Circling the Square: Deforming fractional D-branes in Type II/$\Omega \mathcal{R}$ orientifolds

Abstract

We study complex structure deformations of special Lagrangian cycles associated to fractional D-branes at ${\mathbb{Z}}_2$ singularities in Type II/$\Omega \mathcal{R}$ 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 D-brane 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.

52 pages, 11 figures, 13 tables; minor clarifications, typos corrected, accepted by JHEP

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• From Type II string theory towards BSM/dark sector physics
• Towards Geometric D6-Brane Model Building on non-Factorisable Toroidal ${\mathbb{Z}}_4$-Orbifolds
• Massless Spectra and Gauge Couplings at One-Loop on Non-Factorisable Toroidal Orientifolds