Self-gravity of brane worlds: a new hierarchy twist

We examine the inclusion of brane self-gravity in brane-world scenarios withthree or more compact extra dimensions. If the brane is a thin, localized one,then we find that the geometry in its vicinity is warped in such a way thatgravity on the brane can become very weak, independently of the volume of theextra dimensions. As a consequence, self-gravity can make the brane structureenter into the determination of the hierarchy between the Planck scale and alower fundamental scale. In an extreme case, one can obtain a novelreformulation of the hierarchy problem in brane worlds, without the need forlarge-size extra dimensions; the hierarchy would be generated when the ratiobetween the scales of brane tension and brane thickness is large. In a sense,such a scenario is half-way between the one of Arkani-Hamed et al.(ADD)(although with TeV-mass Kaluza-Klein states) and that of Randall and Sundrum(RS1) (but with only a TeV brane, and of positive tension). We discuss indetail the propagation of fields in the background of this geometry, and findthat no problems appear even if the brane is taken to be very thin. We alsodiscuss the presence of black branes and black holes in this setting, and thepossibility of having a Planck brane.Comment: 22 pages, 2 figures. v2: comments added on (a) the generality of the effect described; (b) the possibility of generating a large tension/thickness ratio by stacking brane