Four-modulus "Swiss Cheese" chiral models
  We study the 'Large Volume Scenario' on explicit, new, compact, four-modulus Calabi-Yau manifolds. We pay special attention to the chirality problem pointed out by Blumenhagen, Moster and Plauschinn. Namely, we thoroughly analyze the possibility of generating neutral, non-perturbative superpotentials from Euclidean D3-branes in the presence of chirally intersecting D7-branes. We find that taking proper account of the Freed-Witten anomaly on non-spin cycles and of the Kaehler cone conditions imposes severe constraints on the models. Nevertheless, we are able to create setups where the constraints are solved, and up to three moduli are stabilized. 
Andres Collinucci, Maximilian Kreuzer, Christoph Mayrhofer and   Nils-Ole Walliser