Effective field theory in AdS: Continuum regime, soft bombs, and IR emergence

We consider a scalar field in a slice of Lorentzian five-dimensional AdS at arbitrary energies. We show that the presence of bulk interactions separates 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 arc 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 glue balls and some implications for dark sector models.