Recent Advances in Supersymmetric Gauge Theories

In the past decades supersymmetric field theories have been the subject of intense research activity and represent an important theoretical laboratory which allows us to investigate the dynamics of strongly-coupled field theories. In particular, recently there has been a huge progress in our understanding of N=2 theories in four dimensions. The scope of this book is on the one hand to provide a review of these new developments and on the other to illustrate what one can learn from these results about intrinsically strongly-coupled phenomena, such as confinement and dynamical symmetry breaking. We review the Seiberg-Witten solution of four dimensional N=2 gauge theories, the six-dimensional construction of these models recently proposed by Gaiotto and the BPS quiver technique for the determination of the BPS spectrum of N=2 theories. Equipped with this machinery we then turn our attention to the analysis of softly broken N=2 SQCD, finding an unusual realization of the 't Hooft-Mandelstam mechanism for confinement. The book is addressed to graduate students and researchers interested in formal aspects of supersymmetric theories and with a good field theory background.