Abstract
The idea of modular invariance provides a novel explanation of flavour mixing. Within the context of finite modular symmetries ΓN and for a given element γ ∈ ΓN, we present an algorithm for finding stabilisers (specific values for moduli fields τγ 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, Γ2 ≃ S3, Γ3 ≃ A4, Γ4 ≃ S4 and Γ5 ≃ A5. These stabilisers then leave preserved a specific cyclic subgroup of ΓN. This is of interest to build models of fermionic mixing where each fermionic sector preserves a separate residual symmetry.
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de Medeiros Varzielas, I., Levy, M. & Zhou, YL. Symmetries and stabilisers in modular invariant flavour models. J. High Energ. Phys. 2020, 85 (2020). https://doi.org/10.1007/JHEP11(2020)085
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DOI: https://doi.org/10.1007/JHEP11(2020)085