# “Hard wall”/ “soft wall”

I have encountered those terms in various places. As I understand it, "soft wall" can correspond to a smooth cutoff of some spacetime, while "hard wall" can be a sharp one, which can be described in terms of D-branes. Could somebody please explain the terminology, and in which context it can occur?

-

You are right about your understanding of these terms. This terminology appears in extensions of the Randall-Sundrum type brane world models. The original model contains a single compact extra dimension bounded by two branes and is known as a hard wall model with the "hard wall" referring to the hard cutoff of space by the IR brane. With such a geometry it is found that the Kaluza Klein (KK) masses of particles that live in the bulk scale as $m_n^2 \sim n^2$ (like the energy levels of a particle in a box).
Attempts were made to use RS type setups to be dual to QCD in order to calculate meson masses etc. This is known as ADS/QCD. However the meson mass spectrum is what is called a Regge spectrum i.e. $m_n^2 \sim n$ and so the RS type model needed to be adapted. This paper first introduced the idea of a soft wall to solve this problem. One of the branes in the hard wall model is removed and a dilaton field $\Phi$ is introduced which dynamically cuts off the space-time $$S= \int d^5x \,\sqrt{g}\, e^{-\Phi}\mathcal{L}.$$ The profile of the dilaton in the extra dimension then determines the KK spectrum of bulk fields and for a quadratic dilaton profile ($\Phi(z) \sim z^2$) a Regge spectrum is produced.