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We investigate deformations of $\mathbb{Z}_2$ orbifold singularities on thetoroidal orbifold $T^6/(\mathbb{Z}_2\times\mathbb{Z}_6)$ with discrete torsionin the framework of Type IIA orientifold model building with intersectingD6-branes wrapping special Lagrangian cycles. To this aim, we employ thehypersurface formalism developed previously for the orbifold$T^6/(\mathbb{Z}_2\times\mathbb{Z}_2)$ with discrete torsion and adapt it tothe $\mathbb{Z}_2\times\mathbb{Z}_6\times\Omega\mathcal{R}$ point group bymodding out the remaining $\mathbb{Z}_3$ subsymmetry and the orientifoldprojection $\Omega\mathcal{R}$. We first study the local behaviour of the$\mathbb{Z}_3\times\Omega\mathcal{R}$ invariant deformation orbits undernon-zero deformation and then develop methods to assess the deformation effectson the fractional three-cycle volumes globally. We confirm that D6-branessupporting USp(2N) or SO(2N) gauge groups do not constrain any deformation,while deformation parameters associated to cycles wrapped by D6-branes withU(N) gauge groups are constrained by D-term supersymmetry breaking. Thesefeatures are exposed in global prototype MSSM, Left-Right symmetric andPati-Salam models first constructed in arXiv:1509.00048 and arXiv:1409.1236,for which we here count the number of stabilised moduli and study flatdirections changing the values of some gauge couplings. Finally, we confrontthe behaviour of tree-level gauge couplings under non-vanishing deformationsalong flat directions with the one-loop gauge threshold corrections at theorbifold point and discuss phenomenological implications, in particular onpossible LARGE volume scenarios and the corresponding value of the string scale$M_{\text{string}}$, for the same global D6-brane models.

Deformations, Moduli Stabilisation and Gauge Couplings at One-Loop