Hierarchies Without Symmetries from Extra Dimensions Page: 3 of 26
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The usual way of organizing our thinking about physics beyond the Standard
Model (SM) is the effective field theory paradigm: all operators consistent
with the symmetries are present in the theory, with higher-dimension oper-
ators suppressed by powers of the ultraviolet cutoff. The SM itself provides
an exception to this expectation: the Yukawa couplings for all the fermions
other than the top quark are much smaller than 0(1). This does not lead to
any fine-tuning problems since small Yukawa couplings are technically nat-
ural. Nevertheless, we are normally led to suspect that the fermion mass
hierarchy is controlled by (weakly broken) flavor symmetries operative at
shorter distances. Similar issues surround the question of proton decay in
extensions submof the SM, especially when there is new physics at the TeV
scale. Once again, some symmetry is normally invoked to forbid danger-
ous 1/(TeV) suppressed interactions mediating proton decay. Furthermore,
imposing global symmetries on low-energy effective theories, for instance, sta-
bilizing the proton by declaring that the low-energy theory respects baryon
number, is widely considered to be unsatisfactory given the lore that black-
holes/wormholes violate all non-gauged symmetries. This seems particularly
problematic for theories where the fundamental Planck scale is lowered close
to the TeV scale [1, 2, 3, 4, 5, 6], and suggests that some sort of continu-
ous [3, 7] or discrete  gauge symmetry is required to adequately suppress
In this paper, we will show that all of this lore can easily and generically
be violated in theories where the SM fields are constrained to live on a wall
in n extra dimensions, where gravity and perhaps other SM singlet fields
are free to propagate. We will construct a simple model where our wall is
slightly thick in one of the extra dimensions. The wall will have interesting
sub-structure: while the Higgs and SM gauge fields are free to propagate
inside it, the SM fermion are "stuck" at different points in the wall, with
wave functions given by narrow Gaussians as shown in Figure 1.
Without imposing any flavor symmetries on the short-distance theory,
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Arkani-Hamed, Nima. Hierarchies Without Symmetries from Extra Dimensions, report, March 22, 1999; Menlo Park, California. (digital.library.unt.edu/ark:/67531/metadc621313/m1/3/: accessed June 20, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.