# Resolving the vDVZ and Strong Coupling Problems in Massive Gravity and Bigravity

## TL;DR

This paper proposes a novel 5D warped geometry embedding for massive gravity and bigravity, which removes the vDVZ and strong coupling problems by inducing a large kinetic term for the longitudinal mode, ensuring weak coupling up to high energies.

## Contribution

It introduces a 5D warped geometry framework that alleviates vDVZ and strong coupling issues in 4D massive gravity by generating a kinetic term through bulk graviton mass induction.

## Key findings

- Removes vDVZ discontinuity via 5D embedding.
- Ensures weak coupling of longitudinal mode up to high energy scales.
- Provides a holographic interpretation linking 4D massive gravity to 4D CFT.

## 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.