  The effect of fluxes on open string moduli is studied by analyzing the
constraints imposed by supersymmetry on D-branes in type IIB flux backgrounds.
We show that generically the conditions of supersymmetry cannot be maintained
when moving along the geometrical moduli space of the brane, so that open
string moduli are lifted. We argue that there is a disconnected and discrete
set of supersymmetric solutions to the open string equations of motion, which
extends the familiar closed string landscape to the open string sector.
