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In this paper, we discuss the behavior of conformal field theoriesinteracting at a single point. The edge states of the quantum Hall effect (QHE)system give rise to a particular representation of a chiral Kac-Moody currentalgebra. We show that in the case of QHE systems interacting at one point weobtain a ``twisted'' representation of the current algebra. The condition forstationarity of currents is the same as the classical Kirchoff's law applied tothe currents at the interaction point. We find that in the case of two discstouching at one point, since the currents are chiral, they are not stationaryand one obtains current oscillations between the two discs. We determine thefrequency of these oscillations in terms of an effective parametercharacterizing the interaction. The chiral conformal field theories can berepresented in terms of bosonic Lagrangians with a boundary interaction. Wediscuss how these one point interactions can be represented as boundaryconditions on fields, and how the requirement of chirality leads torestrictions on the interactions described by these Lagrangians. By gaugingthese models we find that the theory is naturally coupled to a Chern-Simonsgauge theory in 2+1 dimensions, and this coupling is completely determined bythe requirement of anomaly cancellation.Comment: 32 pages, LateX. Uses amstex, amssymb. Typos corrected. To appear in  Int. J. Mod. Phys.

CURRENT OSCILLATIONS, INTERACTING HALL DISCS AND BOUNDARY CFTs