Double and cyclic λ-deformations and their canonical equivalents

We prove that the doubly λ-deformed σ-models, which include integrable cases, are canonically equivalent to the sum of two single λ-deformed models. This explains the equality of the exact β-functions and current anomalous dimensions of the doubly λ-deformed σ-models to those of two single λ-deformed models. Our proof is based upon agreement of their Hamiltonian densities and of their canonical structure. Subsequently, we show that it is possible to take a well defined non-Abelian type limit of the doubly-deformed action. Last, but not least, by extending the above, we construct multi-matrix integrable deformations of an arbitrary number of WZW models.