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

TL;DR

This paper calculates mass spectra in various supersymmetric QCD theories, examines the validity of Seiberg duality, and explores phase transitions and confinement mechanisms in these models.

Contribution

It provides detailed mass spectrum calculations and clarifies the conditions under which Seiberg duality holds, also proposing a confinement mechanism for YM and SYM theories.

Findings

Seiberg duality applies mainly to massless quarks in the conformal window.

Introduces a gauge invariant order parameter distinguishing confinement and Higgs phases.

Describes phase transitions between confinement and Higgs phases in supersymmetric theories.

Abstract

Mass spectra are calculated for ${\cal N}=1$ SQCD and SQCD-type theories and for softly broken ${\cal N}=2$ SQCD in vacua with unbroken $Z_{(2N_c-N_F)\geq 2}$ symmetry. It is shown that the Seiberg ${\cal N}=1$ 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 ${\cal N}=1$ SQCD-type and broken ${\cal N}=2$ SQCD theories between confinement and higgs phases, c) the confinement mechanism is proposed for the ordinary YM and ${\cal N}=1$ SYM theories.