Confronting Seiberg's Duality with r Duality in N=1 Supersymmetric QCD
release_pdbtmhiognfxvan6g5ep44pd2m
by
M. Shifman, A. Yung
2012
Abstract
Systematizing our results on r duality obtained previously we focus on
comparing r duality with the generalized Seiberg duality in the r vacua of N=2
and N=1 super-Yang-Mills theories with the U(N) gauge group and N_f matter
flavors (N_f>N). The number of condensed (s)quarks r is assumed to be in the
interval 2N_f/3 < r < N. To pass to N=1 we introduce an N=2-breaking
deformation, a mass term μ for the adjoint matter, eventually decoupling the
adjoint matter in the limit of large μ. If one starts from a large value of
the parameter ξ∼μ m, where the original theory is at weak coupling, and
decreases ξ one hits a a crossover transition from weak to strong coupling
(here m is a typical value of the quark masses). Below this transition the
original theory is described in terms of a weakly coupled infrared-free r dual
theory with the U(N_f-r) gauge group and N_f light quark-like dyon flavors.
Dyon condensation leads to confinement of monopoles, defying a naive
expectation of quark confinement. The quarks and gauge bosons of the original
theory are in an "instead-of-confinement" phase. The r and Seiberg dualities
are demonstrated to coincide in the r=N vacua. In the (2/3) N_f <r<N vacua two
dualities do not match. In this window Seiberg's dual is at strong coupling
while our r-dual model is at weak coupling. Thus, we can speak of triality.
Seiberg's dual solution at weak coupling reappears again at r<N_f-N< (1/3)
N_f.
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