Exponential and power-law hierarchies from supergravity

TL;DR

This paper explores how different supergravity theories can generate hierarchical mass scales through geometric configurations, revealing that gauged supergravity produces exponential hierarchies akin to Randall-Sundrum models.

Contribution

It demonstrates that gauged supergravity naturally yields exponential mass hierarchies from higher-dimensional setups, extending previous power-law results from Poincare supergravity.

Findings

Gauged supergravity produces exponential hierarchies.

Standard Poincare supergravity results in power-law hierarchies.

Solutions involve domain walls and AdS geometries in higher dimensions.

Abstract

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 Horava-Witten topology R^d X S^1/Z^2 with domain walls at the fixed points and anti-de Sitter geometry in the bulk. We show that while standard Poincare 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.