CP violation and target-space modular invariance

TL;DR

This paper demonstrates that in certain string models, CP violation can be absent if the complex moduli's vacuum expectation values are related to target-space duality symmetries, extending previous conjectures and results.

Contribution

It establishes a link between CP conservation and target-space duality invariance in string models with complex moduli, generalizing prior findings and exploring implications for brane world scenarios.

Findings

CP is conserved if the modulus v.e.v. is a duality group element.

Confirms conjecture that CP is conserved for T modulus on the boundary of the fundamental domain.

Results apply to models with spontaneous CP violation where the CP-odd scalar transforms under unbroken symmetries.

Abstract

We show that, in perturbative string models where the source of CP violation is a complex vacuum expectation value (v.e.v.) for one or more compactification moduli, CP is conserved if a CP transformation acting on the modulus values is an element of a target-space (self-)duality group. Where the duality group is SL(2,Z) the result confirms a conjecture of Bailin et al. that CP is conserved for v.e.v.'s of the T modulus on the boundary of the fundamental domain, and generalises Giedt's result on the removability of complex Yukawa couplings in such models. Our result applies to any model of spontaneous CP violation where the CP-odd scalar transforms under a symmetry that is not explicitly broken. We consider whether similar results could be obtained in ``brane worlds''.