Integrable flows between exact CFTs

Abstract

We explicitly construct families of integrable σ-model actions smoothly inter-polating between exact CFTs. In the ultraviolet the theory is the direct product of two current algebras at levels k1 and k2. In the infrared and for the case of two deformation matrices the CFT involves a coset CFT, whereas for a single matrix deformation it is given by the ultraviolet direct product theories but at levels k1 and k2 − k1. For isotropic deformations we demonstrate integrability. In this case we also compute the exact beta-function for the deformation parameters using gravitational methods. This is shown to coincide with previous results obtained using perturbation theory and non-perturbative symmetries.