3
As within any extension of the standard model at the weak scale, some
mechanism is needed in the theory above to forbid dangerous higher
dimension operators (suppressed only by ) which lead to proton decay,
neutral meson mixing etc. In our case, the theory above is unknown,
being whatever gives a sensible quantum theory of gravity in (4 + n) dimensions!
We therefore simply assume that these dangerous operators are not
induced. Any extension of the SM at the weak scale must also not give dangerously
large corrections to precision electroweak observables. Again, there
could be unknown contributions from the physics above . However,
at least the purely gravitational corrections do not introduce any new electroweak
breakings beyond the W, Z masses, and therefore should decouple as
loop factor , which is already quite small even for ~1TeV.
Summarizing the framework, we are imagining that the space-time is
, where is an n dimensional compact manifold of volume
, with R given by eq. (4). The (4+n) dimensional Planck mass is ,
the only short-distance scale in the theory. Therefore the gravitational force
becomes comparable to the gauge forces at the weak scale. The usual 4
dimensional is not a fundamental scale at all, rather, the e.ective 4
dimensional gravity is weakly coupled due to the large size R of the extra
dimensions relative to the weak scale. While the graviton is free to propagate
in all (4+n) dimensions, the SM fields must be localized on a 4-dimensional
submanifold of thickness in the extra n dimensions.
Of course, the non-trivial task in any explicit realization of this framework
is localization of the SM fields. A number of ideas for such localizations have
been proposed in the literature, both in the context of trapping zero modes on
topological defects [7] and within string theory. In section 3, we will construct
models of the first type, in which there are two extra dimensions and, given
a dynamical assumption, the SM fields are localized within the throat of a
weak scale vortex in the 6 dimensional theory. We want to stress, however,
that this particular construction must be viewed at best as an "existence
proof" and there certainly are other possible ways for realizing our proposal,
without affecting its most important consequences.
It is interesting that in our framework supersymmetry is no longer needed
from the low energy point of view for stabilizing the hierarchy, however, it
may still be crucial for the self-consistency of the theory of quantum gravity
above the scale; indeed, the theory above may be a superstring
theory.
Independently of any specific realization, there are a number of dramatic
experimental consequences of our framework. First, as already mentioned,
gravity becomes comparable in strength to the gauge interactions at energies
~TeV. The LHC and NLC would then not only probe the mechanism of
electroweak symmetry breaking, they would probe the true quantum theory of gravity!
The major part of the content is taken from:
N. Arkani-Hamed, S. Dimopoulos, and G. Dvali, "The Hierarchy Problem and New Dimensions at a Millimeter," Phys. Lett. B 429, 263 (1998)
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