Open string multi-branched and Kähler potentials

We consider type II string compactications on Calabi-Yau orientifolds with uxes and D-branes, and analyse the F-term scalar potential that simultaneously involves closed and open string modes. In type IIA models with D6-branes this potential can be directly computed by integrating out Minkowski three-forms. The result shows a multi- branched structure along the space of lifted open string moduli, in which discrete shifts in special Lagrangian and Wilson line deformations are compensated by changes in the RR ux quanta. The same sort of discrete shift symmetries are present in the superpotential and constrain the Kahler potential. As for the latter, inclusion of open string moduli breaks the factorisation between complex structure and Kahler moduli spaces. Nevertheless, the 4d Kahler metrics display a set of interesting relations that allow to rederive the scalar potential analytically. Similar results hold for type IIB ux compactications with D7- brane Wilson lines.