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We consider a scalar field in a slice of Lorentzian five-dimensional AdS atarbitrary energies. We show that the presence of bulk interactions separate thebehavior of the theory into two different regimes: Kaluza--Klein and continuum.We determine the transition scale between these regimes and show that UV branecorrelation functions are independent of IR brane-localized operators forfour-momenta beyond this transition scale. The same bulk interactions thatinduce the transition also give rise to cascade decays. We study these cascadedecays for the case of a cubic self-interaction in the continuum regime. Wefind that the cascade decay progresses slowly towards the IR region and givesrise to soft spherical final states, in accordance with former results fromboth gravity and CFT. We identify a recursion relation between integratedsquared amplitudes of different leg numbers and thus evaluate the total rate.We find that cascade decays in the continuum regime are exponentiallysuppressed. This feature completes the picture of the IR brane as an emergentsector as seen from the UV brane. We briefly discuss consistency with theholographic dual description of glueballs and some implications for dark sectormodels.

Effective Field Theory in AdS: Continuum Regime, Soft Bombs, and IR Emergence