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arXiv · 1512.06838

Non-compact nonlinear sigma models

Claudia de Rham·Andrew J. Tolley·Shuang-Yong Zhou
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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 $Λ_2$ decoupling limit can be defined on these vacua.

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Claudia de Rham, Andrew J. Tolley, Shuang-Yong Zhou. 2016-03-21. Non-compact nonlinear sigma models. https://doi.org/10.1016/j.physletb.2016.07.035

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