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

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 $Q_1^a$. We also evaluate some energy spectra of $H_2$, by acting it on multi-spinon states.

12 pages, Latex; Errors in the previous version are corrected and new results on spinons are included

References in corpus (7)

• W-symmetry in Conformal Field Theory
• Exchange Operator Formalism for Integrable Systems of Particles
• Yang-Baxter equation in spin chains with long range interactions
• Spinon Bases, Yangian Symmetry and Fermionic Representations of Virasoro Characters in Conformal Field Theory
• Spinons in Conformal Field Theory
• Yangian Symmetry in Conformal Field Theory
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Cited by in corpus (2)

• The SU(n)_1 WZW Models: Spinon Decomposition and Yangian Structure
• Yangian-invariant field theory of matrix-vector models