8 Beyond the Standard Model
459
idea that the underlying theory of nature depends only on topology have both
been extensively studied but at this stage still more in the realm of mathematics.
The various theoretical ideas mentioned above were extensively studied in the
second part of the twentieth century. The respective developments are documented
in many books covering thousands of pages. In this review we have made the
following choices. The emphasis is on various aspects of SUSY. There has been
significant progress in understanding the dynamics of systems which have in some
form or another supersymmetric features. These systems have been researched
in the weak coupling and the strong coupling regimes, perturbatively and nonperturbatively. The properties uncovered are remarkable in some cases. We also
review, more briefly, the attempts to lay out a framework suitable for extracting
supersymmetric signatures of nature. This rich area of research will better receive
its due rewards after the accumulation of actual experimental data. The more
“senior” areas of research such as examining the possibility of the existence of
extra dimensions, grand unified theories and superstring theory will be reviewed
in a much more descriptive manner. This choice was influenced by the possibility
that the LHC will shed some concrete light on what is beyond the standard model.
8.2 Super Symmetry [1]
Super Symmetry (SUSY) embodies several forms of unification and generalization.
It joins space time and internal symmetries and it generalizes the meaning of
space time by adding fermionic components to the canonical space time bosonic
coordinates. An original stated motivation for SUSY in field theory was to have a
symmetry which was able to relate the self couplings of bosons, the self coupling
of fermions and the Yukawa couplings of fermions to bosons. Eventually SUSY
while indeed unifying such couplings has given rise to a multitude of possible nonequivalent ground states. Such a degeneracy of ground states was of a magnitude
unknown before. In string theory, SUSY stabilized superstring theories by removing
the tachyions which plagued the bosonic string theories. Over the years the
motivations have varied and evolved. SUSY was called upon to emeliorate the so
called hierarchy problem which will be reviewed below and it was perceived as
an omen that in a SUSY theory one was able to arrange that the colored, weak
and electromagnetic couplings unify at a single high energy scale. That scale not
far from the Planck scale. In addition it was discovered that this enriched structure
allows to obtain exact results in situations were only approximations were available
before. In particular for four and higher dimensional systems. In its presence a very
rich dynamics has been unraveled.
459
idea that the underlying theory of nature depends only on topology have both
been extensively studied but at this stage still more in the realm of mathematics.
The various theoretical ideas mentioned above were extensively studied in the
second part of the twentieth century. The respective developments are documented
in many books covering thousands of pages. In this review we have made the
following choices. The emphasis is on various aspects of SUSY. There has been
significant progress in understanding the dynamics of systems which have in some
form or another supersymmetric features. These systems have been researched
in the weak coupling and the strong coupling regimes, perturbatively and nonperturbatively. The properties uncovered are remarkable in some cases. We also
review, more briefly, the attempts to lay out a framework suitable for extracting
supersymmetric signatures of nature. This rich area of research will better receive
its due rewards after the accumulation of actual experimental data. The more
“senior” areas of research such as examining the possibility of the existence of
extra dimensions, grand unified theories and superstring theory will be reviewed
in a much more descriptive manner. This choice was influenced by the possibility
that the LHC will shed some concrete light on what is beyond the standard model.
8.2 Super Symmetry [1]
Super Symmetry (SUSY) embodies several forms of unification and generalization.
It joins space time and internal symmetries and it generalizes the meaning of
space time by adding fermionic components to the canonical space time bosonic
coordinates. An original stated motivation for SUSY in field theory was to have a
symmetry which was able to relate the self couplings of bosons, the self coupling
of fermions and the Yukawa couplings of fermions to bosons. Eventually SUSY
while indeed unifying such couplings has given rise to a multitude of possible nonequivalent ground states. Such a degeneracy of ground states was of a magnitude
unknown before. In string theory, SUSY stabilized superstring theories by removing
the tachyions which plagued the bosonic string theories. Over the years the
motivations have varied and evolved. SUSY was called upon to emeliorate the so
called hierarchy problem which will be reviewed below and it was perceived as
an omen that in a SUSY theory one was able to arrange that the colored, weak
and electromagnetic couplings unify at a single high energy scale. That scale not
far from the Planck scale. In addition it was discovered that this enriched structure
allows to obtain exact results in situations were only approximations were available
before. In particular for four and higher dimensional systems. In its presence a very
rich dynamics has been unraveled.