A remarkably simple theory of 3d massive gravity

Geiller, Marc (Univ Lyon, ENS de Lyon, Univ Claude Bernard Lyon 1, CNRS, Laboratoire de Physique, UMR 5672, F-69342, Lyon, France) ; Noui, Karim (0000 0001 2182 6141, Institut Denis Poisson, Université de Tours, Université d’Orléans, CNRS, UMR 7013, 37200, Tours, France) (Laboratoire Astroparticule et Cosmologie, Université Paris Diderot, CNRS, UMR 7164, 75013, Paris, France)

13 April 2019

Abstract: We propose and study a new action for three-dimensional massive gravity. This action takes a very simple form when written in terms of connection and triad variables, but the connection can also be integrated out to obtain a triad formulation. The quadratic action for the perturbations around a Minkowski background reproduces the action of self-dual massive gravity, in agreement with the expectation that the theory propagates a massive graviton. We confirm this result at the non-linear level with a Hamiltonian analysis, and show that this new theory does indeed possess a single massive degree of freedom. The action depends on four coupling constants, and we identify the various massive and topological (or massless) limits in the space of parameters. This richness, along with the simplicity of the action, opens a very interesting new window onto massive gravity.

Published in: JHEP 1904 (2019) 091
Published by: Springer/SISSA
DOI: 10.1007/JHEP04(2019)091
arXiv: 1812.01018
License: CC-BY-4.0

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