The SU(n)_1 WZW Models: Spinon Decomposition and Yangian Structure

TL;DR

This paper introduces a spinon-based formulation of the $SU(n)_1$ WZW models, revealing their Yangian symmetry structure and providing explicit character formulas for related spin chains.

Contribution

It develops a novel spinon formulation for $SU(n)_1$ WZW models, connecting multi-spinon states to Yangian representations and deriving explicit character formulas.

Findings

Multi-spinon states form irreducible Yangian $Y(sl_n)$ representations.

Explicit $su(n)$ content of Yangian representations provided.

Closed-form characters for $su(n)$ Haldane-Shastry spin chains derived.

Abstract

We present a `spinon formulation' of the $SU(n)_1$ Wess-Zumino-Witten models. Central to this approach are a set of massless quasi-particles, called `spinons', which transform in the representation ${\bf \bar{n}}$ of $su(n)$ and carry fractional statistics of angle $\theta = \pi/n$. Multi-spinon states are grouped into irreducible representations of the yangian $Y(sl_n)$. We give explicit results for the $su(n)$ content of these yangian representations and present $N$-spinon cuts of the WZW character formulas. As a by-product, we obtain closed expressions for characters of the $su(n)$ Haldane-Shastry spin chains.