Candidate de Sitter Vacua (2406.13751v2)

Abstract: We construct compactifications of type IIB string theory that yield, at leading order in the $\alpha^\prime$ and $g_s$ expansions, de Sitter vacua of the form envisioned by Kachru, Kallosh, Linde, and Trivedi. We specify explicit Calabi-Yau orientifolds and quantized fluxes for which we derive the four-dimensional effective supergravity theories, incorporating the exact flux superpotential, the nonperturbative superpotential from Euclidean D3-branes, and the K\"ahler potential at tree level in the string loop expansion but to all orders in $\alpha'$. Each example includes a Klebanov-Strassler throat region containing a single anti-D3-brane, whose supersymmetry-breaking energy, computed at leading order in $\alpha'$, causes an uplift to a metastable de Sitter vacuum in which all moduli are stabilized. Finding vacua that demonstrably survive subleading corrections, and in which the quantization conditions are completely understood, is an important open problem for which this work has prepared the foundations.

• The paper constructs candidate de Sitter vacua by implementing explicit Calabi-Yau orientifold compactifications with quantized fluxes and an anti-D3-brane uplift.
• It uses rigorous numerical analysis to stabilize the moduli with perturbative and nonperturbative corrections, ensuring a comprehensive treatment of the scalar potential.
• The work outlines future challenges in higher-order corrections and flux quantization, laying the groundwork for addressing the cosmological constant problem.

Analysis of "Candidate de Sitter Vacua"

This paper presents a detailed investigation into the construction of candidate de Sitter vacua within the framework of type IIB string theory compactifications, specifically targeting scenarios that potentially exhibit metastable de Sitter solutions. The research builds upon the Kachru, Kallosh, Linde, and Trivedi (KKLT) scenario, initially proposed about two decades ago, which suggests a method to realize de Sitter vacua by compactifying string theory on Calabi-Yau orientifolds with the inclusion of quantized fluxes, nonperturbative effects, and anti-D3-brane uplift.

Key Contributions

1. Construction of de Sitter Vacua: The authors successfully construct compactifications yielding de Sitter vacua at leading order in the $\alpha'$ and $g_s$ expansions. These constructions adhere closely to the KKLT blueprint, leveraging explicit Calabi-Yau orientifolds and specified quantized fluxes.
2. Detailed Theoretical Setup: A suite of 33,371 compactifications is considered, each featuring a Klebanov-Strassler throat with a single anti-D3-brane. This specific configuration supplies the necessary uplift energy to transition from a supersymmetric anti-de Sitter (AdS) vacuum to a metastable de Sitter vacuum. Stabilization of the complex structure moduli, Kähler moduli, and the axion-dilaton is achieved through a combination of classical and nonperturbative mechanisms, including gaugino condensation and Euclidean D3-brane instantons.
3. Numerical and Analytical Techniques: The research implements rigorous numerical methods to handle the intricacies of moduli stabilization and potential landscape exploration. The authors incorporate perturbative $\alpha'^3$ corrections and nonperturbative corrections tied to worldsheet instantons into the calculations of the Kähler potential and Kähler coordinates, ensuring a more comprehensive treatment of the scalar potential.
4. Future Implications and Challenges: The paper identifies critical open questions, particularly the existence and characterization of KKLT de Sitter vacua under the inclusion of higher-order corrections and stringent flux quantization conditions. Furthermore, it highlights the need for continued advancement in the computational technology employed to navigate these complex landscapes more efficiently.

Results and Implications

The paper signifies a substantial step toward the practical construction of de Sitter vacua within string theory frameworks, contributing valuable methodologies and insights into the physics of the early universe and the cosmological constant problem. A robust analysis of the moduli stabilization problem within the rich tapestry of string compactifications could lead to shedding light on real-world phenomena such as inflation and dark energy.

Moreover, this work sets the stage for future investigations into string landscape dynamics, the profound interplay between geometry and field theory, and the broader implications of the string landscape for theoretical and observational cosmology.

Concluding Remarks

In conclusion, while the paper does not claim definitive proof of existing physical de Sitter vacua in string theory, it lays the groundwork for a systematic effort to understand the underlying structures and potentialities inherent in string compactifications. The combination of detailed theoretical models, computational advances, and empirical utilization of available data points toward a promising avenue for addressing some of the most enigmatic questions in modern theoretical physics.