  We study the effects of the interaction between electrons and holes on the
conductance G of quasi-one-dimensional graphene systems.
  We first consider as a benchmark the limit in which all interactions are
negligible, recovering the predictions of the tight-binding approximation for
the spectrum of the system, and the well-known result G=4 e^2/h for the lowest
conductance quantum. Then we consider an exactly solvable field theoretical
model in which the electro-magnetic interactions are effectively local.
Finally, we use the effective field theory formalism to develop an exactly
solvable model in which we also include the effect of non-local interactions.
We find that such interactions turn the nominally metallic armchair graphene
nanoribbon into a semi-conductor, while the short-range interactions lead to a
correction to the G=4 e^2/h formula.
