Two-zero textures of the Majorana neutrino mass matrix from ℤ3 gauging of ℤN non-invertible symmetry

A bstract Texture-zero ansatze offer an economical description of neutrino masses, with current data allowing only seven inequivalent two-zero Majorana textures in the charged-lepton mass basis. We investigate how such textures can arise from non-invertible symmetries realized through ℤ 3 gauging of ℤ N . In contrast to ℤ 2 gauging, which necessarily induces diagonal neutrino mass terms via the Weinberg operator, ℤ 3 gauging admits complex representations and allows a richer class of neutrino mass textures. If the light neutrino mass is described by the Weinberg operator, we find that the textures A 1,2 , B 3,4 , and C can be realized from the ℤ 3 gauging of ℤ 13 symmetry, while all the seven phenomenologically viable two-zero textures can emerge from ℤ 3 gauging of ℤ 19 symmetry without requiring supersymmetry. When the neutrino mass is generated by the type-I seesaw mechanism, the structure of the non-invertible symmetry is more restrictive, yielding only texture C for N ≠ 7. These results demonstrate the strong predictive power of non-invertible symmetries for neutrino mass textures. Furthermore, the more general ℤ n gauging of the ℤ N symmetry with n > 3 is analyzed, which results in novel fusion rules.