nonperturbative factor provides the exponential suppression of the neutrino Yukawa couplings, while the FN charges determine the powers of ε. For the chosen FN charges and generic order-one coefficients, m_2/m_3∼ε, favoring normal ordering. An independent ℤ_8^D gauge symmetry forbids Majorana masses. The same FN charge assignment reproduces the leading quark and charged-lepton Yukawa hierarchies.
ER -