8 Beyond the Standard Model
477
Fig. 8.2 Possible phases of
gauge theories (g 1 and g 2 are
some relevant couplings)
g
g
2
1
SU (2)
HIGGS
U (1)
COULOMB
SU (3)
CONFINEMENT
phase structure of gauge theories was exactly obtained in some cases. Most earlier
exact important results in field theories, such as asymptotic freedom, were obtained
in circumstances in which the couplings are weak. SUSY enables to obtain also
results in the strong coupling regime. The analytic control seems to become larger
the more supersymmetries the system possesses. This has been achieved in four
dimensions for supersymmetric gauge theories with N = 1,2,4 supersymmetries.
There are many new methods that have been utilized and the phase structures of
these theories have been well investigated. Novel properties of these theories have
been discovered such as new types of conformal field theories and new sorts of
infra-red duality. To these we turn next (Fig. 8.2).
8.2.5.2 SUSY QCD: The Setup
The goal will be to examine theories that are simple supersymmetric extensions of
QCD. Consider the case of a N = 1 vector multiplet with gauge group SU(N C ), and
N F chiral multiplets in the fundamental representation of SU(N C ), and N F chiral
multiplets in the antifundamental representation. The Lagrangian is:
L =
(−iτ ) TrW α W α d 2 θ + h.c.
+ Q
+
F exp (−2V ) Q F + ˜
Q exp(2V ) Q
+
F
θθθθ
+ m F ˜
Q F Q| θθ
(8.75)
where the coupling is:
τ =
θ
2π
+ i
4π
g 2 .
(8.76)
477
Fig. 8.2 Possible phases of
gauge theories (g 1 and g 2 are
some relevant couplings)
g
g
2
1
SU (2)
HIGGS
U (1)
COULOMB
SU (3)
CONFINEMENT
phase structure of gauge theories was exactly obtained in some cases. Most earlier
exact important results in field theories, such as asymptotic freedom, were obtained
in circumstances in which the couplings are weak. SUSY enables to obtain also
results in the strong coupling regime. The analytic control seems to become larger
the more supersymmetries the system possesses. This has been achieved in four
dimensions for supersymmetric gauge theories with N = 1,2,4 supersymmetries.
There are many new methods that have been utilized and the phase structures of
these theories have been well investigated. Novel properties of these theories have
been discovered such as new types of conformal field theories and new sorts of
infra-red duality. To these we turn next (Fig. 8.2).
8.2.5.2 SUSY QCD: The Setup
The goal will be to examine theories that are simple supersymmetric extensions of
QCD. Consider the case of a N = 1 vector multiplet with gauge group SU(N C ), and
N F chiral multiplets in the fundamental representation of SU(N C ), and N F chiral
multiplets in the antifundamental representation. The Lagrangian is:
L =
(−iτ ) TrW α W α d 2 θ + h.c.
+ Q
+
F exp (−2V ) Q F + ˜
Q exp(2V ) Q
+
F
θθθθ
+ m F ˜
Q F Q| θθ
(8.75)
where the coupling is:
τ =
θ
2π
+ i
4π
g 2 .
(8.76)