  We formulate and study a class of massive N=2 supersymmetric gauge field
theories coupled to boundary degrees of freedom on the strip. For some values
of the parameters, the infrared limits of these theories can be interpreted as
open string sigma models describing D-branes in large-radius Calabi-Yau
compactifications. For other values of the parameters, these theories flow to
CFTs describing branes in more exotic, non-geometric phases of the Calabi-Yau
moduli space such as the Landau-Ginzburg orbifold phase. Some simple properties
of the branes (like large radius monodromies and spectra of worldvolume
excitations) can be computed in our model. We also provide simple worldsheet
models of the transitions which occur at loci of marginal stability, and of
Higgs-Coulomb transitions.
