Readdressing the hierarchy problem in a Randall-Sundrum scenario with bulk Kalb-Ramond background

TL;DR

This paper investigates how a bulk Kalb-Ramond field affects the hierarchy problem in Randall-Sundrum models, revealing that it introduces new fine-tuning issues and fails to stabilize the extra dimension.

Contribution

It provides an exact correction to the RS metric considering the KR field and analyzes its implications on the hierarchy problem and model stability.

Findings

KR field modifies the RS metric and warps the Higgs mass.

Requires extreme suppression of KR density, reintroducing fine-tuning.

Fails to stabilize the braneworld with the KR field.

Abstract

We re-examine the fine tuning problem of the Higgs mass, when an antisymmetric two form Kalb-Ramond (KR) field is present in the bulk of a Randall-Sundrum (RS) braneworld. Taking into account the back-reaction of the KR field, we obtain the exact correction to the RS metric. The modified metric also warps the Higgs mass from Planck scale (in higher dimension) to TeV scale (on the visible brane) for a range of values of $kr$ exceeding the original RS value (where $k=$ Planck mass and $r=$ size of extra dimension). However, it requires an extraordinary suppression of the KR field density, indicating the re-appearence of the fine tuning problem in a different guise. The new spacetime also generates a small negative cosmological constant on the visible brane. These results are particularly relevant for certain string based models, where the KR field is unavoidably present in the bulk. We further show that such a bulk antisymmetric KR field fails to stabilize the braneworld.