PoS - Proceedings of Science
Volume 455 - International Conference on Particle Physics and Cosmology (ICPPCRubakov2023) - Parallel session Quantum chromodynamics, strong interactions
Phase transitions between confinement and higgs phases in ${\cal N}=1\, SU(N_c)$ SQCD with $1\leq N_F\leq N_c$ quark flavors
V.L. Chernyak
Full text: pdf
Pre-published on: April 11, 2024
Published on: May 17, 2024
Considered is 4-dimensional ${\cal N}=1$ supersymmetric $SU(N_c)$ QCD (SQCD) with $1\leq N_F\leq N_c$ quark flavors with masses $m_{Q,i}$ in the bi-fundamental representation. {\bf The gauge invariant order parameter $\rho$ is introduced distinguishing confinement (with $\rho=0$) and higgs (with $\rho\neq 0$) phases}.

Using a number of independent arguments for different variants of transition between the confinement and higgs regimes in these theories, it is shown that {\bf transitions between these regimes are not crossovers but the phase transitions}.

In \cite{FS} the very special $SU(N_c)$ QCD theory with $N_F=N_c$ defective scalar "quarks" in the unitary gauge:
$\Phi ^i_{\beta}= \delta^i_{\beta}(|v|={\rm const}) > 0,\,\,
i,{\beta}=1,...,N_F=N_c$, was considered by E.Fradkin and S.H.Shenker. The conclusion of \cite{FS} was that the transition between the confinement at $0 < |v|\ll\Lambda_{QCD}$ (according to \cite{FS}) and higgs (i.e. with condensed quarks) at $|v|\gg
\Lambda_{QCD}$ regimes is the analytic crossover. And although the theory considered in \cite{FS} was very specific, the experience shows that up to now there is a widely spread opinion that this conclusion has general applicability.

This model \cite{FS} is criticized as incompatible with and very different from the standard non-SUSY $SU(N_c)\,\,N_F=N_c$ QCD theory with standard scalar quarks $\phi^i_{\beta}$ with all
$2 N^2_c$ their physical real degrees of freedom. It is emphasized that this model \cite{FS} is really {\bf the Stuckelberg $SU(N_c)$ YM-theory with no dynamical electric quarks and massive all $N_c^2-1$ electric gluons with fixed by hands nonzero masses $g|v| > 0$}. There is no genuine confinement in this theory, it stays permanently in the completely higgsed (i.e. condensed) by hands 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 (at $0 < |v|
\ll\Lambda_{QCD}$) and higgs (at $|v|\gg\Lambda_{QCD}$) regimes.

Besides, the arguments presented in \cite{IS} 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 \cite{FS} are criticized as erroneous.
DOI: https://doi.org/10.22323/1.455.0036
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