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E. Rabinovici
• There is a Higgs like feature for such systems. The massless gravitino became
massive when spontaneous breaking of supersymmetry occurred. The would-be
goldstino became part of the massive gravitino. This may resolve the issue of the
missing Goldstino.
• SUSY may persist in the presence of a negatively valued cosmological constant.
Thus the spontaneous breaking of supersymmetry may be fine tuned so as to
obtain a zero value or very small value for the cosmological constant. This is done
by balancing the positive vacuum energy resulting from breaking supersymmetry
against the value of the negative cosmological constant.
• The presence of gravity renders the Lagrangians to be superficially nonrenormalizable. In fact in these theories the ultra violet divergences are much
less severe than what would be expected by power counting. In the presence of
local SUSY the supersymmetry can be enhanced up to N = 8 in four dimensions.
Such a theory is intimately related to a ten dimensional theory with N = 1
supersymmetry in ten dimensions. Some scientists have the hope that this very
special theory is in fact finite. Time will tell.
• Once global SUSY is embedded in supergravity one can imagine also terms
which softly break supersymmetry and do not result from spontaneous breaking,
i.e. one can add relevant terms to a Lagrangian describing for low energies a
systems of particles containing superparticles with non-supersymmetric masses
and interactions.
8.2.8 The Hierarchy Problem
SUSY was uncovered on the route of circumventing the no go theorem concerning
the unification of a internal and space time symmetries into a unified group as well
as attempting to find a symmetry which relates the different couplings in a rather
general Lagrangian involving both bosons and fermions. It was taken up again when
it was decided to declare the very large value of the ratio of the planck scale and
the weak interaction scale as a problem. On a more technical level the problem was
stated as follows. Consider a theory with an interacting scalar particle. Notice that to
this date no fundamental spin zero elementary particles were observed, the discovery
of an elementary spin zero Higgs particle would change this unfamiliar situation,
a situation in which the simplest realization of a symmetry is not manifested in
nature on an elementary level. No matter what the original mass of the scalar
is, the interactions shift the mass. The mass shift is divergent as is the case for
renormalizable theories. However according to the renormalization group ideas one
always encodes the present knowledge valid up to an energy scale in an effective
low energy theory. In that case the mass shift is proportional to the cutoff . As
long as there is no physical scale near that of the weak interaction’s scale of 1
TeV one needs to fine tune the input initial mass to obtain a Higgs mass of the
weak interaction scale. This is to be contrasted with the case of a fermion mass.
In that case the fermion mass is shifted by the interactions by an amount which is
E. Rabinovici
• There is a Higgs like feature for such systems. The massless gravitino became
massive when spontaneous breaking of supersymmetry occurred. The would-be
goldstino became part of the massive gravitino. This may resolve the issue of the
missing Goldstino.
• SUSY may persist in the presence of a negatively valued cosmological constant.
Thus the spontaneous breaking of supersymmetry may be fine tuned so as to
obtain a zero value or very small value for the cosmological constant. This is done
by balancing the positive vacuum energy resulting from breaking supersymmetry
against the value of the negative cosmological constant.
• The presence of gravity renders the Lagrangians to be superficially nonrenormalizable. In fact in these theories the ultra violet divergences are much
less severe than what would be expected by power counting. In the presence of
local SUSY the supersymmetry can be enhanced up to N = 8 in four dimensions.
Such a theory is intimately related to a ten dimensional theory with N = 1
supersymmetry in ten dimensions. Some scientists have the hope that this very
special theory is in fact finite. Time will tell.
• Once global SUSY is embedded in supergravity one can imagine also terms
which softly break supersymmetry and do not result from spontaneous breaking,
i.e. one can add relevant terms to a Lagrangian describing for low energies a
systems of particles containing superparticles with non-supersymmetric masses
and interactions.
8.2.8 The Hierarchy Problem
SUSY was uncovered on the route of circumventing the no go theorem concerning
the unification of a internal and space time symmetries into a unified group as well
as attempting to find a symmetry which relates the different couplings in a rather
general Lagrangian involving both bosons and fermions. It was taken up again when
it was decided to declare the very large value of the ratio of the planck scale and
the weak interaction scale as a problem. On a more technical level the problem was
stated as follows. Consider a theory with an interacting scalar particle. Notice that to
this date no fundamental spin zero elementary particles were observed, the discovery
of an elementary spin zero Higgs particle would change this unfamiliar situation,
a situation in which the simplest realization of a symmetry is not manifested in
nature on an elementary level. No matter what the original mass of the scalar
is, the interactions shift the mass. The mass shift is divergent as is the case for
renormalizable theories. However according to the renormalization group ideas one
always encodes the present knowledge valid up to an energy scale in an effective
low energy theory. In that case the mass shift is proportional to the cutoff . As
long as there is no physical scale near that of the weak interaction’s scale of 1
TeV one needs to fine tune the input initial mass to obtain a Higgs mass of the
weak interaction scale. This is to be contrasted with the case of a fermion mass.
In that case the fermion mass is shifted by the interactions by an amount which is