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Register a new userQuark Confinement from Color Confinement
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We relate quark confinement, as measured by the Polyakov-loop order parameter, to color confinement, as described by the Kugo-Ojima/Gribov-Zwanziger scenario. We identify a simple criterion for quark confinement based on the IR behaviour of ghost and gluon propagators, and compute the order-parameter potential from the knowledge of Landau-gauge correlation functions with the aid of the functional RG. Our approach predicts the deconfinement transition in quenched QCD to be of first order for SU(3) and second order for SU(2) -- in agreement with general expectations. As an estimate for the critical temperature, we obtain T_c=284MeV for SU(3).
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We propose a unified description of two important phenomena: color confinement in large-$N$ gauge theory, and Bose-Einstein condensation (BEC). We focus on the confinement/deconfinement transition characterized by the increase of the entropy from $N^0$ to $N^2$, which persists in the weak coupling region. Indistinguishability associated with the symmetry group -- SU($N$) or O($N$) in gauge theory, and S$_N$ permutations in the system of identical bosons -- is crucial for the formation of the condensed (confined) phase. We relate standard criteria, based on off-diagonal long range order (ODLRO) for BEC and the Polyakov loop for gauge theory. The constant offset of the distribution of the phases of the Polyakov loop corresponds to ODLRO, and gives the order parameter for the partially-(de)confined phase at finite coupling. We demonstrate this explicitly for several quantum mechanical systems (i.e., theories at small or zero spatial volume) at weak coupling, and argue that this mechanism extends to large volume and/or strong coupling. This viewpoint may have implications for confinement at finite $N$, and for quantum gravity via gauge/gravity duality.
It is shown that an effective theory with meron degrees of freedom produces confinement in SU(2) Yang Mills theory. This effective theory is compatible with center symmetry. When the scale is set by the string tension, the action density and topological susceptibility are similar to those arising in lattice QCD.
The color-flavor locking phenomenon in the magnetic picture can be the microscopic description of the quark confinement in QCD. We demonstrate it in an N=2 supersymmetric SU(Nc)xSU(Nc) quiver gauge theory coupled to Nf flavors of quarks (Nf<Nc). This model reduces to SU(Nc) gauge theory with Nf flavors when the vacuum expectations value of the link field is much larger than the dynamical scales, and thus provides a continuous deformation of the N=2 supersymmetric QCD. We study a vacuum which survives upon adding a superpotential term to reduce to N=1 while preserving the vectorial SU(Nf) flavor symmetry. We find a region of the parameter space where the confinement is described by the Higgsing of a weakly coupled magnetic SU(Nf)xU(1) gauge theory. The Higgsing locks the quantum numbers of SU(Nf) magnetic color to those of SU(Nf) flavor symmetry, and thus the massive magnetic gauge bosons become the singlet and adjoint representations of the flavor group, i.e, the vector mesons. If the qualitative picture remains valid in non-supersymmetric QCD, one can understand the Hidden Local Symmetry as the magnetic dual description of QCD, and the confining string is identified as the vortex of vector meson fields.
Some aspects are discussed of the mechanism of color confinement in QCD by condensation of magnetic monopoles in the vacuum.
Using the BF version of pure Yang-Mills, it is possible to find a covariant representation of the t Hooft magnetic flux operator. In this framework, t Hoofts pioneering work on confinement finds an explicit realization in the continuum. Employing the Abelian projection gauge we compute the expectation value of the magnetic variable and find the expected perimeter law. We also check the area law behaviour for the Wilson loop average and compute the string tension which turns out to be of the right order of magnitude.
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