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

Understand

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.