  We investigate the localization of stiff directed lines with bending energy
by a short-range random potential. We apply perturbative arguments, Flory
scaling arguments, a variational replica calculation, and functional
renormalization to 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 in
detail. 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. We support the proposed relation to
directed lines via multifractal analysis revealing an analogous Anderson
transition-like scenario and a matching correlation length exponent.
Furthermore, we quantify how the persistence length of the stiff directed line
is reduced by disorder.
