  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 $\theta=\beta
\pi$.
