Mass spectra in ${\cal N}=1\, SU(N_c)$ SQCD with $N_F=N_c$ and problems with S-confinement

TL;DR

This paper compares the mass spectra of ${ m N}=1$ SQCD with $N_F=N_c$ in direct and dual formulations, critiques the applicability of non-SUSY lattice models, and discusses the nature of confinement and phase transitions in these theories.

Contribution

It demonstrates the parametric differences in mass spectra between direct and dual ${ m N}=1$ SQCD and critiques the non-SUSY lattice model's relevance to standard QCD.

Findings

Mass spectra differ parametrically between direct and dual theories.

The non-SUSY lattice model considered is incompatible with standard QCD.

A qualitative mechanism of confinement in ordinary QCD is proposed.

Abstract

The low energy mass spectra of the direct $SU(N_c)$, $\,N_F=N_c$ $\,{\cal N}=1$ SQCD theory and its N.Seiberg's dual variant [1], are calculated in sections 2 and 3. It is shown that these two mass spectra are parametrically different, both for equal or unequal small quark masses $m_{Q,i}\neq 0$. In [17] the very special non-SUSY lattice $SU(N_c)$ QCD theory with $N_F=N_c$ scalar defective "quarks" was considered by E.Fradkin and S.H.Shenker. The conclusion of [17] was that the transition between the confinement and higgs regimes in this theory is the analytic crossover, not the non-analytic phase transition. And although the theory considered in [17] was very specific, the experience shows that up to now there is a widely spread opinion that this conclusion has general applicability. This model used in [17] is criticized in section 5 of this paper as incompatible with and qualitatively different from the standard non-SUSY $SU(N_c)$ $N_F=N_c$ QCD theory with standard scalar quarks $\phi^i_{\beta}$ with all their $2N^2_F$ real degrees of freedom. It is emphasized that this model [17] is really the Stuckelberg $SU(N_c)$ YM-theory with no dynamical electric quarks and with massive all $N_c^2-1$ electric gluons with fixed by hands nonzero masses. There is no genuine confinement in this theory, it stays permanently in the completely higgsed phase only. And this is a reason for a crossover in this theory. While in the theory with standard scalar quarks there is the phase transition between the confinement and higgs phases. Besides, in section 5, the arguments presented in [2] by K.Intriligator and N.Seiberg for the standard direct $SU(N_c)$, $N_F=N_c$ $\,{\cal N}=1$ SQCD in support of the crossover from [17] are criticized as erroneous. Besides, in section 5 a qualitative mechanism of confinement in our ordinary (i.e. not SUSY) QCD is proposed.