Mass Spectra in $\mathcal{N}=1$ SQCD, in $\mathcal{N}=1$ SQCD-type theory and in softly broken $\mathcal{N}=2\to \mathcal{N}=1$ SQCD. And problems with the $\mathcal{N}=1$ Seiberg duality

Abstract

Mass spectra are calculated for $\mathcal{N}=1$ SQCD and SQCD-type theories and for softly broken $\mathcal{N}=2$ SQCD in vacua with unbroken $Z_{(2N_c-N_F)\ge 2}$ symmetry. It is shown that the Seiberg $\mathcal{N}=1$ duality works, at best, for massless quarks within the conformal window only. Besides: a) the gauge invariant order parameter for scalar quarks is introduced which distinguishes confinement and higgs phases, b) the phase transition are described in $\mathcal{N}=1$ SQCD-type and broken $\mathcal{N}=2$ SQCD theories between confinement and higgs phases, c) the confinement mechanism is proposed for the ordinary YM and $\mathcal{N}=1$ SYM theories.

Comments: The review paper. 228 pages, no figures. Minor corrections in the text, results unchanged. arXiv admin note: substantial text overlap with arXiv:1711.01169; text overlap with arXiv:1906.08643, arXiv:1603.04255, arXiv:0811.4283, arXiv:1608.06452, arXiv:2306.12994