Moduli Stabilisation versus Chirality for MSSM like Type IIB Orientifolds (0711.3389v2)

Abstract: We investigate the general question of implementing a chiral MSSM like D-brane sector in Type IIB orientifold models with complete moduli stabilisation via F-terms induced by fluxes and space-time instantons, respectively gaugino condensates. The prototype examples are the KKLT and the so-called large volume compactifications. We show that the ansatz of first stabilising all moduli via F-terms and then introducing the Standard Model module is misleading, as a chiral sector notoriously influences the structure of non-perturbative effects and induces a D-term potential. Focusing for concreteness on the large volume scenario, we work out the geometry of the swiss-cheese type Calabi-Yau manifold P_[1,3,3,3,5][15]_(3,75) and analyse whether controllable and phenomenologically acceptable Kaehler moduli stabilisation can occur by the combination of F- and D-terms.

Moduli Stabilization versus Chirality for MSSM-like Type IIB Orientifolds

This paper presents a detailed investigation into the challenge of integrating a chiral Minimal Supersymmetric Standard Model (MSSM)-like D-brane sector within Type IIB orientifold models, while achieving complete moduli stabilization through fluxes and non-perturbative effects, such as F-terms. The authors specifically critique and extend the well-known KKLT and large volume scenarios for moduli stabilization by considering the impact of including a chiral MSSM sector.

In Type IIB string theory scenarios, moduli stabilization is crucial as it involves fixing the values of various scalar fields that represent the sizes and shapes of extra-dimensional spaces. This stabilization often relies on introducing fluxes and non-perturbative effects, which are expected to fix all moduli at a point in the scalar potential to avoid any runaway directions. The paper questions the traditional approach of first stabilizing all moduli and subsequently embedding the MSSM sector, arguing that such a sequence may lead to inconsistencies, particularly due to the effects of a chiral sector on the structure of non-perturbative effects and the induction of D-term potentials.

Key numerical insights are discussed regarding the potential minimization and stabilization of moduli, with particular emphasis on the large volume compactification method. The paper focuses on the Swiss-cheese type Calabi-Yau manifold $_{[1,3,3,3,5]}[15]_{(3,75)}$ as a concrete example, investigating the interplay between F- and D-term potentials in moduli stabilization. The F-term potential, driven by non-perturbative superpotential contributions, is scrutinized for its capability to stabilize the Kähler moduli effectively, while D-terms are explored for their role in addressing charged states from the MSSM sector.

The paper presents the following significant findings and claims:

1. Interdependency of Moduli Stabilization and MSSM Embedding: The MSSM-like chiral D-branes affect the landscape of possible non-perturbative effects, often generating D-term potentials which might compromise the initial large volume minimum.
2. Geometric Dependency: The choice of geometrical setup, particularly rigid and singular divisors, significantly impacts the ability to generate viable superpotentials that contribute to moduli stabilization without breaking MSSM phenomenology at high scales.
3. Kähler Moduli Stabilization: For the $_{[1,3,3,3,5]}[15]_{(3,75)}$ manifold, the stabilization involves a combination of rigid cycle-choosing that supports E3-instanton contributions to the superpotential. However, maintaining a consistent large volume minimum requires careful attention to additional moduli-dependent terms introduced by D-brane chirality.
4. Phenomenological Impact and Predictivity: The approach underscores a reduction in predictivity for low-energy parameters due to the complex interactions between chiral sectors and moduli stabilization mechanisms. The paper promotes the potential of the large volume scenario as a fertile ground for predictive string phenomenology, provided these intricate interdependencies are adequately managed.
5. Implications for Future Research: The paper opens pathways for further research to develop more robust models that reconcile the incorporation of chiral matter sectors with consistent and stable moduli configurations. This includes exploring other Calabi-Yau spaces with potentially more favorable topological properties for supporting such configurations.

In conclusion, the research sheds light on critical challenges at the intersection of string phenomenology and moduli stabilization, emphasizing the need for refined strategies that account for the complexities introduced by chiral D-brane sectors in Type IIB orientifold models. This work is foundational for advancing towards more comprehensive string model constructions with the capability to derive realistic low-energy phenomenology from fundamental string theory principles. Future advancements in this field will likely involve deeper explorations into geometric configurations, flux choices, and their implications on both cosmological and MSSM-like phenomenology.