  Particle physics models with extra dimensions of space (EDS's) and branes
shed new light on electroweak and flavor hierarchies with a rich TeV scale
phenomenology. This article highlights new model building issues with EDS's and
branes, arising in the framework of weakly nonlocal field theories. It is shown
that a brane-localized field is still delocalized in the bulk on a small
distance from the brane position: fields localized on such distant fuzzy branes
are thus allowed to interact directly with suppressed couplings. Directions for
model building are also given: (i) with fuzzy branes, a new realization of
split fermions in an EDS is presented, naturally generating flavor hierarchies;
(ii) with a warped EDS, the usual warp transmutation of a brane-localized mass
term is revisited, where it is shown that the nonlocal scale is also redshifted
and provides a smooth UV cutoff for the Higgs boson mass. This framework is
expected to have natural UV completions in string theory, but the possibility
to embed it in recent UV complete weakly nonlocal quantum field theories is
commented.
