Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1998-04-21
Int.J.Mod.Phys. A14 (1999) 1061-1086
Physics
High Energy Physics
High Energy Physics - Theory
32 pages, LateX. Uses amstex, amssymb. Typos corrected. To appear in Int. J. Mod. Phys. A
Scientific paper
10.1142/S0217751X99000531
In this paper, we discuss the behavior of conformal field theories interacting 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 current algebra. We show that in the case of QHE systems interacting at one point we obtain a ``twisted'' representation of the current algebra. The condition for stationarity of currents is the same as the classical Kirchoff's law applied to the currents at the interaction point. We find that in the case of two discs touching at one point, since the currents are chiral, they are not stationary and one obtains current oscillations between the two discs. We determine the frequency of these oscillations in terms of an effective parameter characterizing the interaction. The chiral conformal field theories can be represented in terms of bosonic Lagrangians with a boundary interaction. We discuss how these one point interactions can be represented as boundary conditions on fields, and how the requirement of chirality leads to restrictions on the interactions described by these Lagrangians. By gauging these models we find that the theory is naturally coupled to a Chern-Simons gauge theory in 2+1 dimensions, and this coupling is completely determined by the requirement of anomaly cancellation.
Balachandran Aiyalam P.
Bimonte Giuseppe
Govindarajan T. R.
Gupta Kumar S.
John Varghese
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