Abstract
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.
Highlights
Introduction and summaryNonlinear sigma models (NLSMs) [1] are the umbrella name for many effective field theories [2] from various areas of physics
We introduce a unique class of nonlinear sigma models where the target space metric has a Lorentzian signature, the associated group being non-compact
A NLSM maps from a base manifold to a target space, a typical action of which is given by SNLSM = −
Summary
Nonlinear sigma models (NLSMs) [1] are the umbrella name for many effective field theories [2] from various areas of physics. C. de Rham et al / Physics Letters B 760 (2016) 579–583 mannian/compact requirement in the sense that first class constraints are manifestly employed to project out the would-be ghosts and after gauge fixing the target metric becomes explicitly positive definite. The uniqueness of ghost-free massive gravity Smg [16] (essentially due to the uniqueness of the special square root and antisymmetrization scheme of the potential) implies that the NLSM Smgσ , which we shall refer to as massive gravity NLSM, is the unique NLSM whose target space can have one negative direction. Since the unique matrix square root and antisymmetrization scheme can only remove one (ghostly) DoF, a nogo theorem may be stated that it is impossible to have a NLSM where there are two and more negative directions in the target space, without incorporating an auxiliary gauge procedure as that mentioned above (in which case the resulting target space becomes again positive definite after integration of those auxiliary variables and gauge fixing)
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