  We consider the possible role that chiral orbifold conformal field theories
may play in describing the edge state theories of quantum Hall systems. This is
a generalization of work that already exists in the literature, where it has
been shown that 1+1 chiral bosons living on a n-dimensional torus, and which
couple to a U_1 gauge field, give rise to anomalous electric currents, the
anomaly being related to the Hall conductivity. The well known $O(n,n;Z)$
duality group associated with such toroidal conformal field theories transforms
the edge states and Hall conductivities in a way which makes interesting
connections between different theories, e.g. between systems exhibiting the
integer and fractional quantum Hall effect. In this paper we try to explore the
extension of these constructions to the case where such bosons live on a
n-dimensional orbifold. We give a general formalism for discussing the relevant
quantities like the Hall conductance and their transformation under the duality
groups present in orbifold compactifications. We illustrate these ideas by
presenting a detailed analysis of a toy model based on the two-dimensional Z_3
orbifold. In this model we obtain new classes of filling fractions, which
generally the correspond to fermionic edge states carrying fractional electric
charge. We also consider the relation between orbifold edge theories and
Luttinger liquids (LL's), which in the past have provided important insights
into the physics of quantum Hall systems.
