  The target space of a nonlinear sigma model is usually required to be
positive definite to avoid ghosts. We introduce a unique class of nonlinear
sigma models where the target space metric has a Lorentzian signature, thus the
associated group being non-compact. We show that the would-be ghost associated
with the negative direction is fully projected out by 2 second-class
constraints, and there exist stable solutions in this class of models. This
result also has important implications for Lorentz--invariant massive gravity:
There exist stable nontrivial vacua in massive gravity that are free from any
linear vDVZ--discontinuity and a $\Lambda_2$ decoupling limit can be defined on
these vacua.
