Brane-induced gravity in more than one extra dimensions: violation of equivalence principle and ghost

TL;DR

The paper analyzes brane-induced gravity in spaces with multiple infinite extra dimensions, using a UV-soft bulk to regularize the theory. Through both a scalar proxy and the full tensor equations, it demonstrates that brane-thickness induces nonuniversal gravitational couplings (violating the equivalence principle) and reveals a tachyonic ghost localized near the brane alongside a quasi-localized graviton. The brane-to-brane propagator features a ghost term that cancels the extra scalar polarization of the massive graviton at intermediate distances, reproducing four-dimensional tensor gravity, but the presence of a ghost and tachyon signals a fundamental inconsistency in this setup for $N>1$. The authors also show that these conclusions persist under a generalized bulk tensor structure, suggesting that this bran-induced gravity scenario cannot arise as a healthy low-energy limit of a consistent microscopic theory. $N>1$, $r_c = M_{Pl}/M_*^2$, and the intermediate regime $\frac{1}{M_*} \ll r \ll r_c$ are central to the results, with a resulting nonuniversal Newton constant and a ghost-driven cancellation mechanism analogous to the GRS model.$

Abstract

We consider brane-induced gravity model in more than one extra dimensions, regularized by assuming that the bulk gravity is soft in ultraviolet. We study linear theory about flat multi-dimensional space-time and flat brane. We first find that this model allows for violation of equivalence between 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 quasi-localized massive graviton. 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.