CP Symmetry and Symplectic Modular Invariance

TL;DR

This paper investigates CP symmetry within symplectic modular-invariant supersymmetric theories, establishing the uniqueness of CP definition for higher genus and constructing a model that predicts lepton mixing parameters.

Contribution

It provides a comprehensive analysis of CP symmetry in these theories, identifying CP-conserving surfaces and developing a predictive lepton mass and mixing model.

Findings

CP definition is unique for genus g≥3.

Two CP possibilities exist for genus g≤2.

The model reproduces known lepton data and predicts observable phases.

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.