Building an explicit de Sitter

TL;DR

The paper tackles the challenge of producing explicit metastable de Sitter vacua in string theory by realizing Kähler uplifting in type IIB setups and by examining how the large-volume limit scales with the rank of the condensing gauge group.A detailed Kreuzer-Skarke survey shows that very large gauge-group ranks are common in the landscape, motivating a concrete explicit model on CP^4_{11169}[18] that achieves large-rank gaugino condensation while satisfying D7/D3 tadpole and flux consistency.The authors present dual IIB and F-theory descriptions of the global model, including a Whitney-brane D7 configuration, rigidification fluxes, and a careful accounting of D3 charges, as well as explicit stabilization of complex-structure moduli and the axio-dilaton via ISD fluxes.In the resulting two-parameter Calabi-Yau, the Kähler moduli are stabilized by a combination of nonperturbative effects and α'-corrections, yielding a metastable dS vacuum with moduli masses in a favorable hierarchy and explicit numerical data for the stabilized values.

Abstract

We construct an explicit example of a de Sitter vacuum in type IIB string theory that realizes the proposal of Kähler uplifting. As the large volume limit in this method depends on the rank of the largest condensing gauge group we carry out a scan of gauge group ranks over the Kreuzer-Skarke set of toric Calabi-Yau threefolds. We find large numbers of models with the largest gauge group factor easily exceeding a rank of one hundred. We construct a global model with Kähler uplifting on a two-parameter model on $\mathbb{CP}^4_{11169}$, by an explicit analysis from both the type IIB and F-theory point of view. The explicitness of the construction lies in the realization of a D7 brane configuration, gauge flux and RR and NS flux choices, such that all known consistency conditions are met and the geometric moduli are stabilized in a metastable de Sitter vacuum with spontaneous GUT scale supersymmetry breaking driven by an F-term of the Kähler moduli.

Figures (6)

• Figure 1: The large gauge group indicator $N_{lg}$ as a function of $h^{1,1}$. The grey dots denote the general set of models, while the blue dots denote the conservative set (for explanations see text). The red dashed line denotes the critical gauge group rank for Kähler uplifting $N_{lg}^{\text{crit.}} = 30$.
• Figure 2: The points represent $W_0, \,S$ pairs that allow a stable de Sitter solution of the potential given in eq. \ref{['VT1T2']} for $A_1=A_2=1$. The curve represents a fit $W_0 = C_1 s^{-C_2}$, with $C_1 = 70.2$ and $C_2 = 2.35$. Note that there is a small deviation from the one modulus case where $C_2=1.5$.
• Figure 3: The scalar potential $V(T_1,T_2)$ is a function of four real scalar fields. We show $V(T_1,T_2)$ as a single valued function with the other three fields evaluated at the minimum.
• Figure 4: Visualization of a blown up $Sp(1)$ singularity.
• Figure 5: 3D projection of the fan of the $Sp(2)$ resolution manifold for the subset of coordinates $\{X,Y,Z,\sigma,v_1,v_3\}$. The top layer of grey lattice points corresponds to the projection $\underline{v}\rightarrow 1$ while the bottom layer to $\underline{0}\rightarrow 0$. The blue point indicates the origin. In the first plot from the LHS, we see the cone spanned by $\{x,y,v_3\}$ is such that the one-cones $x$, $y$ and $z$ can never lie in one cone and hence $XYZ$ is an element of the SR ideal. In the second plot, we see that the cone spanned by $\{x,z,\sigma\}$ is such that $z$, $v_1$ and $z$, $v_3$ respectively can never lie in one cone. In the third plot we see that the cone spanned by $\{x,z,v_3\}$ forces $X \sigma$ and $X v_1$ to lie in the SR ideal. $\sigma v_3$ is an element of the SR ideal because $v_1$ lies on a line that connects them and hence they can never lie in one cone. These are all possible elements of the SR ideal, notice that for example $y$ and $v_1$ lie in one cone: $\{y,v_1,v_3\}$.