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We construct the all loop effective action representing, for small couplings,simultaneously self and mutually interacting current algebra CFTs realized byWZW models. This non-trivially generalizes our previous works where suchinteractions were, at the linear level, not simultaneously present. For the twocoupling case we prove integrability and calculate the coupled RG flowequations. We also consider non-Abelian T-duality type limits. Our modelsprovide concrete realisations of integrable flows between exact CFTs andexhibit several new features which we discuss in detail.

Novel all loop actions of interacting CFTs: Construction, integrability and RG flows