Randall-Sundrum with Kalb-Ramond field: return of the hierarchy problem?

TL;DR

Incorporating the Kalb-Ramond field into the Randall-Sundrum model can address the hierarchy problem but necessitates extreme fine tuning, effectively reintroducing the problem and inducing a small negative cosmological constant on the brane.

Contribution

This paper demonstrates that the Kalb-Ramond field's inclusion in the Randall-Sundrum scenario reintroduces fine tuning issues and affects the cosmological constant on the brane.

Findings

Hierarchy problem solvable with Kalb-Ramond field

Requires fine tuning of about 1 part in 10^62

Induces a small negative cosmological constant

Abstract

We show that when the antisymmetric Kalb-Ramond field is included in the Randall-Sundrum scenario, although the hierarchy problem can be solved, it requires an extreme fine tuning of the Kalb-Ramond field (about 1 part in $10^{62}$). We interpret this as the return of the problem in disguise. Further, we show that the Kalb-Ramond field induces a small negative cosmological constant on the visible brane.