Abstract
The localization of a directed polymer onto an extended defect (such as a line or a plane) in the presence of competing bulk disorder is examined. Based on scaling ideas and exact analysis on a hierarchical lattice, we develop a new renormalization scheme to study the directed polymer localization problem. We establish absence of delocalization transition for attractive columnar defect in the marginal dimension ${\mathit{d}}_{\mathit{c}}$=2, and for attractive planar defect in d=3. For columnar defect in three dimensions, our simulations yield a localization length exponent ${\ensuremath{\nu}}_{\mathrm{\ensuremath{\perp}}}$=1.8\ifmmode\pm\else\textpm\fi{}0.6.
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