| Summary: | Abstract We investigate deformations of ℤ 2 $$ {\mathrm{\mathbb{Z}}}_2 $$ orbifold singularities on the toroidal orbifold T 6 / ℤ 2 × ℤ 6 $$ {T}^6/\left({\mathrm{\mathbb{Z}}}_2\times {\mathrm{\mathbb{Z}}}_6\right) $$ 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 / ℤ 2 × ℤ 6 $$ {T}^6/\left({\mathrm{\mathbb{Z}}}_2\times {\mathrm{\mathbb{Z}}}_6\right) $$ with discrete torsion and adapt it to the ℤ 2 × ℤ 6 × Ω ℛ $$ \left({\mathrm{\mathbb{Z}}}_2\times {\mathrm{\mathbb{Z}}}_6\times \Omega \mathrm{\mathcal{R}}\right) $$ point group by modding out the remaining ℤ 3 $$ {\mathrm{\mathbb{Z}}}_3 $$ subsymmetry and the orientifold projection Ω ℛ $$ \Omega \mathrm{\mathcal{R}} $$ . We first study the local behaviour of the ℤ 3 × Ω ℛ $$ {\mathrm{\mathbb{Z}}}_3\times \Omega \mathrm{\mathcal{R}} $$ 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 M string, for the same global D6-brane models.
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