Multiple modular symmetries as the origin of flavour

Abstract

We develop a general formalism for multiple moduli and their associated modular symmetries. We apply this formalism to an example based on three moduli with finite modular symmetries $S_4^A$, $S_4^B$ and $S_4^C$, associated with two right-handed neutrinos and the charged lepton sector, respectively. The symmetry is broken by two bi-triplet scalars to the diagonal $S_4$ subgroup. The low energy effective theory involves the three independent moduli fields ${\tau }_A$, ${\tau }_B$ and ${\tau }_C$, which preserve the residual modular subgroups $Z_3^A$, $Z_2^B$ and $Z_3^C$, in their respective sectors, leading to trimaximal TM${}_1$ lepton mixing, consistent with current data, without flavons.

Comments: 31 pages, 1 figure, 6 tables, refs and comments added