On the sign of the dilaton in the soft wall models

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.