  We attempt to access the regime of strong coupling between charge carriers
and transverse dynamics of an isolated conducting ``stripe'', such as those
found in cuprate superconductors. A stripe is modeled as a partially doped
domain wall in an antiferromagnet (AF), introduced in the context of two
different models: the t-J model with strong Ising anisotropy, and the Hubbard
model in the Hartree-Fock approximation. The domain walls with a given linear
charge density are supported artificially by boundary conditions. In both
models we find a regime of parameters where doped holes lose their spin and
become holons (charge Q=1, spin S_z=0), which can move along the stripe without
frustrating AF environment. One aspect in which the holons on the AF domain
wall differ from those in an ordinary one-dimensional electron gas is their
transverse degree of freedom: a mobile holon always resides on a transverse
kink (or antikink) of the domain wall. This gives rise to two holon flavors and
to a strong coupling between doped charges and transverse fluctuations of a
stripe.
