Supersymmetric tools in Yang–Mills theories at strong coupling: The beginning of a long journey

Abstract

Development of holomorphy-based methods in super-Yang–Mills theories started in the early 1980s and lead to a number of breakthrough results. I review some results in which I participated. The discovery of Seiberg’s duality and the Seiberg–Witten solution of [Formula: see text] Yang–Mills were the milestones in the long journey of which, I assume, much will be said in other talks. I will focus on the discovery (2003) of non-Abelian vortex strings with various degrees of supersymmetry, supported in some four-dimensional Yang–Mills theories and some intriguing implications of this discovery. One of the recent results is the observation of a soliton string in the bulk [Formula: see text] theory with the [Formula: see text] gauge group and four flavors, which can become critical in a certain limit. This is the case of a “reverse holography,” with a very transparent physical meaning.