On the sign of the dilaton in the soft wall models

TL;DR

This paper investigates the impact of the sign choice in soft-wall models on the presence of a spurious massless scalar mode, emphasizing the importance of correct sign selection for realistic confinement.

Contribution

It clarifies the role of the sign of the exponential profile in soft-wall models and confirms that the presence of a problematic scalar mode depends solely on the wall's infra-red behavior.

Findings

Incorrect sign leads to a spurious massless scalar mode

Correct sign choice avoids the unwanted mode

Confinement properties are achievable with proper sign

Abstract

We elaborate on the existence of a spurious massless scalar mode in the vector channel of soft-wall models with incorrectly chosen sign of the exponential profile defining the wall. We re-iterate the point made in our earlier paper and demonstrate that the presence of the mode is robust, depending only on the infra-red asymptotics of the wall. We also re-emphasize that desired confinement properties can be realized with the correct sign choice.