Brane-induced gravity in more than one extra dimension: Violation of equivalence principle and ghost

We consider a brane-induced gravity model in more than one extra dimension, regularized by assuming that the bulk gravity is soft in the ultraviolet. We study linear theory about a flat multidimensional space-time and a flat brane. We first find that this model allows for the violation of equivalence between the gravitational and inertial masses of brane matter. We then observe that the model has a scalar ghost field localized near the brane, as well as a quasilocalized massive graviton. The pure tensor structure of four-dimensional gravity on the brane at intermediate distances is due to the cancellation between the extra polarization of the massive graviton and the ghost. This is completely analogous to the situation in the GRS model.