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arXiv · hep-th/9510242

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

Changhyun Ahn·Soonkeon Nam
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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.

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Changhyun Ahn, Soonkeon Nam. 1995-11-17. Yangian Symmetries in the $SU(N)_1$ WZW Model and the Calogero-Sutherland Model. https://doi.org/10.1016/0370-2693(96)00402-9

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