The Supersymmetric CP problem in Orbifold Compactifications

TL;DR

This paper investigates how spontaneous CP symmetry breaking can occur in orbifold compactifications of string theory, focusing on the effects of moduli stabilization mechanisms and non-perturbative superpotentials on CP-violating phases in supersymmetric models.

Contribution

It analyzes the impact of different moduli stabilization methods and non-perturbative superpotentials on CP violation in orbifold compactifications, including models with various modular symmetries.

Findings

CP-violating phases depend on moduli stabilization mechanisms

Non-perturbative superpotentials can induce CP violation

Models with $PSL(2,Z)$ symmetry exhibit specific CP-violating behaviors

Abstract

The possibility of spontaneous breaking of CP symmetry by the expectation values of orbifold moduli is investigated with particular reference to $CP$ violating phases in soft supersymmetry breaking terms. The effect of different mechanisms for stabilizing the dilaton and the form of the non-perturbative superpotential on the existence and size of these phases is studied. Models with modular symmetries which are subgroups of $PSL(2,Z)$, as well as the single overall modulus $T$ case with the full $PSL(2,Z)$ modular symmetry, are discussed. Non-perturbative superpotentials involving the absolute modular invariant $j(T)$, such as may arise from F-theory compactifications, are considered.