  The discovery by Tranquada et al. of an ordered phase of charged domain walls
in the high-Tc cuprates leads us to consider the possible existence of a
quantum domain-wall liquid. We propose minimal models for the quantization, by
meandering fluctuations, of isolated charged domain walls. These correspond to
lattice string models. The simplest model of this kind, a directed lattice
string, can be mapped onto a quantum spin chain or on a classical
two-dimensional solid-on-solid surface model. The model exhibits a rich phase
diagram, containing several rough phases with low-lying excitations as well as
ordered phases which are gapped.
