Boundary degrees of freedom in the fractional quantum Hall effect: Excitations on a common boundary of two samples

Using the field-theoretic method we have derived the boundary action for the fermion Chern-Simons theory of the quantum Hall effect on a planar region with a boundary. We have computed both the bulk and edge responses of currents to the external electric field. From these we obtain the well-known anomaly relation and the boundary Hall current without introducing any ad hoc assumptions such as the chirality condition. In addition, the edge current on the common boundary of two samples is found to be proportional to the difference between Chern-Simons coupling strengths.