Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1994-11-08
Nucl.Phys.B443:581-595,1995
Physics
High Energy Physics
High Energy Physics - Theory
17 pages
Scientific paper
10.1016/0550-3213(95)00135-F
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 $\theta=\beta \pi$.
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