η and λ deformations as E -models

We show that the so-called λ deformed σ -model as well as the η deformed one belong to a class of the E -models introduced in the context of the Poisson–Lie-T-duality. The λ and η theories differ solely by the choice of the Drinfeld double; for the λ model the double is the direct product G × G while for the η model it is the complexified group G C . As a consequence of this picture, we prove for any G that the target space geometries of the λ -model and of the Poisson–Lie T-dual of the η -model are related by a simple analytic continuation.