Non-compact nonlinear sigma models

TL;DR

This paper introduces a novel class of nonlinear sigma models with Lorentzian target space metrics, demonstrating that they can be ghost-free and stable, with significant implications for Lorentz-invariant massive gravity theories.

Contribution

It presents the first construction of nonlinear sigma models with Lorentzian target spaces that are free of ghosts due to second-class constraints, and explores their stable solutions and implications for massive gravity.

Findings

Ghosts are projected out by second-class constraints.

Stable solutions exist within these models.

Implications for ghost-free massive gravity vacua.

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.