  We consider a scalar field in a slice of Lorentzian five-dimensional AdS at
arbitrary energies. We show that the presence of bulk interactions separate the
behavior of the theory into two different regimes: Kaluza--Klein and continuum.
We determine the transition scale between these regimes and show that UV brane
correlation functions are independent of IR brane-localized operators for
four-momenta beyond this transition scale. The same bulk interactions that
induce the transition also give rise to cascade decays. We study these cascade
decays for the case of a cubic self-interaction in the continuum regime. We
find that the cascade decay progresses slowly towards the IR region and gives
rise to soft spherical final states, in accordance with former results from
both gravity and CFT. We identify a recursion relation between integrated
squared amplitudes of different leg numbers and thus evaluate the total rate.
We find that cascade decays in the continuum regime are exponentially
suppressed. This feature completes the picture of the IR brane as an emergent
sector as seen from the UV brane. We briefly discuss consistency with the
holographic dual description of glueballs and some implications for dark sector
models.

High Energy Physics - Theory;High Energy Physics - Phenomenology