New origin for approximate symmetries from distant breaking in extra dimensions

The recently proposed theories with TeV-scale quantum gravity do not have the usual ultraviolet desert between $\sim {10}^3-{10}^{19}\hspace{0.5em}\mathrm{GeV}$ where effective field theory ideas apply. Consequently, the success of the desert in explaining approximate symmetries is lost, and theories of flavor, neutrino masses, proton longevity or supersymmetry breaking lose their usual habitat. In this paper we show that these ideas can find a new home in an infrared desert: the large space in the extra dimensions. The main idea is that symmetries are primordially exact on our brane, but are broken at $O\left(1\right)\mathrm{}$ on distant branes. This breaking is communicated to us in a distance-suppressed way by bulk messengers. We illustrate these ideas in a number of settings: (1) We construct theories for the fermion mass hierarchy which avoid problems with large flavor-changing neutral currents; (2) we reiterate that proton stability can arise if baryon number is gauged in the bulk; (3) we study limits on light gauge fields and scalars in the bulk coming from rare decays, astrophysics and cosmology; (4) we remark that the same ideas can be used to explain small neutrino masses, as well as hierarchical supersymmetry breaking; (5) we construct a theory with bulk technicolor, avoiding the difficulties with extended technicolor. There are also a number of interesting experimental signals of these ideas: (1) attractive or repulsive, isotope dependent sub-millimeter forces $\sim {10}^6$ times gravitational strength, from the exchange of light bulk particles; (2) novel Higgs decays to light generation fermions plus bulk scalars; (3) collider production of bulk vector and scalar fields, leading to $\gamma$ or jet+ missing energy signals as in the case of bulk graviton production, with comparable or larger rates.