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:
Abstract
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
How to cite

Metadata are provided both in "article" format (very similar to INSPIRE) as this helps creating very compact bibliographies which can be beneficial to authors and readers, and in "proceeding" format which is more detailed and complete.

Open Access
Creative Commons LicenseCopyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.