Bulk fields in the Randall-Sundrum compactification scenario

Recently, Randall and Sundrum proposed a solution to the hierarchy problem where the background spacetime is five dimensional. There are two 3-branes, and the mass scale for fields that propagate on one of the 3-branes is exponentially suppressed relative to the fundamental scale of the theory, which is taken to be the Planck mass ${M}_{\mathrm{Pl}}.$ In this Brief Report we show that bulk fields with a five dimensional mass term of order ${M}_{\mathrm{Pl}}$ have, after integrating over the extra dimension, modes with four-dimensional masses that are exponentially suppressed as well. This opens the possibility that in this scenario the standard model matter fields may correspond to degrees of freedom that are not confined to a 3-brane.