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Anyon Basis of c=1 Conformal Field Theory

We study the $c=1$ conformal field theory of a free compactified boson with radius $r=\sqrtβ$ ($β$ 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 $r=\sqrtβ$ 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 $θ=π/β$ and particle with statistics $θ=βπ$.