Spinons in Conformal Field Theory

TL;DR

This paper explores the $su(2)$ conformal field theory through a spinon perspective, revealing a new link to the Calogero-Sutherland model with $su(2)$ spin and describing the role of spinons as quasi-particles within Yangian symmetry.

Contribution

It establishes a novel connection between $su(2)$ conformal field theory and the Calogero-Sutherland model, and characterizes spinons as Yangian multiplet quasi-particles.

Findings

Identifies the action of Yangian generators on primary fields.

Describes operators creating $N$-spinon highest weight vectors.

Reveals the spinon description's relation to the Calogero-Sutherland model.

Abstract

We study the $su(2)$ conformal field theory in its spinon description, adapted to the Yangian invariance. By evaluating the action of the Yangian generators on the primary fields, we find a new connection between this conformal field theory and the Calogero-Sutherland model with $su(2)$ spin. We use this connection to describe how the spinons are the quasi-particles spanning the irreducible Yangian multiplet, and also to exhibit operators creating the $N$-spinon highest weight vectors.