A free field perspective of $\lambda$-deformed coset CFT's

We continue our study of $\lambda$-deformed $\sigma$-models by setting up a $1/k$ perturbative expansion around the free field point for cosets, in particular for the $\lambda$-deformed $SU(2)/U(1)$ coset CFT. We construct an interacting field theory in which all deformation effects are manifestly encoded in the interaction vertices. Using this we reproduce the known $\beta$-function and the anomalous dimension of the composite operator perturbing away from the conformal point. We introduce the $\lambda$-dressed parafermions which have an essential Wilson-like phase in their expressions. Subsequently, we compute their anomalous dimension, as well as their four-point functions, as exact functions of the deformation and to leading order in the $k$ expansion. Correlation functions with an odd number of these parafermions vanish as in the conformal case.