Deformations, moduli stabilisation and gauge couplings at one-loop

Abstract

We investigate deformations of {mathrm{mathbb{Z}}}_2 orbifold singularities on the toroidal orbifold {T}^6/left({mathrm{mathbb{Z}}}_2times {mathrm{mathbb{Z}}}_6right) 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/left({mathrm{mathbb{Z}}}_2times {mathrm{mathbb{Z}}}_6right) with discrete torsion and adapt it to the left({mathrm{mathbb{Z}}}_2times {mathrm{mathbb{Z}}}_6times Omega mathrm{mathcal{R}}right) point group by modding out the remaining {mathrm{mathbb{Z}}}_3 subsymmetry and the orientifold projection Omega mathrm{mathcal{R}} . We first study the local behaviour of the {mathrm{mathbb{Z}}}_3times Omega mathrm{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 [1, 2], 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 Mstring, for the same global D6-brane models.