Gravity in Randall-Sundrum brane world revisited

We point out some subtleties with gauge fixings (which sometimes include th e so-called "brane bending" effects) typically used to compute the graviton propagator on the Randall-Sundrum brane. In particular, the brane, which h as nonvanishing tension, explicitly breaks some part of the diffeomorphisms , so that there are subtleties arising in going to, say, the axial gauge or the harmonic gauge in the presence of (nonconformal) matter localized on t he brane. We therefore compute the graviton propagator in the gauge where o nly the graviphoton fluctuations are set to zero (the diffeomorphisms neces sary for this gauge fixing are intact), but the graviscalar component is un touched. We point out that in the Gaussian normal coordinates (where the gr aviscalar component vanishes on the brane) the graviton propagator blows up in the ultraviolet near the brane. In fact, the allowed gauge transformati ons, which do not lead to such ultraviolet behavior of the graviton propaga tor, are such that the coupling of the graviscalar to the brane matter cann ot be gauged away in the ultraviolet. Because of this, at the quantum level , where we expect various additional terms to be generated in the brane wor ld-volume action including those involving the graviscalar, fine-tuning (wh ich is independent of that for the brane cosmological constant) is generica lly required to preserve consistent coupling between bulk gravity and brane matter. We also reiterate that in such warped backgrounds higher curvature terms in the bulk are generically expected to delocalize gravity. (C) 2001 Elsevier Science B.V. All rights reserved.