Anyon Basis of c=1 Conformal Field Theory

TL;DR

This paper explores the $c=1$ conformal field theory of a compactified boson using anyon vertex operators, linking it to the Calogero-Sutherland model and revealing a boson-anyon duality.

Contribution

It introduces a novel framework for describing $c=1$ CFT using anyon vertex operators and establishes a duality between different anyon statistics.

Findings

Wave functions described by Calogero-Sutherland eigenfunctions.

Field theory of CS model at specific radii.

Duality between different anyon statistics.

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 $\theta=\beta \pi$.