Quantum corrections in massive gravity

We compute the one-loop quantum corrections to the potential of ghost-free massive gravity. We show how the mass of external matter fields contributes to the running of the cosmological constant, but does not change the ghost-free structure of the massive gravity potential at one-loop. When considering gravitons running in the loops, we show how the structure of the potential gets destabilized at the quantum level, but in a way which would never involve a ghost with a mass smaller than the Planck scale. This is done by explicitly computing the one-loop effective action and supplementing it with the Vainshtein mechanism. We conclude that to one-loop order the special mass structure of ghost-free massive gravity is technically natural.