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

TL;DR

Braun, Rummel, Sumitomo, and Valandro implement the D-term generated racetrack uplift in type IIB orientifolds, using toric CY hypersurfaces with h^{1,1} ≤ 4 to realize two rigid, non-intersecting small divisors and a D7-brane flux that fixes a linear relation between their volumes via ζ_D=0. After imposing this D-term constraint, the resulting racetrack F-term potential can yield de Sitter minima for β<1, with explicit LVS-based stabilization and controlled non-perturbative effects from E3-instantons or gaugino condensation. The paper conducts a comprehensive scan over Kreuzer–Skarke geometries to assess feasible β values, finding order-one proximity to β≈1 in many cases, and constructs concrete examples with global consistency (tadpoles, instanton zero modes) that achieve dS vacua. The work demonstrates the promise of globally consistent, ten-dimensional uplift mechanisms in a concrete, computable class of Calabi–Yau compactifications, while noting open-string moduli challenges and potential extensions to more general h^{1,1}_- setups for visible sectors.

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.

Figures (4)

• Figure 1: Four D7 branes and rank-one instanton: on the left, we show the distribution of $\beta_{\text{max}}$, i.e. the maximal value of $\beta$ for each polytope that we find in our scan. On the right we show all possible values of $\beta$ and their relative distribution in our scan.
• Figure 2: One D7 brane and rank-one instanton: on the left, we show the distribution of $\beta_{\text{max}}$, i.e. the maximal value of $\beta$ for each polytope that we find in our scan. On the right we show all possible values of $\beta$ and their relative distribution in our scan.
• Figure 3: Four D7 branes and rank-two instanton: on the left, we show the distribution of $\beta_{\text{max}}$, i.e. the maximal value of $\beta$ for each polytope that we find in our scan. On the right we show all possible values of $\beta$ and their relative distribution in our scan.
• Figure 4: One D7 brane and rank-two instanton: on the left, we show the distribution of $\beta_{\text{max}}$, i.e. the maximal value of $\beta$ for each polytope that we find in our scan. On the right we show all possible values of $\beta$ and their relative distribution in our scan.