The relationship between the nonperturbative Green's functions of Yang-Mills theory and the confinement potential is investigated. By rewriting the generating functional of quantum chromodynamics in terms of a heavy quark mass expansion in Coulomb gauge, restricting to leading order in this expansion and considering only the two-point functions of the Yang-Mills sector, the rainbow-ladder approximation to the gap and Bethe-Salpeter equations is shown to be exact in this case and an analytic, nonperturbative solution is presented. It is found that there is a direct connection between the string tension and the temporal gluon propagator. Further, it is shown that for the 4-point quark correlation functions, only confined bound states of color-singlet quark-antiquark (meson) and quark-quark (baryon) pairs exist.
We present various confinement phases of three-dimensional $\mathcal{N}=2$ $Spin(N)$ gauge theories with vector and spinor matters. The quantum Coulomb branch of the moduli space of vacua is drastically changed when the rank of the gauge group and the matter contents are changed. In many examples, the Coulomb branch is one- or two-dimensional but its interpretation varies. In some examples, the Coulomb branch becomes three-dimensional and we need to introduce a "dressed" Coulomb branch operator.
I will review essential features of the Hamiltonian approach to QCD in Coulomb gauge showing that Gribov's confinement scenario is realized in this gauge. For this purpose I will discuss in detail the emergence of the horizon condition and the Coulomb string tension. I will show that both are induced by center vortex gauge field configurations, which establish the connection between Gribov's confinement scenario and the center vortex picture of confinement. I will then extend the Hamiltonian approach to QCD in Coulomb gauge to finite temperatures, first by the usual grand canonical ensemble an…
We study the low-energy dynamics in three-dimensional $\mathcal{N}=2$ exceptional gauge theories with matters in a fundamental representation, especially focusing on confinement phases and on a quantum structure of the Coulomb branch in the moduli space of vacua. We argue that the confinement phases of these exceptional gauge theories have a single Coulomb branch. The 3d s-confinement phases for the exceptional gauge groups are associated with quantum-deformed moduli spaces of the corresponding 4d $\mathcal{N}=1$ exceptional gauge theories.
We elaborate on s-confinement phases in three-dimensional $\mathcal{N}=2$ supersymmetric gauge theory, especially focusing on the $SU(N)$ and $USp(2N)$ gauge theories with anti-symmetric tensors and (anti-)fundamental matters. This will elucidate a quantum structure of the Coulomb moduli space of vacua. We stress the importance of so-called dressed Coulomb branch operators for describing these s-confinement phases. The 3d s-confinement phases are highly richer than the 4d ones since there is no chiral anomaly constraint on the matter contents.
We study confinement-deconfinement phase transition for heavy quarks in a bottom-up holographic QCD model. We consider a black hole background in an Einstein-Maxwell-scalar system and add probe open strings to the background. Combining the various configurations of the open strings and the phase structure of the black hole background itself, we obtain the confinement-deconfinement phase diagram for heavy quarks in the holographic QCD model.
We study low-energy dynamics of three-dimensional $\mathcal{N}=2$ $SU(N)$ "chiral" gauge theories with $F$ fundamental and $\bar{F}$ anti-fundamental matters without a Chern-Simons term. Compared to a naive semi-classical analysis of the Coulomb branch, its quantum structure is highly richer than expected due to so-called "dressed" Coulomb branch (monopole) operators. We propose dualities and confinement phases for the "chiral" $SU(N)$ theories. The theories with $N>F > \bar{F}$ exhibit spontaneous supersymmetry breaking. The very many Coulomb branch operators generally remain exactly massless…
I clarify, restate and show more clearly some key points I raised in a number of papers that discussed the non-linear gauge-fixing condition and quark confinement. I also correct some errors, which do not detract from the key findings, found in the original papers. However, there are two major corrections I will make in this paper, the first is on the proof of the Parisi-Sourlas mechanism and the second is on the effective action for the 'gluons', which leads to a direct proof of gluons being confined inside hadrons. The correction also leads to how the mass gap will be calculated, which was e…
I report on recent results obtained within the Hamiltonian approach to QCD in Coulomb gauge. By relating the Gribov confinement scenario to the center vortex picture of confinement it is shown that the Coulomb string tension is tied to the spatial string tension. For the quark sector a vacuum wave functional is used which results in variational equations which are free of ultraviolet divergences. The variational approach is extended to finite temperatures by compactifying a spatial dimension. For the chiral and deconfinement phase transition pseudo-critical temperatures of 170 MeV and 198 MeV,…
