Absence of a VVDZ Discontinuity in AdS_AdS

TL;DR

The paper addresses whether the VVDZ discontinuity persists for gravity on an $AdS_4$ brane embedded in $AdS_5$ when a graviton mass parameter is present. It combines DOF counting, explicit mode analysis, and considerations of effective 4D descriptions with a locality-based argument to show that all propagating modes are transverse-traceless and that 5D locality prevents the VVDZ discontinuity from reemerging, even at the quantum level. While a local 4D EFT cannot fully capture the brane dynamics, a nonlocal effective action could arise, though it does not undermine the main conclusion about the smooth massless limit. Overall, the work reinforces the consistency of AdS brane gravity by clarifying the role of gauge invariance and higher-dimensional locality in preserving a continuous transition to massless 4D gravity.

Abstract

We clarify the role of gauge invariance for the theory of an AdS4 brane embedded in AdS5. The presence of a nonvanishing mass parameter even for the lightest KK mode of the graviton indicates that all of the spin-2 modes propagate five polarization states. Despite this fact, it was shown earlier that the classical theory has a smooth limit as the mass parameter is taken to zero. We argue that locality in the fifth dimension ensures that this property survives at the quantum level.