## CP symmetry and symplectic modular invariance

Gui-Jun Ding, Ferruccio Feruglio, Xiang-Gan Liu

SciPost Phys. 10, 133 (2021) · published 7 June 2021

### Abstract

We analyze CP symmetry in symplectic modular-invariant supersymmetric theories. We show that for genus $g\ge 3$ the definition of CP is unique, while two independent possibilities are allowed when $g\le 2$. We discuss the transformation properties of moduli, matter multiplets and modular forms in the Siegel upper half plane, as well as in invariant subspaces. We identify CP-conserving surfaces in the fundamental domain of moduli space. We make use of all these elements to build a CP and symplectic invariant model of lepton masses and mixing angles, where known data are well reproduced and observable phases are predicted in terms of a minimum number of parameters.

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