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.

中文翻译：

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CP 对称性和辛模不变性

我们在辛模不变超对称理论中分析 CP 对称性。我们表明，对于属 $g\ge 3$，CP 的定义是唯一的，而当 $g\le 2$ 时允许两种独立的可能性。我们讨论了 Siegel 上半平面以及不变子空间中模量、物质多重态和模形式的变换性质。我们在模空间的基本域中识别 CP 守恒表面。我们利用所有这些元素来构建轻子质量和混合角的 CP 和辛不变模型，其中可以很好地再现已知数据，并根据最少数量的参数预测可观察的相位。