Geometric Aspects of the `Deformation Method'
  At the classical level, redefinitions of the field content of a Lagrangian allow to rewrite an interacting model on a flat target space, in the form of a free field model (no potential term) on a curved target space. In the present work we extend the idea of the `deformation method' introduced in \cite{defmet}, to show that it is possible to write an explicit correspondence between the metrics of the curved target spaces that arise in the free versions of distinct scalar field models. This is accomplished by obtaining an explicit relation between the map function linking the fields and the free models' metrics. By considering complex and even quaternionic field models, we extend the procedure --initially proposed for models of a single scalar field-- to systems with a content of two and four (despite constrained) real fields, respectively, widening the range of applicability. We also analyze supersymmetric models to illustrate more possibilities. In particular, we show how to relate a flat Minkowskian metric to a Fubini-Study space. 
Victor I. Afonso and Diego J. Cirilo-Lombardo
hep-th