Abstract
As is well known, both massive gravity and bigravity exhibit the linear van Dam-Veltman-Zakharov (vDVZ) discontinuity that is cured classically by the nonlinear Vainshtein mechanism due to certain low scale strongly coupled interactions. Here we show how both the vDVZ and strong coupling problems can be removed by embedding 4D covariant massive gravity into a certain 5D warped geometry. The 4D theory is a nonlinear strongly coupled massive gravity, that is being coupled to a 5D bulk theory that generates a bulk graviton mass via a one loop diagram. This induced mass leads to an additional 4D kinetic term for the 4D longitudinal mode, even on flat space. Due to this kinetic term the 4D massive theory becomes weakly coupled all the way up to a high energy scale set by the bulk cosmological constant. The same effect leads to a suppression of the interactions of the 4D longitudinal mode with a 4D matter stress-tensor, thus removing the vDVZ discontinuity. The proposed mechanism has a pure 4D holographic interpretation: a 4D nonlinear massive gravity mixes to a non-conserved symmetric tensor of a 4D CFT that has a cutoff; the latter mixing generates a large kinetic term for the longitudinal mode, and this makes the longitudinal mode be weakly coupled to a matter stress-tensor, and weakly self-coupled, all the way up to the scale of the 4D CFT cutoff.
Highlights
AND TOY MODELSThe modern view of general relativity (GR) is that it is the unique interacting theory of a massless graviton, valid at distances larger than its short distance cutoff—the Planck length
The purpose of this section is to provide a summary of the mechanism by means of which the UV cutoff of 4D massive gravity is raised from Λ3 ∼ 10−22 GeV to a new scale L−1, which can be as high as L−1 ∼ 1016 GeV
The scale suppressing the strongest interaction is M⋆. This scale is greater than anti de Sitter (AdS) curvature, and it turns out not to have physical meaning—the true cutoff of the 4D theory is set by L−1
Summary
The modern view of general relativity (GR) is that it is the unique interacting theory of a massless graviton, valid at distances larger than its short distance cutoff—the Planck length. We will assume that the gravitational action describes nonlinear, ghostfree dRGT gravity, confined to the 4D boundary at the origin of the z-axis, as well as a massive 5D bulk graviton, whose mass arises from the above-described Higgs mechanism in GR, coupled to scalars on anti de Sitter space. At momenta much lower than the AdS curvature, the bulk-induced 4D effective action for π can be approximated (in a rather subtle way, discussed below) by an ordinary, local kinetic term This makes the 4D boundary dynamics of this field much more weakly coupled than it would be in the absence of the bulk.
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