Perturbative and non-perturbative infrared behavior of ...

8. Supersymmetric QCD and Seiberg duality
show that the magnetic gauge group is Higgsed to SU(Nf −Nc −1) with Nf −1 massless quarks.
The equations of motion of the massive quarks read
M Nf
Nf = Mi Nf
= MNf
i
= 0 (8.2.51)
and substituting them in (8.2.49) we obtain the low energy superpotential as
W = M i j
jqi˜q (8.2.52)
where now i,j = 1,... ,Nf − 1 and qi, ˜q j are the massless quarks which remain in the low energy
theory.
The scale of the magnetic theory is modified from ˜ Λ to ˜ ΛL by
˜Λ 3(N−1)−(Nf −1)
L
= ˜ Λ 3N−Nf
ˆΛm
(8.2.53)
The low energy magnetic theory is at weaker coupling at low energies and is the dual of the
low energy limit of the electric theory. Thus, the duality is preserved when a mass deformation
is introduced and exchanges a more strongly coupled electric description with a more weakly
coupled magnetic one.
For completeness, we include the case Nf = Nc + 2. The mass term for the flavor field
completely breaks the magnetic gauge group. The low energy spectrum contains the mesons M j
i
and the massless singlet quarks qi and ˜q i , with i,j = 1,... ,Nc + 1. The superpotential is
Wm =
1
Λ 2Nc−1
L
Mq˜q (8.2.54)
Because the SU(2) magnetic gauge group is completely Higgsed, we have to include the instanton
contribution
det M
Winst = −
Λ 2Nc−1
L
(8.2.55)
which is the superpotential of the electric theory in the case Nf = Nc + 1. In the electric
description (8.2.55) is a strong coupling effect. In the magnetic description it is associated with
an instanton contribution at weak coupling.
8.3 SQCD with singlets: SSQCD
We now extend the discussion of the above section to a new set of theories, first defined in [117].
Consider SU(Nc) SQCD with Nf fundamental flavors Qi and ˜ Qi, i = 1,... ,Nf and N ′ f additional
flavors Q ′ i ′ and ˜ Q ′ i ′, i ′ = 1,... ,N ′ f
coupled to N ′2
f gauge singlets Si′ j ′
W = hSQ ′ ˜ Q ′
by the superpotential
(8.3.56)
flavors which flows to a nontrivial fixed
For h = 0, the resulting theory is SQCD with Nf + N ′ f
point when 3
2Nc < Nf + N ′ f < 3Nc. The superpotential (8.3.56) is a relevant deformation which
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