@ac]). The question of gravitational backreaction of the Casimir energy onto the background geometry is also discussed in [@FH]. Again, since the gravitational field of the branes is not considered, they do not find static solutions. This is in contrast with our case, where static solutions can be found by suitable adjustment of the brane tensions.

Finally, it should be pointed out that the treatment of backreaction (here and in [@FH]) applies to conformally invariant fields but not to gravitons. Gravitons are similar to minimally coupled scalar fields, for which it is well known that the Casimir energy density diverges near the boundaries [@bida]. Therefore, a physical cut-off related to the brane effective width seems to be needed so that the energy density remains finite everywhere. Presumably, our conclusions will be unchanged provided that this cut-off length is small compared with the interbrane separation, but further investigation of this issue would be interesting.

It seems also interesting to clarify whether the same stabilization mechanism works in other kind of warped compactified brane world models, such as some coming form M-theory [@ovrut]. In this case the bulk instead of a slice of AdS (which is maximally symmetric), consists of a power-law warp factor, and consequently a less symmetric space. This complicates the calculation since, for instance, there are two 4-d massless moduli fields (apart from the 4-d gravitons) to stabilize.

After the work reported here [@gpt; @tesina] was complete, Ref. [@muko] appeared with some overlapping results, and also [@bmno; @noz] with related topics.

Acknowledgements
================

I devote special thanks to Jaume Garriga and Takahiro Tanaka for the entire realization of this work. I would like to thank Enric Verdaguer and Edgar Gunzig for his kind hospitallity in the Peyresq-5 Meeting. I acknowledge support from CICYT, under grant AEN99-0766, and from grant 1998FI 00198.

[99]{} N. Arkani-Hamed, S. Dimopoulos, G. Dvali, “The Hierarchy Problem and New Di