Spontaneous CP violation and partially broken modular flavor symmetries

TL;DR

This paper explores how spontaneous CP violation can arise from moduli stabilization in modular flavor models, highlighting the role of flux compactifications and symmetry breaking in generating CP violation.

Contribution

It demonstrates that combined effects of Type IIB flux compactifications and modular invariance can induce spontaneous CP violation, including scenarios with or without supersymmetry breaking.

Findings

Flux compactifications can induce spontaneous CP violation.

Partial breaking of modular symmetry facilitates CP violation.

Properties of CP and modular invariant scalar potentials are characterized.

Abstract

We study the realization of spontaneous CP violation through moduli stabilization. In modular flavor models, the source of CP violation is the vacuum expectation values of the complex structure moduli of toroidal compact space. We demonstrate that the combined effects of Type IIB flux compactifications with modular invariant couplings between the moduli and matter fields can induce spontaneous CP violation without or with supersymmetry breaking. Furthermore, some general properties of CP and modular invariant scalar potentials are presented. It is found that certain modifications or partial breakings of modular symmetry are useful in generating spontaneous CP violation.