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

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 1062). 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.