ar X iv : 1 51 2 . 06 83 8 v 2 [ he p - th ] 2 1 M ar 2 01 6 Non - compact nonlinear sigma models

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 Λ2 decoupling limit can be defined on these vacua.