RG-flow, gravity and the cosmological constant

We study the low energy effective action $S$ of gravity, induced byintegrating out gauge and matter fields, in a general class of Randall-Sundrumtype string compactification scenarios with exponential warp factors. Ourmethod combines dimensional reduction with the holographic map between between5-d supergravity and 4-d large $N$ field theory. Using the classicalsupergravity approximation, we derive a flow equation of the effective action$S$ that controls its behavior under scale transformations. We find that as aresult each extremum of $S$ automatically describes a complete RG trajectory ofclassical solutions. This implies that, provided the cosmological constant iscanceled in the high energy theory, classical flat space backgrounds naturallyremain stable under the RG-flow. The mechanism responsible for this stabilityis that the non-zero vacuum energy generated by possible phase transitions, isabsorbed by a dynamical adjustment of the contraction rate of the warp factor.Comment: 23 pages, 1 figur