Symmetries and stabilisers in modular invariant flavour models

Abstract

A bstract The idea of modular invariance provides a novel explanation of flavour mixing. Within the context of finite modular symmetries Γ N and for a given element γ ∈ Γ N , we present an algorithm for finding stabilisers (specific values for moduli fields τ γ which remain unchanged under the action associated to γ ). We then employ this algorithm to find all stabilisers for each element of finite modular groups for N = 2 to 5, namely, Γ 2 ≃ S 3 , Γ 3 ≃ A 4 , Γ 4 ≃ S 4 and Γ 5 ≃ A 5 . These stabilisers then leave preserved a specific cyclic subgroup of Γ N . This is of interest to build models of fermionic mixing where each fermionic sector preserves a separate residual symmetry.

Topics & Concepts