  We explore the structure of the $\lambda$-deformed $\sigma$-model action by
setting up a perturbative expansion around the free field point corresponding
to the identity group element. We include all field interaction terms up to
sixth order. We compute the two- and three-point functions of current and
primary filed operators, their anomalous dimensions as well as the
$\beta$-function for the $\lambda$-parameter. Our results are in complete
agreement with those obtained previously using gravitational and/or CFT
perturbative methods in conjunction with the non-perturbative symmetry, as well
as with those obtained using methods exploiting the geometry defined in the
space of couplings. The advantage of this approach is that all deformation
effects are already encoded in the couplings of the interaction vertices and in
the $\lambda$-dressed operators.
