Abstract
We investigate deformations of \( {\mathrm{\mathbb{Z}}}_2 \) orbifold singularities on the toroidal orbifold \( {T}^6/\left({\mathrm{\mathbb{Z}}}_2\times {\mathrm{\mathbb{Z}}}_6\right) \) 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 \( {T}^6/\left({\mathrm{\mathbb{Z}}}_2\times {\mathrm{\mathbb{Z}}}_6\right) \) with discrete torsion and adapt it to the \( \left({\mathrm{\mathbb{Z}}}_2\times {\mathrm{\mathbb{Z}}}_6\times \Omega \mathrm{\mathcal{R}}\right) \) 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 \( {\mathrm{\mathbb{Z}}}_3\times \Omega \mathrm{\mathcal{R}} \) 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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Honecker, G., Koltermann, I. & Staessens, W. Deformations, moduli stabilisation and gauge couplings at one-loop. J. High Energ. Phys. 2017, 23 (2017). https://doi.org/10.1007/JHEP04(2017)023
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DOI: https://doi.org/10.1007/JHEP04(2017)023