  We construct a new class of two-dimensional field theories with target spaces
that are finite multiparameter deformations of the usual coset G/H-spaces. They
arise naturally, when certain models, related by Poisson-Lie T-duality, develop
a local gauge invariance at specific points of their classical moduli space. We
show that canonical equivalences in this context can be formulated in loop
space in terms of parafermionic-type algebras with a central extension. We find
that the corresponding generating functionals are non-polynomial in the
derivatives of the fields with respect to the space-like variable. After
constructing models with three- and two-dimensional targets, we study
renormalization group flows in this context. In the ultraviolet, in some cases,
the target space of the theory reduces to a coset space or there is a fixed
point where the theory becomes free.
