de Sitter vacua in no-scale supergravities and Calabi-Yau string models (0804.1073v3)

Abstract: We perform a general analysis on the possibility of obtaining metastable vacua with spontaneously broken N=1 supersymmetry and non-negative cosmological constant in the moduli sector of string models. More specifically, we study the condition under which the scalar partners of the Goldstino are non-tachyonic, which depends only on the Kahler potential. This condition is not only necessary but also sufficient, in the sense that all of the other scalar fields can be given arbitrarily large positive square masses if the superpotential is suitably tuned. We consider both heterotic and orientifold string compactifications in the large-volume limit and show that the no-scale property shared by these models severely restricts the allowed values for the `sGoldstino' masses in the superpotential parameter space. We find that a positive mass term may be achieved only for certain types of compactifications and specific Goldstino directions. Additionally, we show how subleading corrections to the Kahler potential which break the no-scale property may allow to lift these masses.

Analysis of Metastable Vacua in No-Scale Supergravities and Calabi-Yau String Models

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.