Anyon Basis of c=1 Conformal Field Theory

Abstract

We study the $c=1$ conformal field theory of a free compactified boson with radius $r=\sqrt{\beta }$ ($\beta$ is an integer). The Fock space of this boson is constructed in terms of anyon vertex operators and each state is labeled by an infinite set of pseudo-momenta of filled particles in pseudo-Dirac sea. Wave function of multi anyon state is described by an eigenfunction of the Calogero-Sutherland (CS) model. The $c=1$ conformal field theory at $r=\sqrt{\beta }$ gives a field theory of CS model. This is a natural generalization of the boson-fermion correspondence in one dimension to boson-anyon correspondence. There is also an interesting duality between anyon with statistics $\theta =\pi /\beta$ and particle with statistics $\theta =\beta \pi$.

17 pages

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