Abstract
It is shown that the theory of the quantum Hall effect is closely related to Chern-Simons gauge theory and to rational conformal field theory. In particular, the equations of classical electromagnetism in quantum Hall systems are derived from a pure Chern-Simons action. This permits us to argue that the scaling limit of a quantum Hall system is described by quantum Chern-Simons theory, thereby explaining the discreteness of the set of values of the Hall conductivity. Using the equivalence of Chern-Simons theory to chiral current algebra, a general derivation of the existence of chiral currents circulating near the boundary edges of a quantum Hall system is found. It is indicated how to derive the effective Chern-Simons action of a quantum Hall system from the underlying quantum mechanics. Applications of our results to very weakly doped “high-temperature superconductors” are described.
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