Six cours par Prof. Mikhail Shifman au LPT - les Mercredis 8, 15, 22 et Vendredis 10, 17, 24 Octobre 2008

6 lectures, one hour each

Prof. Mikhail SHIFMAN* (University of Minnesota (USA) et Laboratoire de Physique Théorique (Orsay)

Polyakov’s Confinement in Three and Four Dimensions

3 Mercredis [8, 15 et 22 oct.] et 3 Vendredis [10, 17 et 24 oct] de 15h à 16h, à Orsay - LPT (Bat.210), AMPHI-1

This lecture course begins with a pedagogical presentation of the Polyakov Abelian confinement in three dimensions. The crucial theoretical ingredients are dualization and instantons-monopoles whose contribution is responsible for dual photon mass generation. Dual photon in this theory is a (pseudo)scalar phase field \varphi which lives on S_1. Confining strings are equivalent to domain lines, with vortices of the \varphi field at the endpoints. In the original formulation (before dualization) the vortices are electric charges. Confinement of electric charges is explicit and occurs at weak coupling which makes it fully calculable. Introduction of massless quarks suppresses Polyakov’s confinement.

In the second part of the lecture course I discuss recent developments which may have serious implications for four-dimensional QCD-like theories. If we formulate QCD-like theories on R_3\times S_1 with a small radius of the compactified dimension r(S_1) and stabilize the center symmetry, then we deal with a weakly coupled gauge theory, with SU(N)_{\rm gauge} broken down to U(1)^{N-1}. The low-energy theory confines \`a la Polyakov, even in spite of massless quarks that can be present in the low-energy spectrum. Moreover, with one quark flavor, a discrete chiral symmetry of the theory is spontaneously broken. One can argue that the transition to large r(S_1) (i.e. to four-dimensional one flavor QCD ) is smooth. If so, one can treat qualitatively, and, perhaps, even semiquantitavily, basic regularities of four-dimensional QCD.

With two or more flavors we get a remarkable example of of a dynamical gauge theory with confinement but without chiral symmetry breaking.

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* Prof. M. Shifman est un des 5 lauréats des prestigieuses Chaires internationales de recherche Blaise Pascal 2007.