Spinons as Composite Fermions

TL;DR

This paper demonstrates that gauge-invariant composites in a fermionic realization of $SU(N)_1$ conformal field theory exhibit holomorphic factorization, with the $SU(2)_1$ case revealing a spinon algebra and classifying chiral Fock space via semionic excitations.

Contribution

It provides a new explicit realization of holomorphic factorization in $SU(N)_1$ conformal field theory using composite fermions, and classifies the chiral Fock space in the $SU(2)_1$ case.

Findings

Gauge-invariant composites exhibit holomorphic factorization.

The $SU(2)_1$ case realizes the spinon $Y(sl_2)$ algebra.

Chiral Fock space classified by semionic quasi-particles.

Abstract

We show that gauge invariant composites in the fermionic realization of $SU(N)_1$ conformal field theory explicitly exhibit the holomorphic factorization of the corresponding WZW primaries. In the $SU(2)_1$ case we show that the holomorphic sector realizes the spinon $Y(sl_2)$ algebra, thus allowing the classification of the chiral Fock space in terms of semionic quasi-particle excitations created by the composite fermions.