Mikhail Shifman (Minnesota U.)
Alexei Yung (PNPI St. Petersburg)
In this 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 toolkit was developed which allowed one to obtain a number of elegant exact results.
The tentative plan of the lecture course is:
- A brief introduction to centrally extended superalgebras;
- A review of important models with central charges and their implications;
- Non-Abelian strings; basic bulk gauge theories supporting non-Abelian strings;
- World-sheet theories on non-Abelian strings;
- From the 't Hooft-Polyakov monopoles to confined monopoles: a smooth journey without phase transitions;
- Descending down to N=1 (heterotic non-Abelian strings);
- Beyond Seiberg-Witten dualities.