Scalar geometry and masses in Calabi-Yau string models

TL;DR

This paper analyzes the geometry of scalar manifolds in Calabi-Yau string models, exploring their impact on scalar masses, comparing heterotic and orientifold models, and examining conditions for symmetry and implications for supersymmetry breaking.

Contribution

It provides a general formula for the Kahler potential based on topological data, studies the conditions for symmetric scalar manifolds, and analyzes scalar mass behavior in these geometries.

Findings

Heterotic and orientifold models share the same scalar manifold when the space is symmetric.

Scalar masses depend on geometric parameters controlling deviations from coset structures.

The study of sGoldstino masses informs vacuum stability and scalar mass hierarchies.

Abstract

We study the geometry of the scalar manifolds emerging in the no-scale sector of Kahler moduli and matter fields in generic Calabi-Yau string compactifications, and describe its implications on scalar masses. We consider both heterotic and orientifold models and compare their characteristics. We start from a general formula for the Kahler potential as a function of the topological compactification data and study the structure of the curvature tensor. We then determine the conditions for the space to be symmetric and show that whenever this is the case the heterotic and the orientifold models give the same scalar manifold. We finally study the structure of scalar masses in this type of geometries, assuming that a generic superpotential triggers spontaneous supersymmetry breaking. We show in particular that their behavior crucially depends on the parameters controlling the departure of the geometry from the coset situation. We first investigate the average sGoldstino mass in the hidden sector and its sign, and study the implications on vacuum metastability and the mass of the lightest scalar. We next examine the soft scalar masses in the visible sector and their flavor structure, and study the possibility of realizing a mild form of sequestering relying on a global symmetry.