Supersymmetric Solitons and How They Help Us Understand Non-Abelian Gauge Theories

In the last decade it became clear that methods and techniques based on supersymmetry provide deep insights in quantum chromodynamics and other supersymmetric and non-supersymmetric gauge theories at strong coupling. In this review we summarize major advances in the critical (Bogomol'nyi-Prasad-Sommerfeld-saturated, BPS for short) solitons in supersymmetric theories and their implications for understanding basic dynamical regularities of non-supersymmetric theories. After a brief introduction in the theory of critical solitons (including a historical introduction) we focus on three topics: (i) non-Abelian strings in N=2 and confined monopoles; (ii) reducing the level of supersymmetry; and (iii) domain walls as D brane prototypes.