Gauge Hierarchy from $AdS_5$ Universe with 3-Branes

TL;DR

This paper explores how the hierarchy between the 4D and 5D Planck scales can be generated in an $AdS_5$ universe with 3-branes, proposing an alternative to the Randall-Sundrum scenario and analyzing the role of an additional rescaling constant.

Contribution

It presents a new scenario where the 4D Planck scale arises exponentially from the 5D scale without rescaling the Standard Model mass scale, and discusses the impact of an additional constant in the solution.

Findings

The 4D Planck scale can be generated exponentially from the 5D Planck scale.

An additional constant may exist, affecting the rescaling of the Planck scale.

The scenario is embedded into general $AdS_5$ compactifications.

Abstract

If the universe is (or a slice of) $AdS_5$ space with 3-branes, the 5-dimensional GUT scale on each brane can be indetified as the 5-dimensional Planck scale, but, the 4-dimensional Planck scale is generated from the low 4-dimensional GUT scale exponentially in our world. The 4-dimensional GUT scales and Planck scale are related to the 5-dimensional GUT scales and Planck scale by exponential factors, respectively. One of such scenarios was suggested by Randall and Sundrum recently. We give another scenario that the 4-dimensional Planck scale is generated from the low five-dimensional Planck scale by an exponential hierarchy, and the mass scale in the Standard Model is not rescaled from the 5-dimensional metric to the 4-dimensional metric. We also argue that the additional constant in the solution might exist, which will rescale the 5-dimensional Planck scale and affect the physical scale picture. Finally, we embed those compactifications to the general compactification on $AdS_5$ space and discuss the origin of the additional constant.