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The aim of this talk is to give a brief introduction to the problem of confinement in QCD and to N=2 globally supersymmetric Yang-Mills gauge theories (SYM). While avoiding technicalities as much as possible I will try to emphasize the physical ideas which lie behind the picture of confinement as a consequence of the vacua of QCD to be a dual superconductor. Finally I review the implementation of this picture in the framework of N=2 SYM.
Various gauge invariant but non-Yang-Mills dynamical models are discussed: Precis of Chern-Simons theory in (2+1)-dimensions and reduction to (1+1)-dimensional B-F theories; gauge theories for (1+1)-dimensional gravity-matter interactions; parity and gauge invariant mass term in (2+1)-dimensions.
For all types of N=4 anti-de Sitter (AdS) supersymmetry in three dimensions, we construct manifestly supersymmetric actions for Abelian vector multiplets and explain how to extend the construction to the non-Abelian case. Manifestly N=4 supersymmetri
We calculate the resummed perturbative free energy of ${cal N}=4$ supersymmetric Yang-Mills in four spacetime dimensions ($text{SYM}_{4,4}$) through second order in the t Hooft coupling $lambda$ at finite temperature and zero chemical potential. Our
We consider the pure supersymmetric Yang--Mills theories placed on a small 3-dimensional spatial torus with higher orthogonal and exceptional gauge groups. The problem of constructing the quantum vacuum states is reduced to a pure mathematical proble
We provide a study of the supersymmetric Adler--Bardeen anomaly in the $N=1, d=4,6,10$ super-Yang--Mills theories. We work in the component formalism that includes shadow fields, for which Slavnov--Taylor identities can be independently set for both