Constraints from de Sitter metastability in heterotic string compactifications

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.