Exponential and power-law hierarchies from supergravity
A. Kehagias
TL;DR
The paper investigates whether a $d$-dimensional mass hierarchy can be generated from a $d+1$-dimensional setup using a hierarchon scalar with a gauged-supergravity potential, yielding AdS bulk in a Horava–Witten topology $R^{d}\times S^1/{\bf Z^2}$ with domain walls. It shows that gauged supergravity (α=0) can produce an exponential RS-type hierarchy, with boundary masses separated by factors such as $m_0 \sim e^{-\pi R_c/L} m$, while the opposite wall remains at order $m$; a similar exponential can occur in the shifted-wall case. In contrast, ungauged Poincaré supergravity gives power-law hierarchies, with boundary masses scaling as a power of the compactification radius $R_c$, i.e. the dependence is not exponential. Thus, the presence or absence of gauging (AdS background) dictates whether the high-dimensional construction yields exponential or power-law hierarchies, connecting RS-like warping to domain-wall AdS backgrounds in supergravity.
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.