arXiv subjects
Publications and source records attributed to D. Zwanziger.
The participants in this discussion session of the QCHS 9 meeting were each asked the following question: "What would be the most useful piece of information that you could obtain, by whatever means, that would advance your own program, and/or our general understanding of confinement?" This proceedings contains a brief summary of each panel member's contribution to the discussion, provided by the panel members themselves.
During recent years, a good agreement was found between the analytical derivation and the numerical simulation of the Landau gauge gluon and ghost propagators. We mention the Schwinger-Dyson and Gribov-Zwanziger formalism for the analytical work. Although the agreement between several approaches is nice, these propagators do not correspond to the relevant physical degrees of freedom. In the case of pure gauge theories, one should start to study the glueball correlators. We shall try to explain why it looks like a hard challenge to go from the unphysical to the physical propagators in the case of the Gribov-Zwanziger theory (but similar conclusions might hold for other approaches giving similar propagators).
Restricting the functional integral to the Gribov region $Ω$ leads to a deep modification of the behavior of Euclidean Yang-Mills theories in the infrared region. For example, a gluon propagator of the Gribov type, $\frac{k^2}{k^4+{\hat γ}^4}$, can be viewed as a propagating pair of unphysical modes, called here $i$-particles, with complex masses $\pm i{\hat γ}^2$. From this viewpoint, gluons are unphysical and one can see them as being confined. We introduce a simple toy model describing how a suitable set of composite operators can be constructed out of $i$-particles whose correlation functions exhibit only real branch cuts, with associated positive spectral density. These composite operators can thus be called physical and are the toy analogy of glueballs in the Gribov-Zwanziger theory.
We summarize the construction of the Gribov-Zwanziger action and how it leads to a scenario which explains the confinement of gluons, in the sense that the elementary gluon excitations violate positivity. Then we address the question of how one can construct operators within this picture whose one-loop correlation functions have the correct analytic properties in order to correspond to physical excitations. For this we introduce the concept of i-particles.
We study the properties of the color-Coulomb string tension obtained from the instantaneous part of gluon propagators in Coulomb gauge using quenched SU(3) lattice simulation. In the confinement phase, the dependence of the color-Coulomb string tension on the QCD coupling constant is smaller than that of the Wilson loop string tension. On the other hand, in the deconfinement phase, the color-Coulomb string tension does not vanish even for $T/T_c = 1 \sim 5$, the temperature dependence of which is comparable with the magnetic scaling, dominating the high temperature QCD. Thus, the color-Coulomb string tension is not an order parameter of QGP phase transition.
We review numerical evidence on connections between the center-vortex and Gribov-horizon confinement scenarios.
It is shown numerically that the Coulomb self-energy of an isolated, color non-singlet source diverges in an infinite volume. This is in accord with the Gribov Horizon scenario of confinement advocated by Gribov and Zwanziger. It is also shown that this divergence can be attributed to the presence of center vortices in thermalized lattice configurations.
A gauge theory with 4 physical dimensions can be consistently expressed as a renormalizable topological quantum field theory in 5 dimensions. We extend the symmetries in the 5-dimensional framework to include not only a topological BRST operator S that encodes the invisibility of the "bulk" (the fifth dimension), but also a gauge BRST operator W that encodes gauge-invariance and selects observables. These symmetries provide a rich structure of Ward identities which assure the renormalizability of the theory, including non-renormalization theorems. The 5-dimensional approach considerably simplifies conceptual questions such as for instance the Gribov phenomenon and fermion doubling. A confinement scenario in the 5-dimensional framework is sketched. We detail the five-dimensional mechanism of anomalies, and we exhibit a natural lattice discretization that is free of fermion doubling.
To study ``physical'' gauges such as the Coulomb, light-cone, axial or temporal gauge, we consider ``interpolating'' gauges which interpolate linearly between a covariant gauge, such as the Feynman or Landau gauge, and a physical gauge. Lorentz breaking by the gauge-fixing term of interpolating gauges is controlled by extending the BRST method to include not only the local gauge group, but also the global Lorentz group. We enumerate the possible divergences of interpolating gauges, and show that they are renormalizable, and we show that the expectation value of physical observables is the same as in a covariant gauge. In the second part of the article we study the Coulomb-gauge as the singular limit of the Landau-Coulomb interpolating gauge. We find that unrenormalized and renormalized correlation functions are finite in this limit. We also find that there are finite two-loop diagrams of ``unphysical'' particles that are not present in formal canonical quantization in the Coulomb gauge. We verify that in the same limit, the Gauss-BRST Ward identity holds, which is the functional analog of the operator statement that a BRST transformation is generated by the Gauss-BRST charge. As a consequence, $gA_0$ is invariant under renormalization, whereas in a covariant gauge, no component of the gluon field has this property.
It is proven that the "horizon condition", which was found to characterize the fundamental modular region in continuum theory and the thermodynamic limit of gauge theory on a periodic lattice, holds for every (transverse) configuration on a finite lattice with free boundary conditions.