The exact $C$-function in integrable $\lambda$-deformed theories

By employing CFT techniques, we show how to compute in the context of λ -deformations of current algebras and coset CFTs the exact in the deformation parameters C -function for a wide class of integrable theories that interpolate between a UV and an IR point. We explicitly consider RG flows for integrable deformations of left–right asymmetric current algebras and coset CFTs. In all cases, the derived exact C -functions obey all the properties asserted by Zamolodchikov's c -theorem in two-dimensions.