When one tries to analyze the renormalization group of marginal perturbations of Wess-Zumino-Witten (WZW) model in 1+1d, only those "integrable perturbations" can be computed analytically. I wonder what is, in practice, the integrablity condition for WZW model with simple current algebras, in particular, the $SU(N)_k$ CFT.
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