Integrable flows between exact CFTs

Understand

We explicitly construct families of integrable $\sigma$-model actions smoothly interpolating between exact CFTs.

• In the ultraviolet the theory is the direct product of two current algebras at levels $k_1$ and $k_2$.
• 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 $k_1$ and $k_2-k_1$.
• For isotropic deformations we demonstrate integrability.