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

Extra Dimensions and Fuzzy Branes in String-inspired Nonlocal Field Theory