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

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 $θ= π/n$. 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.