Yangian Symmetries in the $SU(N)_1$ WZW Model and the Calogero-Sutherland Model

TL;DR

This paper explores the connection between the $SU(N)_1$ WZW model and the Calogero-Sutherland model through Yangian symmetries, revealing new insights into their algebraic structures and energy spectra.

Contribution

It establishes a novel link between the $SU(N)_1$ WZW model and the Calogero-Sutherland model by analyzing Yangian generators and Hamiltonian actions on spinon states.

Findings

Confirmed the necessity of the $W_3$ generator in $H_2$

Identified additional terms in the Yangian generators

Computed energy spectra of multi-spinon states

Abstract

We study the $SU(N)$, level $1$ Wess-Zumino-Witten model, with affine primary fields as spinon fields of fundamental representation. By evaluating the action of the Yangian generators $Q_{0}^{a}, Q_{1}^{a}$ and the Hamiltonian $H_2$ on two spinon states we get a new connection between this conformal field theory and the Calogero-Sutherland model with $SU(N)$ spin. This connection clearly confirms the need for the $W_3$ generator in $H_2$ and an additional term in the $Q^{a}_{1}$. We also evaluate some energy spectra of $H_2$, by acting it on multi-spinon states.