In this lecture course we intend to give an introduction and review recent developments in nonperturbative aspects of supersymmetric gauge theories. Accumulation of results obtained in the 1980s culminated in a breakthrough discovery of the Seiberg–Witten solution (1994) in N=2 Yang-Mills theories. This was the first analytic demonstration ever of the dual Meissner effect as the underlying mechanism of color confinement. Since then we witnessed a remarkable progress in understanding non-Abelian string formation and their structure. A full understanding of what happens with the ‘t Hooft-Polyakov monopoles in the Higgsed theories and how they get confined was achieved. There are high expectations (supported in part by a number of recent results) that using certain dualities we will be able to pass from confined monopoles to confined quarks in N=1 theories. Dualities going beyond those of Seiberg and Seiberg and Witten were discovered and exploited, with great success, in dealing with various gauge theories at strong coupling. A tool kit was developed which allowed one to obtain a number of elegant exact results. The tentative plan of the lecture course is: 1. A brief introduction to centrally extended superalgebras; 2. A review of important models with central charges and their implications; 3. Non-Abelian strings; basic bulk gauge theories supporting non-Abelian strings; 4. World-sheet theories on non-Abelian strings; 5. From the ‘t Hooft-Polyakov monopoles to confined monopoles: a smooth journey without phase transitions; 6. Descending down to N=1 (heterotic non-Abelian strings); 7. Beyond Seiberg-Witten’s dualities. (Cour organisé en collaboration avec l’Ecole Doctorale de Physique de la Région Parisienne – ED 107)

Minnesota U et Chaire Blaise Pascal (Etat et IdF)