De Sitter vacua from a D-term generated racetrack potential in hypersurface Calabi-Yau compactifications

TL;DR

This paper explores a specific string theory mechanism to achieve de Sitter vacua using D-term generated racetrack potentials in hypersurface Calabi-Yau compactifications, systematically identifying suitable geometries and D-brane configurations.

Contribution

It provides a systematic search and explicit examples of Calabi-Yau manifolds with the right properties to realize de Sitter vacua via D-term racetrack potentials.

Findings

Identified Calabi-Yau three-folds with suitable divisors for the mechanism.

Constructed consistent D7-brane flux configurations inducing D-terms.

Computed potential minima confirming de Sitter vacua.

Abstract

In arXiv:1407.7580 a mechanism to fix the closed string moduli in a de Sitter minimum was proposed: a D-term potential generates a linear relation between the volumes of two rigid divisors which in turn produces at lower energies a race-track potential with de Sitter minima at exponentially large volume. In this paper, we systematically search for implementations of this mechanism among all toric Calabi-Yau hypersurfaces with $h^{1,1}\leq 4$ from the Kreuzer-Skarke list. For these, topological data can be computed explicitly allowing us to find the subset of three-folds which have two rigid toric divisors that do not intersect each other and that are orthogonal to $h^{1,1}-2$ independent four-cycles. These manifolds allow to find D7-brane configurations compatible with the de Sitter uplift mechanism and we find an abundance of consistent choices of D7-brane fluxes inducing D-terms leading to a de Sitter minimum. Finally, we work out a couple of models in detail, checking the global consistency conditions and computing the value of the potential at the minimum.