We study complex structure deformations of special Lagrangian cycles associated to fractional D-branes at Z 2 singularities in Type II/ΩR orientifold models. By means of solving hypersurface constraints, we show how to compute the volumes of the most simple D-brane configurations. These volumes are given as a function of the deformation parameters depending on the Dbrane position relative to the smoothed out singularity. We observe which cycles keep the special Lagrangian property in various deformation scenarios and what orientifold involutions are allowed. As expected, the volume and thus the tree level value of the gauge coupling hardly change for D-branes not wrapping the exceptional cycle on the deformed singularity, whereas the volume of D-branes passing through the singularity depends on the deformation parameter by some power law.

We discuss deformations of orbifold singularities on tilted tori in the context of Type IIA orientifold model building with D6-branes on special Lagrangian cycles. Starting from T 6 /(Z 2 × Z 2 ), we mod out an additional Z 3 symmetry to describe phenomenologically appealing backgrounds and reduce to Z 3 and ΩR invariant orbits of deformations. While D6-branes carrying SO(2N ) or USp(2N ) gauge groups do not constrain deformations, D6-branes with U(N ) gauge groups develop non-vanishing D-terms if they couple to previously singular, now deformed cycles. We present examples for both types of D6-branes, and in a three-generation Pati-Salam model on T 6 /(Z 2 × Z 6 ) we find that ten out of 15 twisted complex structure moduli are indeed stabilised at the orbifold point by the existence of the brane stacks.

We review the stabilisation of complex structure moduli in Type IIA orientifolds, especially on T 6 /(Z 2 × Z 6 × ΩR) with discrete torsion, via deformations of Z 2 × Z 2 orbifold singularities. While D6-branes in SO(2N ) and USp(2N ) models always preserve gauge groups ten out of the 15 deformation moduli can be stabilised at the orbifold point.

We investigate deformations of Z 2 orbifold singularities on the toroidal orbifold T 6 /(Z 2 × 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 /(Z 2 × Z 2 ) with discrete torsion and adapt it to the (Z 2 × Z 6 × ΩR) point group by modding out the remaining Z 3 subsymmetry and the orientifold projection ΩR. We first study the local behaviour of the Z 3 ×ΩR 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 U Sp(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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