Yangian Symmetry in Conformal Field Theory

TL;DR

This paper demonstrates that the $SU(N)$ level-1 Wess-Zumino-Witten conformal field theory naturally realizes the Yangian $Y(sl_N)$ algebra, extending the algebraic structure of certain integrable spin chains to a field theory context.

Contribution

It constructs a Hamiltonian commuting with Yangian generators within the conformal field theory framework, generalizing previous algebraic structures to field theories.

Findings

Realization of Yangian symmetry in $SU(N)$ WZW model

Construction of a commuting Hamiltonian $H_2$

Extension of $SU(N)$ Haldane-Shastry spin chain algebraic structure

Abstract

We show that the $SU(N)$, level-1 Wess-Zumino-Witten conformal field theory provides a natural realization of the Yangian $Y(sl_N)$ for $N\geq 3$. We also construct a hamiltonian $H_2$ which commutes with the Yangian generators and study its spectrum. Our results, which generalize work by Haldane et al.\ \cite{hhtbp}, provide the field theory extension of the algebraic structure of the $SU(N)$ Haldane-Shastry spin chains with $1/r^2$ exchange.