490
E. Rabinovici
There will be condensation of the magnetic charge, confinement has been
demonstrated to be indeed driven by monopole condensation. A monopole is usually
a very heavy collective excitation. It is only the large amount of SUSY which allows
one to follow the monople as it becomes massless and even condenses.
8.2.6 Dynamics of SUSY Gauge Theories with N > 1 SUSY
8.2.6.1 N = 4 Supersymmetry
In the presence of this large amount of supersymmetry in four space-time dimensions the particle content was described in an earlier section. It consists of spin
one, spin one half and spin zero particles. The particles are all in the adjoint
representation of the gauge group. They fall into representations of the SU(4) global
symmetry group as well. The full Lagrangian is fully dictated by the symmetry. The
large symmetry leads to several properties which can be demonstrated.
• The theory is scale invariant quantum mechanically. This was shown to all orders
in perturbation theory as well as non-perturbatively. This served as an example
of non-trivial four dimensional scale invariant theories.
• The theory has thus a meaningful coupling constant on which the physics truly
depends (unlike massless QCD in which dimensionless quantities do not depend
on the coupling). Moreover the coupling can be complexified by adding the θ
parameter. (In the absence of a chiral anomaly the theory truly depends also on
θ even though massless fermions are present). The theory is invariant under the
modular group SL(2,Z), this group relates in particular small and large values of
the coupling.
• The theory has flat directions along the scalar fields for any value of the coupling.
The different points along the flat directions are not generically related by any
symmetry. Each point characterizes a different vacuum choice for the system.
These different vacua are called moduli. There is a special point in the moduli
space and that is the point at the origin of field space where all scalar fields obtain
a zero expectation value. At that point the theory is realized in a scale invariant
manner. The massless fields rendering the theory with a rather complex analytic
structure. Choosing different vacua along the moduli space leads to different
residual gauge symmetries, as the scalar fields are in the adjoint representations
the residual gauge group is at least U(1) r where r is the rank of the group. In each
of these vacua the scale symmetry is spontaneously broken leading to a presence
of a dilaton, the Goldstone Boson of broken scale invariance, in the spectrum.
The vacuum energy is the same in all the phases associated with the different
vacua choice. It has no dependence on any of the expectation values of the scalar
fields. The spectrum includes massless and massive gauge particles.
• In the broken phases of the theory the conditions are appropriate for the presence
of various solitons in the system. In general they contain particles particles which
E. Rabinovici
There will be condensation of the magnetic charge, confinement has been
demonstrated to be indeed driven by monopole condensation. A monopole is usually
a very heavy collective excitation. It is only the large amount of SUSY which allows
one to follow the monople as it becomes massless and even condenses.
8.2.6 Dynamics of SUSY Gauge Theories with N > 1 SUSY
8.2.6.1 N = 4 Supersymmetry
In the presence of this large amount of supersymmetry in four space-time dimensions the particle content was described in an earlier section. It consists of spin
one, spin one half and spin zero particles. The particles are all in the adjoint
representation of the gauge group. They fall into representations of the SU(4) global
symmetry group as well. The full Lagrangian is fully dictated by the symmetry. The
large symmetry leads to several properties which can be demonstrated.
• The theory is scale invariant quantum mechanically. This was shown to all orders
in perturbation theory as well as non-perturbatively. This served as an example
of non-trivial four dimensional scale invariant theories.
• The theory has thus a meaningful coupling constant on which the physics truly
depends (unlike massless QCD in which dimensionless quantities do not depend
on the coupling). Moreover the coupling can be complexified by adding the θ
parameter. (In the absence of a chiral anomaly the theory truly depends also on
θ even though massless fermions are present). The theory is invariant under the
modular group SL(2,Z), this group relates in particular small and large values of
the coupling.
• The theory has flat directions along the scalar fields for any value of the coupling.
The different points along the flat directions are not generically related by any
symmetry. Each point characterizes a different vacuum choice for the system.
These different vacua are called moduli. There is a special point in the moduli
space and that is the point at the origin of field space where all scalar fields obtain
a zero expectation value. At that point the theory is realized in a scale invariant
manner. The massless fields rendering the theory with a rather complex analytic
structure. Choosing different vacua along the moduli space leads to different
residual gauge symmetries, as the scalar fields are in the adjoint representations
the residual gauge group is at least U(1) r where r is the rank of the group. In each
of these vacua the scale symmetry is spontaneously broken leading to a presence
of a dilaton, the Goldstone Boson of broken scale invariance, in the spectrum.
The vacuum energy is the same in all the phases associated with the different
vacua choice. It has no dependence on any of the expectation values of the scalar
fields. The spectrum includes massless and massive gauge particles.
• In the broken phases of the theory the conditions are appropriate for the presence
of various solitons in the system. In general they contain particles particles which