Anyon Basis of c=1 Conformal Field Theory

الأصل · EN

We study the c=1 conformal field theory of a free compactified boson with radius r=√β (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=√β 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.