Flavor at the TeV scale with extra dimensions

Theories where the standard model fields reside on a 3-brane, with a low fundamental cutoff and extra dimensions, provide alternative solutions to the gauge hierarchy problem. However, generating flavor at the TeV scale while avoiding flavor-changing difficulties appears prohibitively difficult at first sight. We argue to the contrary that this picture allows us to lower flavor physics close to the TeV scale. Small Yukawa couplings are generated by “shining” badly broken flavor symmetries from distant branes, and flavor and $\mathrm{CP}$-violating processes are adequately suppressed by these symmetries. We further show how the extra dimensions avoid four dimensional disasters associated with light fields charged under flavor. We construct elegant and realistic theories of flavor based on the maximal ${U\left(3\right)\mathrm{}}^5$ flavor symmetry which naturally generate the simultaneous hierarchy of masses and mixing angles. Finally, we introduce a new framework for predictive theories of flavor, where our 3-brane is embedded within highly symmetrical configurations of higher-dimensional branes.