This paper presents a rigorous analysis of metastable vacua within the framework of no-scale supergravities and Calabi-Yau string models with a focus on de Sitter (dS) solutions that arise with spontaneously broken N=1 supersymmetry. The authors examine conditions under which the scalar partners of the Goldstino are non-tachyonic, a requirement that hinges exclusively on the structure of the Kahler potential. The significance of this rests on its sufficiency: other scalars can be assigned arbitrarily large positive square masses by judiciously tuning the superpotential parameters.
Key Insights and Numerical Results
The paper explores both heterotic and orientifold string compactifications, emphasizing large-volume limits, and illustrates that the no-scale nature of these models constrains the feasible masses for the 'sGoldstinos' based on superpotential configurations. A notable finding is that instances of positive sGoldstino mass terms only emerge in select compactifications or Goldstino orientations, leveraging subleading corrections to the Kahler potential that override the no-scale property. This coincides with the fact that a positive sGoldstino mass is essential for establishing metastable dS vacua, simplifying the quest for viable dS ground states.
A deeper inquiry into specific compactifications reveals certain classes that altogether fail to accommodate metastable dS vacua, irrespective of superpotential structure or moduli vacuum expectation values. Particularly, K3-fibrations demonstrate an intrinsic exclusion for such vacua, regardless of moduli count or configurations.
Theoretical and Practical Implications
The analysis provides useful conditions for constructing dS vacua in low-energy compactifications, advancing our understanding of string models and their compatibility with positive cosmological constants. The paper highlights a notable restriction in the quest for stable vacua: the preferred supersymmetry-breaking directions are those in which the metastability condition necessitates a positive sGoldstino mass independent of the superpotential - a factor that considerably eases the pursuit of viable solutions.
Future Directions
There remains an unexplored potential for implementing these findings in the development of models suitable for cosmological applications, such as slow-roll inflationary scenarios. Although not addressed in the paper, insights into metastability conditions may offer a pathway to identify prospective moduli stabilization and inflationary mechanisms in string-theoretical settings. Furthermore, computationally driven scans of string vacua could benefit from the proposed methodology in evaluating Kahler potential configurations against metastability conditions.
Conclusion
The exploration conducted in this paper elucidates the intricate dynamics governing metastable vacua in string theory compactifications. By establishing the principal role of the Kahler potential in determining sGoldstino masses, the paper fosters a pathway towards viable dS vacua solutions, achieving coherence between theory constraints and supersymmetry-breaking dynamics.