  We develop a renormalized continuum field theory for a directed polymer
interacting with a random medium and a single extended defect. The
renormalization group is based on the operator algebra of the pinning
potential; it has novel features due to the breakdown of hyperscaling in a
random system. There is a second-order transition between a localized and a
delocalized phase of the polymer; we obtain analytic results on its critical
pinning strength and scaling exponents. Our results are directly related to
spatially inhomogeneous Kardar-Parisi-Zhang surface growth.
