  Recent transport experiments have established that two-dimensional electron
systems with high-index partial Landau level filling, $\nu^{*} =\nu - \lbrack
\nu \rbrack$, have ground states with broken orientational symmetry. In a
mean-field theory, the broken symmetry state consists of electron stripes with
local filling factor $\lbrack \nu \rbrack + 1 $, separated by hole stripes with
filling factor $\lbrack \nu \rbrack$. We have recently developed a theory of
these states in which the electron stripes are treated as one-dimensional
electron systems coupled by interactions and described by using a Luttinger
liquid model. Among other things, this theory predicts non-linearities of
opposite sign in easy and hard direction resistivities. In this article we
briefly review our theory, focusing on its predictions for the dependence of
non-linear transport exponents on the separation $d$ between the
two-dimensional electron system and a co-planar screening layer.
