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 consider 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 R × S/Z 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. CERN-TH/99-192 June 1999