Nonlinear Dynamics of 3D Massive Gravity

TL;DR

The paper addresses the nonlinear dynamics and ghost issues of 3D massive gravity by studying New Massive Gravity (NMG). It shows that in the decoupling limit the helicity-0 sector reduces to a cubic Galileon interaction, the conformal mode aligns with the helicity-0 mode, and a nonperturbative symmetry argument implies no BD ghost, with a consistent extension to cubic-order models. The authors provide an exact decoupling-limit form for NMG, analyze the conformal sector, and perform a nonperturbative degree-of-freedom count to establish ghost-free behavior beyond perturbative regimes; they further construct a general class of cubic-order ghost-free 3D massive gravity theories. These results offer a robust 3D laboratory for understanding ghost-free massive gravity and Galileon-like interactions, with potential implications for AdS$_3$/CFT and lower-dimensional gravity models.

Abstract

We explore the nonlinear classical dynamics of the three-dimensional theory of "New Massive Gravity" proposed by Bergshoeff, Hohm and Townsend. We find that the theory passes remarkably highly nontrivial consistency checks at the nonlinear level. In particular, we show that: (1) In the decoupling limit of the theory, the interactions of the helicity-0 mode are described by a single cubic term -- the so-called cubic Galileon -- previously found in the context of the DGP model and in certain 4D massive gravities. (2) The conformal mode of the metric coincides with the helicity-0 mode in the decoupling limit. Away from this limit the nonlinear dynamics of the former is described by a certain generalization of Galileon interactions, which like the Galileons themselves have a well-posed Cauchy problem. (3) We give a non-perturbative argument based on the presence of additional symmetries that the full theory does not lead to any extra degrees of freedom, suggesting that a 3D analog of the 4D Boulware-Deser ghost is not present in this theory. Last but not least, we generalize "New Massive Gravity" and construct a class of 3D cubic order massive models that retain the above properties.