Deformations, Moduli Stabilisation and Gauge Couplings at One-Loop

Abstract

We investigate deformations of ${\mathbb{Z}}_2$ orbifold singularities on the toroidal orbifold $T^6/({\mathbb{Z}}_2\times {\mathbb{Z}}_6)$ with discrete torsion in the framework of Type IIA orientifold model building with intersecting D6-branes wrapping special Lagrangian cycles. To this aim, we employ the hypersurface formalism developed previously for the orbifold $T^6/({\mathbb{Z}}_2\times {\mathbb{Z}}_2)$ with discrete torsion and adapt it to the ${\mathbb{Z}}_2\times {\mathbb{Z}}_6\times \Omega \mathcal{R}$ point group by modding out the remaining ${\mathbb{Z}}_3$ subsymmetry and the orientifold projection $\Omega \mathcal{R}$. We first study the local behaviour of the ${\mathbb{Z}}_3\times \Omega \mathcal{R}$ invariant deformation orbits under non-zero deformation and then develop methods to assess the deformation effects on the fractional three-cycle volumes globally. We confirm that D6-branes supporting USp(2N) or SO(2N) gauge groups do not constrain any deformation, while deformation parameters associated to cycles wrapped by D6-branes with U(N) gauge groups are constrained by D-term supersymmetry breaking. These features are exposed in global prototype MSSM, Left-Right symmetric and Pati-Salam models first constructed in arXiv:1509.00048 and arXiv:1409.1236, for which we here count the number of stabilised moduli and study flat directions changing the values of some gauge couplings. Finally, we confront the behaviour of tree-level gauge couplings under non-vanishing deformations along flat directions with the one-loop gauge threshold corrections at the orbifold point and discuss phenomenological implications, in particular on possible LARGE volume scenarios and the corresponding value of the string scale $M_{\text{string}}$, for the same global D6-brane models.

1+84 pages, 16 figures, 32 tables

References in corpus (20)

• Four-dimensional String Compactifications with D-Branes, Orientifolds and Fluxes
• GUTs in Type IIB Orientifold Compactifications
• Moduli Stabilisation versus Chirality for MSSM like Type IIB Orientifolds
• Moduli Stabilization in Type IIB Orientifolds (II)
• The LHC String Hunter's Companion
• From strings to the MSSM
• Millions of Standard Models on Z6-prime?
• Instantons and Holomorphic Couplings in Intersecting D-brane Models
• Open string multi-branched and Kahler potentials
• Thresholds for Intersecting D-branes Revisited
• The effective action of D6-branes in N=1 type IIA orientifolds
• The Importance of Being Rigid: D6-Brane Model Building on T6/Z2xZ6' with Discrete Torsion
• Gauge Thresholds and Kaehler Metrics for Rigid Intersecting D-brane Models
• Model building with intersecting D6-branes on smooth Calabi-Yau manifolds
• Twisting K3 x T^2 Orbifolds
• Rigour and Rigidity: Systematics on particle physics D6-brane models on Z(2)xZ(6)
• Circling the Square: Deforming fractional D-branes in Type II/$\Omega \mathcal{R}$ orientifolds
• From Type II string theory towards BSM/dark sector physics
• Phases of Inflation
• Towards Geometric D6-Brane Model Building on non-Factorisable Toroidal ${\mathbb{Z}}_4$-Orbifolds

Cited by in corpus (3)

• Kähler moduli stabilization in semi-realistic magnetized orbifold models
• String-scale Gauge Coupling Relations in the Supersymmetric Pati-Salam Models from Intersecting D6-branes
• Strong Dynamics and Natural Inflation