η and λ deformations as ε-models

We show that the so-called lambda deformed sigma-model as well as the eta deformed one belong to a class of the epsilon-models introduced in the context of the Poisson-Lie-T-duality. The lambda and eta theories differ solely by the choice of the Drinfeld double; for the lambda model the double is the direct product G xG while for the eta 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 lambda-model and of the Poisson-Lie T-dual of the eta-model are related by a simple analytic continuation. (C) 2015 The Author. Published by Elsevier B.V.