On the stability of field-theoretical regularizations of negative tension branes

TL;DR

The paper demonstrates that regularizing negative tension branes with bulk scalar fields inevitably introduces ghost modes, and attempts to stabilize the system by sign-changing kinetic terms are ineffective due to mode localization.

Contribution

It proves that physical perturbations cannot extend across zeros of the kinetic term, confirming the persistence of ghosts regardless of the scalar's kinetic and potential functions.

Findings

Modes are localized either where the kinetic term is positive or negative.

Ghost modes are unavoidable in regularizations involving sign-changing kinetic terms.

The conclusion holds for arbitrary choices of kinetic and potential functions.

Abstract

Any attempt to regularize a negative tension brane through a bulk scalar requires that this field is a ghost. One can try to improve in this aspect in a number of ways. For instance, it has been suggested to employ a field whose kinetic term is not sign definite, in the hope that the background may be overall stable. We show that this is not the case; the physical perturbations (gravity included) of the system do not extend across the zeros of the kinetic term; hence, all the modes are entirely localized either where the kinetic term is positive, or where it is negative; this second type of modes are ghosts. We show that this conclusion does not depend on the specific choice for the kinetic and potential functions for the bulk scalar.