Covariant Locally Localized Gravity and vDVZ Continuity
The Karch-Randall braneworld concerns the physics of an AdS$_{d}$ brane embedded in an ambient gravitational AdS$_{d+1}$ spacetime. The gravitational theory induced on the AdS$_{d}$ brane has a very light but massive graviton. It has been established that the zero graviton mass limit of the $d$-dimensional graviton propagator is smooth at tree-level. Furthermore, this smoothness was conjectured to persist to the quantum level. This conjecture suggests that the massive graviton on the AdS$_{d}$ brane is due to spontaneous symmetry breaking, which is consistent with its holographic dual description. In this letter, we show that the zero mass limit of the partition function is a theory of a massless graviton and a decoupled massive vector. The zero mass limit is not the basic Randall-Sundrum II model, but a theory with these additional decoupled vector degrees of freedom coupled only to gravity. The proof relies on deriving the fully covariant description of the $d$-dimensional gravity theory which enables us to compute the one-loop partition function. At the end, we comment on the implications of this result to the physics of entanglement islands.