Modular symmetry at level 6 and a new route towards finite modular groups

Abstract

Abstract We propose to construct the finite modular groups from the quotient of two principal congruence subgroups as Γ(N′)/Γ(N″), and the modular group SL(2, ℤ) is ex- tended to a principal congruence subgroup Γ(N′). The original modular invariant theory is reproduced when N′ = 1. We perform a comprehensive study of Γ 6 ′ $$ {\Gamma}_6^{\prime } $$ modular symmetry corresponding to N′ = 1 and N″ = 6, five types of models for lepton masses and mixing with Γ 6 ′ $$ {\Gamma}_6^{\prime } $$ modular symmetry are discussed and some example models are studied numerically. The case of N′ = 2 and N″ = 6 is considered, the finite modular group is Γ(2)/Γ(6) ≅ T′, and a benchmark model is constructed.

Keywords

• Discrete Symmetries
• Neutrino Physics