Supersymmetric solitons

Abstract

In the past ten years it has become clear that methods and techniques based on supersymmetry provide deep insights into quantum chromodynamics and other nonsupersymmetric gauge theories at strong coupling. This review summarizes major advances in critical (Bogomol'nyi-Prasad- Sommerfield--saturated) solitons in supersymmetric theories and their implications for understanding basic dynamical regularities of nonsupersymmetric theories. After a brief introduction to the theory of critical solitons (including a historical introduction), three topics are discussed: (i) non-Abelian strings in $\mathcal{N}=2$ and confined monopoles, (ii) reducing the level of supersymmetry, and (iii) domain walls as D-brane prototypes.