Gauge hierarchy from a topological viewpoint?

TL;DR

This paper proposes a topological approach to the hierarchy problem, reproducing Randall-Sundrum results without a special metric background by focusing on brane existence and topological gravity interactions.

Contribution

It introduces a topological gravity framework that explains the hierarchy problem without relying on a specific metric background, unlike the original Randall-Sundrum model.

Findings

Reproduces Randall-Sundrum exponential factor topologically

Achieves hierarchy solution with a single 3-brane

Shows the importance of brane existence over metric choice

Abstract

In this work we explore an alternative to the central point of the Randall-Sundrum brane world scenario, namely, the particular nonfactorizable metric, in order to solve the hierarchy problem. From a topological viewpoint, we show that the exponential factor, crucial in the Randall-Sundrum model, appears in our approach, only due to the brane existence instead of a special metric background. Our results are based in a topological gravity theory via a non-standard interaction between scalar and non-abelian degrees of freedom and in calculations about localized modes of matter fields on the brane. We point out that we obtain the same results of the Randall-Sundrum model using only one 3-brane, since a specific choice of a background metric is no longer required.