Exponential and power-law hierarchies from supergravity

We examine how a d-dimensional mass hierarchy can be generated from a d+1-dimensional set up. We introduce a d+1-dimensional scalar, the hierarchon, which has a potential as in gauged supergravities. We find that when it is in its minimum, there exist solutions of Hořava-Witten topology Rd×S1/Z2 with domain walls at the fixed points and anti-de Sitter geometry in the bulk. We show that while standard Poincaré supergravity leads to power-law hierarchies, (e.g. a power law dependence of masses on the compactification scale), gauged supergravity produce an exponential hierarchy as recently proposed by Randall and Sundrum.