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We construct a generalization of the cyclic $\lambda$-deformed models of\cite{Georgiou:2017oly} by relaxing the requirement that all the WZW modelsshould have the same level $k$. Our theories are integrable and flow from asingle UV point to different IR fixed points depending on the differentorderings of the WZW levels $k_i$. First we calculate the Zamolodchikov'sC-function for these models as exact functions of the deformation parameters.Subsequently, we fully characterize each of the IR conformal field theories.Although the corresponding left and right sectors have different symmetries,realized as products of current and coset-type symmetries, the associatedcentral charges are precisely equal, in agreement with the valuesobtained fromthe C-function.

Asymmetric CFTs arising at the IR fixed points of RG flows