  We investigate the localization of stiff directed lines with bending energy
by a short-range random potential. Using perturbative arguments, Flory
arguments, and a replica calculation, we show that a stiff directed line in 1+d
dimensions undergoes a localization transition with increasing disorder for
$d>2/3$. We demonstrate that this transition is accessible by numerical
transfer matrix calculations in 1+1 dimensions and analyze the properties of
the disorder-dominated phase. On the basis of the two-replica problem, we
propose a relation between the localization of stiff directed lines in 1+d
dimensions and of directed lines under tension in 1+3d dimensions, which is
strongly supported by identical free energy distributions. This shows that pair
interactions in the replicated Hamiltonian determine the nature of directed
line localization transitions with consequences for the critical behavior of
the Kardar-Parisi-Zhang (KPZ) equation. Furthermore, we quantify how the
persistence length of the stiff directed line is reduced by disorder.
