Confinement and deconfinement for any gauge group from dyons viewpoint

Basing on a semiclassical picture of dyons, we present a nonperturbative model of a pure Yang--Mills theory at any temperatures, for an arbitrary simple gauge group. We argue that at low temperatures dyons drive the Yang--Mills system for all groups to a phase where the `eigenphases' of the Polyakov line are, as a vector, proportional to the Weyl vector being the half sum of positive roots. For most gauge groups it means confinement, in particular for `quarks' in any N-ality nonzero representation of the SU(N) gauge group. At a critical temperature there is a 1st order phase transition for all groups (except SU(2) where the transition is 2nd order), characterized by a jump of Polyakov lines, irrespectively of whether the gauge group has a nontrivial center, or not.Comment: Plenary talk at Quark Confinement and Hadron Spectrum 2010 (Madrid, Aug. 29 - Sep. 3, 2010), to be published in the Proceedings by the AI

A theory of baryon resonances at large N_c

At large number of colors, N_c quarks in baryons are in a mean field of definite space and flavor symmetry. We write down the general Lorentz and flavor structure of the mean field, and derive the Dirac equation for quarks in that field. The resulting baryon resonances exhibit an hierarchy of scales: The crude mass is O(N_c), the intrinsic quark excitations are O(1), and each intrinsic quark state entails a finite band of collective excitations that are split as O(1/N_c). We build a (new) theory of those collective excitations, where full dynamics is represented by only a few constants. In a limiting (but unrealistic) case when the mean field is spherically-and flavor-symmetric, our classification of resonances reduces to the SU(6) classification of the old non-relativistic quark model. Although in the real world N_c is only three, we obtain a good accordance with the observed resonance spectrum up to 2 GeV.Comment: 27 pages, 4 figures, minor changes, resembles published versio