J. Greensite

I show that i) a recent proposal for the Yang-Mills vacuum wavefunctional in D=2+1 leads to a linear Coulomb potential; ii) constituent gluons in quark-antiquark states bring the value of the Coulomb string tension in D=3+1 much closer to that of the static quark potential. If time permits, I may also discuss a new semi-perturbative treatment of the Fadeev-Popov eigenvalue spectrum

Y. Simonov

Nonperturbative (np) phenomena in QCD are shown to be generated by strong vacuum fields, which are naturally measured by field correlators. In the first part of talk it is shown that np quantities are expressed through the lowest (quadratic) correlators with few percent accuracy, and one specific correlator explains quantitatively confinement and chiral symmetry breaking, while its vanishing at $T>T_c$ explains deconfinement. In the second part of talk, field correlators themselves are calculated in background field formalism and are shown to be generated by gluelumps, which are again calculated via field correlators. In this way one obtains a selfconsistent set of equations. Convergence and accuracy of this set is discussed, and it is explained how seemingly different
scales: string tension, gluonic condensate, glueball mass and $\Lambda_{QCD}$ are expressed through the only one scale.

J.M. Cornwall

Center vortices have been around for more than thirty years, well-confirmed on the lattice, and very successful in explaining the basics of confinement, yet there are still open questions unstudied either on the lattice or in theory. The first is that basic confinement in the center vortex picture is topological and makes no reference to any particular surface (whose area would appear in the area law) or fluctuation dynamics of this surface. Only in d=2 (flat Wilson loops) is it obvious what surface must be involved, and in this dimension there is no room for fluctuations. This makes it hard to understand the Luscher term and other properties of the fluctuating confinement surface for d>2. I make the obvious, but unconfirmed to date, conjecture that in topological confinement for non-planar Wilson loops the area law is the exponential of a string tension times the area of a
minimal surface spanning the Wilson loop, which would lead to a Luscher term. Closely-related issues are the structure of the area law for two coaxial Wilson loops, as the distance between them along the axis grows; the resulting Casimir force between hadrons; and the behavior of k-string.

Ph. de Forcrand

Drawing on the analogy with U(1) lattice gauge theory in (3+1) dimensions, I explain how to study confinement in 4d Yang-Mills theory with one extra, compact dimension on the lattice. The phase diagram of this theory and the limits placed by its non-renormalizability are clarified.

V. Zakharov

Generically, dual formulations of Yang-Mills theory possess classical solutions due to non-trivial topology of extra dimensions. We concentrate on the geometry of the Sakai-Sugimoto model and consider both confining and deconfined phases. The topological solutions might play crucial role in understanding physics of the deconfining phase transition, viscosity of the Yang-Mills plasma, observation of 'event-by-event' violations of CP invariance in heavy ion collisions.

A. Szczepaniak

We discuss construction of the Coulomb gauge vacuum wave functional which is dominated by a disordered gas of magnetic domains. The effect of vortices and monopoles on the Wilson loop and gluon and ghost propagators will be discussed. We show how to reconcile screening of the gluon propagator observed in the infrared with the long-range disorder demanded by confinement.

J-P. Blaizot

TBA

M. D’Elia

We discuss recent lattice results concerning the properties and the role of abelian magnetic monopoles in the high temperature phase of Yang-Mills theories..

W. Weise

TBA

G.V. Semenoff

We consider the expectation value of the Polyakov loop operator in large representations of the gauge group in the deconfined phase of large N finite temperature Yang-Mills theory. We argue that this expectation value has some properties which are a diagnostic of features of the large N limit. We comment on the k-string tension.