Constraints from de Sitter metastability in heterotic string compactifications

TL;DR

This paper investigates the constraints on achieving metastable de Sitter vacua in heterotic string compactifications on Calabi-Yau threefolds, focusing on the K"ahler moduli sector and using tensor eigenvalue analysis.

Contribution

It introduces a tensor eigenvalue framework for analyzing K"ahler potential constraints and extends known results from two to three-dimensional moduli spaces.

Findings

Identifies the discriminant of the Calabi-Yau intersection tensor for three-dimensional moduli.

Provides explicit examples illustrating the constraints.

Generalizes previous two-dimensional moduli space results.

Abstract

We study the possibility of obtaining metastable de Sitter vacua of heterotic string theory compactified on a Calabi-Yau threefold which are classical and simple in the K\"ahler moduli sector of the theory. For this, we exploit a known necessary condition on the K\"ahler potential in N=1-supergravity, which we, under the assumption that only moduli fields contribute to supersymmetry breaking, express in terms of a tensorial eigenvalue problem for the Calabi-Yau triple intersection tensor. For three-dimensional moduli spaces we are able to identify the discriminant of the Calabi-Yau intersection tensor in the analysis, generalizing a known result for two-dimensional moduli spaces. We also discuss explicit examples and possible generalizations.