  We present a microscopic model for a line junction formed by counter or
co-propagating single mode quantum Hall edges corresponding to different
filling factors. The ends of the line junction can be described by two possible
current splitting matrices which are dictated by the conditions of both lack of
dissipation and the existence of a linear relation between the bosonic fields.
Tunneling between the two edges of the line junction then leads to a
microscopic understanding of a phenomenological description of line junctions
introduced some time ago. The effect of density-density interactions between
the two edges is considered, and renormalization group ideas are used to study
how the tunneling parameter changes with the length scale. This leads to a
power law variation of the conductance of the line junction with the
temperature. Depending on the strength of the interactions the line junction
can exhibit two quite different behaviors. Our results can be tested in bent
quantum Hall systems fabricated recently.
