Towards Classical de Sitter Solutions in String Theory

Abstract: We investigate the type II string effective potential at tree-level and derive necessary ingredients for having de Sitter solutions in orientifold models with fluxes. Furthermore, we examine some explicit O6 compactifications in IIA supergravity on manifolds with SU(3)-structure in the limit where the orientifold sources are smeared. In particular, we use a simple ten-dimensional Ansatz for four-dimensional de Sitter solutions and find the explicit criteria in terms of the torsion classes such that these de Sitter solutions solve the equations of motion. We have verified these torsion conditions for the cosets and the Iwasawa manifold and it turns out that the conditions cannot be fulfilled for these spaces. However, this investigation allows us to find new non-supersymmetric AdS solutions for some cosets. It remains an open question whether there exist SU(3)-structure manifolds that satisfy the conditions on the torsion classes for these simple de Sitter solutions to exist.

Towards Classical de Sitter Solutions in String Theory

The work titled "Towards Classical de Sitter Solutions in String Theory" explores an intricate analysis of the potential existence of de Sitter (dS) solutions in the framework of string theory with a specific emphasis on classical ingredients. It methodically evaluates the parameters essential to acquire these solutions in orientifold models enhanced by fluxes, advancing our understanding of the underlying requirements and challenges.

Summary

The central theme of the paper is the exploration of tree-level potentials within Type IIA supergravity compactifications on spaces possessing a $(3)$-structure manifold, under circumstances where the orientifold sources are effectively spread or "smeared". This approach relies on thoroughly analyzing the conditions under which the de Sitter solutions emerge as valid solutions from the equations of motion.

The research confirms that while de Sitter solutions are computationally feasible under specific torsion conditions, they generally cannot be satisfied in the commonly examined coset spaces and the Iwasawa manifold. Despite this, the study extends to uncover alternative non-supersymmetric Anti-de Sitter (AdS) solutions within certain cosets.

Significant Findings

Key insights from the paper reveal that:

• The presence of classical ingredients like background fluxes and orientifold planes contributes significantly to fixing the moduli, which is pivotal in the stabilization of potential minima for de Sitter solutions.
• Several no-go theorems illustrate the prohibitive conditions against obtaining dS solutions, sharpening our comprehension of the constraints involved.
• The stability of potential dS solutions remains a complex aspect, especially since the conditions verified for torsion classes in common geometrical frameworks meet considerable hindrances.

Implications and Future Developments

The implications of this research are profound both theoretically and practically:

• The exploration opens up new avenues in the detailed study of string vacua, potentially guiding future research toward identifying specific manifold geometries that satisfy the proposed torsion criteria.
• By elaborating on the restrictions posed by no-go theorems, the study enriches the dialogue on alternative methods to circumnavigate these limitations.
• The discovery of non-supersymmetric AdS solutions for coset geometries paves the way for further investigations into the landscape of possible string vacua.

The theoretical ramifications extend to deepening our understanding of the interplay between supergravity formulations and string compactifications. Practically, this could polish the framework within which models handle characteristics like positive energy density in four-dimensional space-times derived from ten-dimensional supergravity.

Looking forward, it becomes essential to continue evaluating different manifold configurations in search of viable dS solutions and ascertain if the stated conditions can be relaxed or redefined. Furthermore, future research could involve a more profound examination of compactification theories integrated with non-classical aspects and the effects of flux quantization, aiming toward a holistic understanding of string theory vacua.

In conclusion, while the quest for classical de Sitter solutions within string theory endures complex challenges and stringent conditions, the insights garnered from this research inject vital knowledge into the discourse, setting the stage for continued innovations and discoveries.