  Braneworld theories are often described as low-energy effective field
theories (EFTs) featuring an infinitely thin 3-brane and 4D fields exactly
localized on it. We investigate whether an exactly localized braneworld can
arise as a limit of a theory of 5D fields. Using a holographic formalism we
argue that such limit does not exist in the presence of gravity, therefore
implying a discontinuity in the space of EFTs. We then present specific models
involving exactly localized fields in which inconsistencies appear, which are
solved when fields are taken as quasilocalized. Part of our arguments rely on
conjectures from the "swampland" program. Our investigation motivates
braneworld EFTs built from 5D fields, i.e. quasilocalized braneworlds.
Observable effects from quasilocalization are significant for warped
braneworlds such as Randall-Sundrum II (RSII), and are reminiscent of a
conformal hidden sector. Focusing on the gauge-gravity sector we show that
manifestations of the quasilocalized warped braneworld include i) an anomalous
running of SM gauge couplings ii) a conformal contribution to SM gauge boson
scattering induced by 5D gravity. Constraining these effects puts an upper
bound on the 5D EFT cutoff, implying that the warped braneworld hypothesis
could---at least in principle---be tested completely.
