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Register a new userFurther discussion of Tomboulis approach to the confinement problem
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We discuss in some detail certain gaps and open problems in the recent paper by E. T. Tomboulis, which claims to give a rigorous proof of quark confinement in 4D lattice Yang-Mills theory for all values of the bare coupling. We also discuss what would be needed to fill the gaps in his proof.
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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 members contribution to the discussion, provided by the panel members themselves.
I will review essential features of the Hamiltonian approach to QCD in Coulomb gauge showing that Gribovs 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 Gribovs 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 and second by the compactification of a spatial dimension. I will present results for the pressure, energy density and interaction measure as well as for the Polyakov loop.
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).
We study the Gribov problem within a Hamiltonian formulation of pure Yang-Mills theory. For a particular gauge fixing, a finite volume modification of the axial gauge, we find an exact characterization of the space of gauge-inequivalent gauge configurations.
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.
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