8 Beyond the Standard Model
487
In these cases the UV structure of the Infrared dual theories is very different,
the dual systems have a different numbers of colors. The common wisdom in
hadronic physics has already identified very important cases of infra-red duality.
For example, QCD, whose gauge group is SU(N C ) and whose flavor group is
SU(N F ) × SU(N F ) × U(1), is expected to be infra-red dual to a theory of massless
pions which are all color singlets. The pions, being the spin-0 Goldstone Bosons
of the spontaneously broken chiral symmetry, are actually infra-red free in four
dimensions. We have thus relearned that free spin-0 massless particles can actually
be the infra-red ashes of a strongly-interacting theory, QCD whose ultraviolet
behavior is described by other particles. By using supersymmetry, one can realize
a situation where free massless spin1
2 particles are also the infra-red resolution
of another theory. This duality allows for the first time to ascribe a similar role
to massless infra-red free spin-1 particles. Massless spin-1 particles play a very
special role in our understanding of the basic interactions. This comes about in the
following way: Consider, for example, the N = 1 supersymmetric model with N C
colors and N F flavors. It is infra-red dual to a theory with N F − N C colors and
N F flavors and N 2
F color singlets. For a given N C , if the number of flavors, N F ,
is in the interval N C + 1 < N F <
3N C
2 , the original theory is strongly coupled
in the infra-red, while the dual theory has such a large number of flavors that it
becomes infrared free. Thus the infra-red behavior of the strongly-coupled system
is described by infrared free spin-1 massless fields (as well as its superpartners), i.e.
infrared free massless spin-1 particles (for example photons in a SUSY system)
could be, under certain circumstances, just the infra-red limit of a much more
complicated ultraviolet theory. This is the first example of a weakly interacting
theory in which spin one particles that in the infra-red may be viewed as bound
states of the dual theory. The duality has passed a large number of consistency
checks under many circumstances. The infrared duality relates two disconnected
systems. From the point of view of string theory the two systems are embedded in a
larger space of models, such that a continuous trajectory relates them. An additional
new consequence of this duality follows for the case
3N C
2
< N F < 3N C
the two dual theories are both asymptotically free in the UV and are describe
by the same nontrivial conformal field theory in the infrared. The panorama of
these structures is given in Fig. 8.8. Finally a class of examples was found among
N = 2 SUSY conformal systems for which there are two very different Lagrangian
descriptions as far as the local symmetries are involved which are actually identical
at all distance scales.
487
In these cases the UV structure of the Infrared dual theories is very different,
the dual systems have a different numbers of colors. The common wisdom in
hadronic physics has already identified very important cases of infra-red duality.
For example, QCD, whose gauge group is SU(N C ) and whose flavor group is
SU(N F ) × SU(N F ) × U(1), is expected to be infra-red dual to a theory of massless
pions which are all color singlets. The pions, being the spin-0 Goldstone Bosons
of the spontaneously broken chiral symmetry, are actually infra-red free in four
dimensions. We have thus relearned that free spin-0 massless particles can actually
be the infra-red ashes of a strongly-interacting theory, QCD whose ultraviolet
behavior is described by other particles. By using supersymmetry, one can realize
a situation where free massless spin1
2 particles are also the infra-red resolution
of another theory. This duality allows for the first time to ascribe a similar role
to massless infra-red free spin-1 particles. Massless spin-1 particles play a very
special role in our understanding of the basic interactions. This comes about in the
following way: Consider, for example, the N = 1 supersymmetric model with N C
colors and N F flavors. It is infra-red dual to a theory with N F − N C colors and
N F flavors and N 2
F color singlets. For a given N C , if the number of flavors, N F ,
is in the interval N C + 1 < N F <
3N C
2 , the original theory is strongly coupled
in the infra-red, while the dual theory has such a large number of flavors that it
becomes infrared free. Thus the infra-red behavior of the strongly-coupled system
is described by infrared free spin-1 massless fields (as well as its superpartners), i.e.
infrared free massless spin-1 particles (for example photons in a SUSY system)
could be, under certain circumstances, just the infra-red limit of a much more
complicated ultraviolet theory. This is the first example of a weakly interacting
theory in which spin one particles that in the infra-red may be viewed as bound
states of the dual theory. The duality has passed a large number of consistency
checks under many circumstances. The infrared duality relates two disconnected
systems. From the point of view of string theory the two systems are embedded in a
larger space of models, such that a continuous trajectory relates them. An additional
new consequence of this duality follows for the case
3N C
2
< N F < 3N C
the two dual theories are both asymptotically free in the UV and are describe
by the same nontrivial conformal field theory in the infrared. The panorama of
these structures is given in Fig. 8.8. Finally a class of examples was found among
N = 2 SUSY conformal systems for which there are two very different Lagrangian
descriptions as far as the local symmetries are involved which are actually identical
at all distance scales.