Deformations on Tilted Tori and Moduli Stabilisation at the Orbifold Point

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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 T⁶/(Z₂ × Z₂), we mod out an additional Z₃ symmetry to describe phenomenologically appealing backgrounds and reduce to Z₃ 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 T⁶/(Z₂ × Z₆') 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.