Symmetries and stabilisers in modular invariant flavour models

• Published in: The journal of high energy physics Vol. 2020; no. 11; pp. 1 - 20
• Main Authors: de Medeiros Varzielas, Ivo, Levy, Miguel, Zhou, Ye-Ling
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2020; SpringerOpen
• Subjects: Beyond Standard Model; Classical and Quantum Gravitation; Elementary Particles; Neutrino Physics; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Quark Masses and SM Parameters; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Neutrino Physics; Beyond Standard Model; Quark Masses and SM Parameters
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP11(2020)085

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.