Supersymmetric scale-separated AdS$_3$ orientifold vacua of type IIB (2502.04791v2)

Abstract: I construct supersymmetric AdS$_3$ vacua of type IIB string theory that exhibit parametric scale separation in the controlled regime. These solutions arise from compactifications on seven-dimensional manifolds equipped with co-closed $G_2$-structures, in the presence of orientifold planes preserving minimal supersymmetry. I focus on $\mathbb{Z}_2^3$ orbifolds of a specific solvmanifold and all seven-dimensional nilmanifolds, each requiring distinct configurations of intersecting O5-planes, which are treated in the smeared approximation. Weak string coupling, large volumes and scale separation for the classical backgrounds on the nilmanifolds are achieved by tuning unbounded fluxes to large values. Furthermore, for some solutions, the holographic field theory operators dual to the lightest scalar fields have integer conformal dimensions at tree level, as in other scale-separated type II orientifold backgrounds.

• The paper constructs supersymmetric, scale-separated AdS3 vacua in Type IIB string theory by compactifying on seven-dimensional solvmanifolds with co-closed G2-structures.
• Analysis of the scalar mass spectra reveals operators in the dual field theory have integer conformal dimensions, consistent with previous findings.
• These constructions challenge existing notions on scale separation in string compactifications and offer new avenues for model-building.

Supersymmetric Scale-Separated AdS\textsubscript{3} Vacua in Type IIB String Theory

The paper addresses the construction of supersymmetric AdS\textsubscript{3} vacua within the framework of Type IIB string theory, achieved through compactification on seven-dimensional solvmanifolds characterized by a co-closed $G_2$-structure. The research showcases innovative approaches in achieving parametric scale separation, effectively exploring the frontiers of string phenomenology, particularly considering the stringent requirements on scale separation in lower-dimensional vacua.

Key Contributions

The main contributions of this research are as follows:

1. Construction of Vacua: The study successfully constructs AdS\textsubscript{3} vacua by compactifying Type IIB string theory on specific seven-dimensional solvmanifolds. These solvmanifolds possess co-closed $G_2$-structures and are further orbifolded and orientifolded, culminating in vacua with minimal supersymmetry in three dimensions.
2. Orientifold Content: Two distinct setups are explored: one involving four sets of O5-planes and another involving a solitary set of O5-planes. This distinction is significant in maintaining the requisite O5-plane charge balance without the need for additional ingredients like D5-branes in some configurations.
3. Parametric Scale Separation: Achieving parametric scale separation, a crucial aspect in lower-dimensional compactifications, is demonstrated by manipulating unbounded flux parameters. The study establishes the feasibility of scale separation, which is often a challenging factor in inducing phenomenologically relevant features.
4. Mass Spectra Analysis: The analysis of the scalar mass spectra reveals that operators in the holographically dual field theory possess integer conformal dimensions, providing a consistent extension to prior observations in four-dimensional setups within massive Type IIA string theory.
5. Unique Orientifolding and Orbifolding: The chosen orientifolding and orbifolding strategies not only facilitate the required O5-plane content but also ensure the removal of unwanted lower-dimensional cycles, crucial for meeting phenomenological demands and enabling scale separation.

Theoretical and Practical Implications

The theoretical implications are profound, as these constructions challenge existing notions and conjectures regarding scale separation in string compactifications. The emergence of integer scaling dimensions supports the consistency of supersymmetric field theories emerging from string theory. Practically, these findings open new avenues in model-building, especially in scenarios where achieving a controlled and separated hierarchy of scales in lower dimensions is quintessential.

Future Directions

This research paves the way for further exploration of co-closed $G_2$-structure manifolds to uncover additional scale-separated solutions in Type IIB string theory. Analyzing the backreaction of O-planes and the potential extension to models incorporating weak $G_2$-structures could enrich the understanding of the underlying geometry and its physical ramifications. Additionally, resolving the orbifold singularities and exploring the implications for heterotic-M theory dualities could offer deeper insights into the connectivity of string theories across various dimensional frameworks.

In conclusion, this paper provides a significant step forward in the construction of scale-separated vacua in string theory, offering both challenges and opportunities for future theoretical and practical advancements. It serves as a foundational contribution to the ongoing quest to reconcile string phenomenology with observable universe models.