8 Beyond the Standard Model
491
have both electric and magnetic charges, called dyons. The massess of many of
these particles, called BPS states is protected by the large SUSY to the extent that
the mass dependence on the coupling is exactly known. This has applications in
the counting microscopically the entropy of some black holes.
• Moreover, a hidden wish of theoreticians is that not only will one theory describe
all physical phenomena but that that theory be exactly solvable. Given the
complexity of four dimensional field theory this hope was suppressed. It had
resurfaced when it was uncovered that quite a few properties of the N = 4 theory
are exactly calculable. The system seems to have a large number of conserved
quantities and this results in many so called integrability features.
• As will be discussed in the section on string theory, there is a large body of
evidence that N = 4 theory encodes in it the information of special string theories
which include gravity and black holes. These are string theories for strings
propagation on a manifold part of which has a negative curvature and a negative
cosmological constant.
To conclude, supersymmetric gauge theories have a very rich phase structure and
many outstanding dynamical issues can be discussed reliably in the supersymmetric
arena that are hard to address elsewhere.
8.2.7 Gauging Supersymmetry
During most of the second part of the twentieth century local symmetries were
at center stage. The model unifying the electromagnetic and weak interactions
actually united them mainly by using the concept that gauge theories do describe
both. The stronger unification using only one non-semi simple group is yet to be
achieved. The gauge theories have allowed to make precise calculable predictions
for experimentally measurable quantities. Yet in the last year of that century some
scientists suggested to move on and accept that gauge symmetries are simply
redundent descriptions (choosing not to emphasize that this description allows for
a local description of the theory). Be that as it may, at the time it was natural to
promote global symmetry into a local symmetry. The result was very rewarding, it
turned out that the “gauge particle” of local supersymmetry is a masselss fermion
of the spin 3/2, called the gravitino, whose partner in the same supermultiplet is
a massless spin two particle, the graviton. Local supersymmetry led to general
coordinate invariance and the presence of gravity. This is called supergravity
(SUGRA).
Lagrangians invariant under this local symmetry were found. Writing them down
required even more efforts than those needed for the global supersymmetry case.
Nevertheless this was achieved and a superfield notation was discovered as well.
The Lagrangians are rather lengthy and we do not display them here. The system
had additional interesting features.
491
have both electric and magnetic charges, called dyons. The massess of many of
these particles, called BPS states is protected by the large SUSY to the extent that
the mass dependence on the coupling is exactly known. This has applications in
the counting microscopically the entropy of some black holes.
• Moreover, a hidden wish of theoreticians is that not only will one theory describe
all physical phenomena but that that theory be exactly solvable. Given the
complexity of four dimensional field theory this hope was suppressed. It had
resurfaced when it was uncovered that quite a few properties of the N = 4 theory
are exactly calculable. The system seems to have a large number of conserved
quantities and this results in many so called integrability features.
• As will be discussed in the section on string theory, there is a large body of
evidence that N = 4 theory encodes in it the information of special string theories
which include gravity and black holes. These are string theories for strings
propagation on a manifold part of which has a negative curvature and a negative
cosmological constant.
To conclude, supersymmetric gauge theories have a very rich phase structure and
many outstanding dynamical issues can be discussed reliably in the supersymmetric
arena that are hard to address elsewhere.
8.2.7 Gauging Supersymmetry
During most of the second part of the twentieth century local symmetries were
at center stage. The model unifying the electromagnetic and weak interactions
actually united them mainly by using the concept that gauge theories do describe
both. The stronger unification using only one non-semi simple group is yet to be
achieved. The gauge theories have allowed to make precise calculable predictions
for experimentally measurable quantities. Yet in the last year of that century some
scientists suggested to move on and accept that gauge symmetries are simply
redundent descriptions (choosing not to emphasize that this description allows for
a local description of the theory). Be that as it may, at the time it was natural to
promote global symmetry into a local symmetry. The result was very rewarding, it
turned out that the “gauge particle” of local supersymmetry is a masselss fermion
of the spin 3/2, called the gravitino, whose partner in the same supermultiplet is
a massless spin two particle, the graviton. Local supersymmetry led to general
coordinate invariance and the presence of gravity. This is called supergravity
(SUGRA).
Lagrangians invariant under this local symmetry were found. Writing them down
required even more efforts than those needed for the global supersymmetry case.
Nevertheless this was achieved and a superfield notation was discovered as well.
The Lagrangians are rather lengthy and we do not display them here. The system
had additional interesting features.