Related papers: On Gribov's Ideas on Confinement
I point out two of the subtleties referred to in the title. The first is that gauge-invariant magnetic systems may realized under general circumstances, as suggested by a simple theorem. The second subtlety is that care is needed to…
We discuss questions related to renormalization group and to nonperturbative aspects of non-Abelian gauge theories with N=2 and/or N=1 supersymmetry. Results on perturbative and nonperturbative $\beta$ functions of these theories are…
Some notions in non-perturbative dynamics of supersymmetric gauge theories are being reviewed. This is done by touring through a few examples.
Numerical results for the (rest-frame) $Q\bar{Q}$ potential in light-front quantized $QCD_{2+1}$ on a $\perp$ lattice are presented. Both in the longitudinal as well as the $\perp$ spatial directions one obtains linear confinement. The…
We study the relation between quark confinement and chiral symmetry breaking in QCD. Using lattice QCD formalism, we analytically express the various "confinement indicators", such as the Polyakov loop, its fluctuations, the Wilson loop,…
We review some recent ideas regarding classical topological objects in dual superconductor models that could represent different confining states of the gluon field. We also comment about natural components in (magnetic) ensembles that…
We discuss $5d$ and $6d$ supersymmetric gauge theories in the target-space with compactified directions and with the matter hypermultiplets in fundamental representations in the framework of integrable systems. In particular, we consider…
In this lecture I will explain the established pictures of the QCD vacuum and, in particular, the underlying confinement mechanism. These are: the magnetic monopole condensation (dual Mei\ss ner effect), the center vortex picture and the…
I give a brief description of Gribov's light quark confinement scenario and of the Gribov--Dyson--Schwinger equation for light quarks. It is shown that the Green function obtained from this equation exhibits chiral symmetry breaking.
To obtain some exact results of U(1) gauge theory (QED), we construct the low energy effective action of N=2 supersymmetric QED with a massless matter and Fayet-Iliopoulos term, assuming no confinement. The harmonic superspace formalism for…
In this paper we construct a wide class of Gribov copies in Coulomb gauge SU(2) gauge theory. Infinitesimal copies are studied in some detail and their non-perturbative nature is made manifest. As an application it is shown that the copies…
Pure lattice gauge theories in three dimensions are widely expected to confine. A rigorous proof of confinement for three-dimensional $\mathrm{U}(1)$ lattice gauge theory with Villain action was given by G\"opfert and Mack. Beyond the…
We show that in SU(2) Yang-Mills theories a simple relation exists between lattice gluon propagators in Coulomb and Landau gauge and discuss the physical implications of such result. In particular, the realization of the Gribov-Zwanziger…
I give an elementary introduction to the study of gauge theories coupled to fermions with many degrees of freedom. Besides their intrinsic interest, these theories are candidates for nonperturbative extensions of the Higgs sector of the…
We investigated the gauge (in)dependence of the confinement mechanism due to monopole condensation in SU(2) lattice QCD by various abelian projections. We found (1) the string tension can be reproduced by monopoles alone also in Polyakov…
In this article, we provide a short review (written in Chinese) on the Bethe/Gauge correspondence. We first explain the basic idea in an explicit example of the correspondence between XXX spin chains and 2d $\mathcal{N}=(2,2)$ gauge…
Much about the confinement and dynamical symmetry breaking in QCD might be learned from models with supersymmetry. In particular, models based on N=2 supersymmetric theories with gauge groups SU(N), SO(N) and $USp(2 N)$ and with various…
The question of the role of the center of the gauge group in the phenomenon of confinement in Yang-Mills theory is addressed. The investigation is performed from the most general perspective of considering all possible choices for the gauge…
We consider a 1+3 dimensional spin system. The spin-wave (magnon) field is described by the O(3) non-linear sigma model with a symmetry-breaking potential. This interacts with a slow spin SU(2) doublet Schrodinger fermion. The interaction…
In these lectures I present a basic introduction to supersymmetry, especially to N=1 supersymmetric gauge theories and their renormalization, in the Wess-Zumino gauge. I also discuss the various ways supersymmetry may be broken in order to…