Towards de Sitter from 10D

TL;DR

This work analyzes de Sitter uplifts in type IIB string theory by lifting KKLT volume-stabilization to a full 10D framework. It shows that a single gaugino-condensed Kahler modulus cannot be uplifted to de Sitter due to strong backreaction on the volume modulus, but racetrack stabilization with multiple condensates can decouple the AdS depth from the light modulus and enable de Sitter uplift, with a consistent 10D picture. The authors develop a detailed 10D treatment of gaugino backreaction and ISD flux, demonstrating how the uplift dynamics arise from global volume backreaction rather than local throat physics, and they discuss how alpha-prime corrections could further facilitate controlled uplifts. Overall, the 10D perspective reinforces racetrack stabilization as a robust route to de Sitter vacua in warped IIB compactifications, while highlighting caveats and directions for future work, including explicit backreacted racetrack solutions and extensions to LVS-type setups.

Abstract

Using a 10D lift of non-perturbative volume stabilization in type IIB string theory we study the limitations for obtaining de Sitter vacua. Based on this we find that the simplest KKLT vacua with a single Kahler modulus stabilized by a gaugino condensate cannot be uplifted to de Sitter. Rather, the uplift flattens out due to stronger backreaction on the volume modulus than has previously been anticipated, resulting in vacua which are meta-stable and SUSY breaking, but that are always AdS. However, we also show that setups such as racetrack stabilization can avoid this issue. In these models it is possible to obtain supersymmetric AdS vacua with a cosmological constant that can be tuned to zero while retaining finite moduli stabilization. In this regime, it seems that de Sitter uplifts are possible with negligible backreaction on the internal volume. We exhibit this behavior also from the 10D perspective.

Figures (6)

• Figure 1: Left: Off-shell potential $V(l)$ for the $S^2$ volume modulus in the case without a $6D$ c.c. for $n=25$ flux units and different values of the dimensionless three-brane tension $\mathcal{T}_3$: $\mathcal{T}_3=0$ in blue, $\mathcal{T}_3=0.1$ in yellow, $\mathcal{T}_3=0.21$ in green, $\mathcal{T}_3=0.4$ in red and $\mathcal{T}_3=0.6$ in purple. As can be seen, the more energy density, the higher the vacuum energy, but the flattening prevents the minimum to go above zero. Right: Off-shell potential $V(l)$ for the $S^2$ volume modulus in the case with a $6D$ c.c. for $n=25$ flux units, $\mathcal{T}_5=0.004$ and different values of the dimensionless three-brane tension $\mathcal{T}_3$: $\mathcal{T}_3=0$ in blue, $\mathcal{T}_3=0.1$ in yellow, $\mathcal{T}_3=0.21$ in green, $\mathcal{T}_3=0.4$ in red and $\mathcal{T}_3=0.6$ in purple. This time it is also possible to find de Sitter minima once enough three-brane tension has been added.
• Figure 2: From the classical $10D$ supergravity to the quantum $4D$ theory with broken supersymmetry. Green arrows denote steps that can be followed through unambiguously and with reasonable amount of control. The dimensional reduction of the classical $10D$ theory is well understood. Incorporating non-perturbative quantum effects in the $4D$ EFT can be performed with reasonable amount of control as well. The de Sitter uplift of the supersymmetric KKLT vacua within $4D$ EFT suffers from ambiguities as explained in section \ref{['KKLT:uplift']}. For this reason we follow the authors of Baumann:2006thBaumann:2007ahDymarsky:2010mfBaumann:2010sx in first lifting the SUSY KKLT vacua to $10D$. Since at this stage we have a quantum deformed $10D$ action we may include the SUSY breaking effects of an anti-brane and thereafter dimensionally reduce the $10D$ potential to $4D$. This prescription avoids the intermediate classical $10D$/$4D$ descriptions with a SUSY breaking runaway potential (marked in red).
• Figure 3: Two aspects of $\overline{D3}$ back-reaction: on the one hand the local throat perturbations sourced by the $\overline{D3}$-brane at the bottom of the throat fall off exponentially towards the bulk Calabi-Yau. Their UV-tail can be neglected in our analysis. On the other hand the overall volume of the bulk Calabi-Yau adjusts and so does the condensate $\langle \lambda \lambda \rangle$. This global back-reaction effect turns out to be crucial for our analysis.
• Figure 4: The F-term potential of \ref{['antibranesuperpot']} for the case $b=0$ as a function of the uplift parameter $c$. In this case the superpotential reads $W=W_0+A\,(1+c\, S) \exp(ia\rho)$. The $\rho$-minimum moves out to larger values and stays $AdS$ as $c$ increases. This behavior is compatible with our $10D$ analysis but does not uniquely follow from it.
• Figure 5: The F-term potential analogous to \ref{['antibranesuperpot']} for the case $b=0$ as a function of the uplift parameter $c$ for racetrack superpotential. In this case the superpotential reads $W=W_0+A_1\,(1+c\, S) \exp(ia_1\rho)+A_2\,(1+c\, S) \exp(ia_2\rho)$. For simplicity we have put the coefficients of the $S$-dependence in both gaugino condensates equal. For vanishing uplift $c=0$ the scalar potential shows the tuned racetrack Minkowski minimum at smaller values of $\rho$ then the co-existing KKLT $AdS$ minimum at larger values or $\rho$. Clearly, the racetrack minimum gets successfully uplifted to de Sitter even for $c\ll 1$ while the KKLT-minimum at larger $\rho$ continues to move out to larger values and stays $AdS$ as $c$ increases. Note, that this a 4D effective extrapolation to the two-condensate case, for which we do not have a fully matching 10D description yet.