Confinement and duality in supersymmetric gauge theories

Abstract

In this thesis 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. We then study how these recent developments allow to better understand nonperturbative aspects such as confinement and dynamical symmetry breaking in the N=1 theories obtained starting from N=2 SQCD and adding a mass term for the chiral multiplet in the adjoint of the gauge group. We find an unusual realization of the 't Hooft-Mandelstam mechanism, in which confinement and dynamical symmetry breaking are due to the condensation of different degrees of freedom.