Synchrotron-based high-pressure research in materials science Page: 3 of 20
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1 Introduction
Data from precision electroweak experiments, which includes evidence in favor of a light Higgs
boson, have made weak scale supersymmetry the leading candidate for a theory beyond the stan-
dard model. Weak scale supersymmetry provides a solution to the gauge hierarchy problem, a
radiative electroweak symmetry breaking mechanism with a light Higgs boson, and a successful
prediction for the weak mixing angle. The critical question for weak scale supersymmetry is:
what breaks supersymmetry? In many schemes this is accomplished in 4d by the dynamics of
some new strong gauge force. In this paper we explore an alternative possibility: the breaking
of supersymmetry by boundary conditions in compact extra dimensions [1]. While such a mech-
anism has been known for many years, it has rarely been applied to realistic models. Models
which have been constructed [2, 3, 4, 5, 6, 7, 8, 9], have taken the view that the compactifica-
tion scale 1/R is of order a TeV, and that beneath this scale supersymmetry is broken. Thus
the picture is of a transition at 1/R from a d > 4 supersymmetric theory directly to a d = 4
non-supersymmetric effective theory. There is never an energy interval in which there is an
effective 4d supersymmetric field theory. Such schemes are extremely exciting, as they predict
that both Kaluza-Klein (KK) modes and superpartners will be discovered by colliders at the TeV
scale. However, in these schemes supersymmetry is apparently not related to the gauge hierarchy
problem, and logarithmic gauge coupling unification is not possible.
In this paper we demonstrate that there is an alternative implementation of boundary con-
dition supersymmetry breaking: the boundary conditions may involve very small dimensionless
parameters, a, so that supersymmetry is broken at a/R rather than 1/R. In this scheme the tran-
sition at scale 1/R is from a 5d supersymmetric theory to a 4d supersymmetric theory with highly
suppressed supersymmetry breaking interactions. In the energy interval from 1/R to a/R physics
is described by a softly broken 4d supersymmetric theory, such as the minimal supersymmetric
standard model. This new viewpoint gives a new origin for the soft supersymmetry-breaking
parameters in terms of orbifold compactification boundary conditions at very high energies. For
1/R sufficiently high, supersymmetry is relevant for solving the gauge hierarchy problem and
logarithmic gauge coupling unification may occur. We do not claim this as a new solution to the
gauge hierarchy problem, as we have not understood why the parameter a is so small, but we
are hopeful that this new view of the problem may lead to a new solution.
In this paper we restrict our analysis to the simplest case of a single compact extra dimen-
sion, in which case there is a unique parameter, a, in the orbifold boundary condition which
breaks supersymmetry [10]. This parameter arises as a twisting of the fields under a translation
symmetry of the extra coordinate. In higher dimensions there will be further parameters. In 5d,
with a single extra dimension, even with arbitrary gauge and matter content of the theory, we are
guaranteed that the soft supersymmetry-breaking parameters depend on only two parameters:
a and 1/R.1
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Synchrotron-based high-pressure research in materials science, article, Date Unknown; [Berkeley, California]. (https://digital.library.unt.edu/ark:/67531/metadc929231/m1/3/: accessed April 19, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.