Gravity in Randall-Sundrum Brane World Revisited

We point out some subtleties with gauge fixings (which sometimes include the so-called “brane bending” effects) typically used to compute the graviton propagator on the Randall-Sundrum brane. In particular, the brane, which has non-vanishing 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. We therefore compute the graviton propagator in the gauge where only the graviphoton fluctuations are set to zero (the diffeomorphisms necessary for this gauge fixing are intact), but the 55 component of the graviton is untouched. We obtain the following result for gravitational interactions between matter sources localized on the brane. At long distances we have the 4-dimensional Newton’s law, and the tensor structure of the graviton propagator is also 4-dimensional. On the other hand, at short distances we have the 5-dimensional Newton’s law as well as 5-dimensional tensor structure of the graviton propagator. In particular, we have a smooth transition between 2 degrees of freedom at long distances to 3 degrees of freedom at short distances which couple to the conserved energy-momentum tensor on the brane. We then point out that, since the scalar 55 component cannot be gauged away, at the quantum level, where we expect various additional terms to be generated in the brane world-volume action, fine-tuning (which is independent of that for the brane cosmological constant) is generically 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. Typeset using REVTEX E-mail: [email protected]