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Moduli Stabilisation versus Chirality for MSSM like Type IIB Orientifolds

Ralph Blumenhagen, Sebastian Moster, Erik Plauschinn

TL;DR

The paper probes whether MSSM-like chiral D7-brane sectors can be embedded in Type IIB orientifolds with complete moduli stabilisation, focusing on the Large Volume Scenario. It shows that chirality induces D-terms and charged zero modes that challenge pure F-term moduli fixing and non-perturbative superpotential generation, arguing for a combined F-term and D-term stabilization mechanism. A concrete swiss-cheese Calabi-Yau, IP_[1,3,3,3,5][15], with explicit orientifold, D7-branes, and E3-instantons is analyzed to realize this mechanism, yielding a LVS-like large volume minimum where some moduli are fixed by D-terms at the boundary of the Kähler cone and the rest by instantons. The authors also discuss subtleties from axions and multiple instantons, and present a globally defined toy model demonstrating feasibility while highlighting the need for broader Calabi-Yau scans and full complex-structure stabilization for realistic vacua.

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 Stabilisation versus Chirality for MSSM like Type IIB Orientifolds

TL;DR

The paper probes whether MSSM-like chiral D7-brane sectors can be embedded in Type IIB orientifolds with complete moduli stabilisation, focusing on the Large Volume Scenario. It shows that chirality induces D-terms and charged zero modes that challenge pure F-term moduli fixing and non-perturbative superpotential generation, arguing for a combined F-term and D-term stabilization mechanism. A concrete swiss-cheese Calabi-Yau, IP_[1,3,3,3,5][15], with explicit orientifold, D7-branes, and E3-instantons is analyzed to realize this mechanism, yielding a LVS-like large volume minimum where some moduli are fixed by D-terms at the boundary of the Kähler cone and the rest by instantons. The authors also discuss subtleties from axions and multiple instantons, and present a globally defined toy model demonstrating feasibility while highlighting the need for broader Calabi-Yau scans and full complex-structure stabilization for realistic vacua.

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.

Paper Structure

This paper contains 16 sections, 77 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Type IIB orientifolds
  3. Large volume scenario
  4. Orientifolds with intersecting D7-branes
  5. Instantons and chirality
  6. The chiral D7-brane sector
  7. E3-brane instantons
  8. Moduli stabilisation for chiral models
  9. F-term scalar potential
  10. The ${\rm I P}_{[1,3,3,3,5]}[15]$ Calabi-Yau
  11. The topology of ${\rm I P}_{[1,3,3,3,5]}[15]$
  12. Moduli stabilisation
  13. Orientifold with tadpole cancellation
  14. Conclusions
  15. Cohomology classes of line bundles
  16. ...and 1 more sections

Figures (3)

  • Figure 1: Singular rigid divisors.
  • Figure 2: The potential $V({\cal V},\tau_b,\tau_{c})$ for $\mathcal{V}=2.15\cdot 10^{16}$.
  • Figure 3: The potential $V( {\cal V}, \tau_b, \tau_c )$ for $\tau_c=0.33$.