Insights on Scale Separation, Rolling Solutions, and Entropy Bounds in Supergravity
This paper explores the concept of scale separation within the framework of ten- and eleven-dimensional supergravity compactifications, examining the conditions under which scale separation can be achieved without invoking orientifolds or corrections to the classical supergravity approximation. The authors explore solutions where supergravity models exhibit rolling solutions in flux-generated potentials and assess these solutions against entropy bounds.
Scale Separation in Supergravity Compactifications
Scale separation is a pivotal concept in supergravity and string theory, evident when the curvature scale of a large, observable universe is significantly smaller than the compactification scale of additional dimensions. The authors revisit this idea, presenting the notion that rolling solutions can naturally lead to scale separation over time. This exploration challenges the traditional reliance on orientifolds or quantum corrections for achieving scale separation, positing that rolling solutions offer an alternative route. This observation has profound implications, especially within swampland constraints, which suggest that real-world physics might reside in the asymptotic regime of moduli space.
Connection with Covariant Entropy Bound
The paper presents an intriguing discussion on entropy bounds, notably the Covariant Entropy Bound (CEB) and the Cohen-Kaplan-Nelson (CKN) bound. These bounds are confronted with lower-dimensional solutions derived from supergravity compactifications. The analysis reveals that rolling solutions sometimes do not adhere to the CEB, implying constraints far beyond the conventional vacua with cosmic horizons. This suggests an intricate relationship between the dynamics of extra dimensions and entropy bounds, as rolling solutions do not exhibit cosmic horizons. Consequently, traditional tools like entropy bounds might require reevaluation in the absence of such horizons.
Implications and Theoretical Development
The exploration into scale separation in rolling solutions sheds light on swampland portals, implying that hierarchies, and hence scale separation, might naturally arise in runaway or asymptotic potentials. This provides a fertile ground for further exploration, especially within the context of string theory and effective field theories. The theoretical implications affect the construction of consistent four-dimensional effective theories with rolling solutions, addressing challenges such as dark energy and cosmic acceleration within string frameworks.
Future Directions
The results of this research prompt several speculative paths for future inquiry. Given that internal curvature-generated potentials fail to achieve scale separation in rolling solutions, flux-supported potentials remain a viable direction for future exploration. Furthermore, the potential violation of entropy bounds in rolling solutions encourages a revision of these bounds or a deeper understanding of their applicability in time-dependent backgrounds. The implications extend to string model building, cosmology, and our understanding of possible higher-dimensional extensions of the Standard Model.
In conclusion, this paper provides substantial theoretical advancements regarding scale separation and entropy bounds in supergravity, highlighting the importance of rolling solutions. It emphasizes the need for revisiting established theoretical frameworks to accommodate the dynamic, time-dependent aspects of compactification scenarios in high-dimensional theories.