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

TL;DR

This review discusses how supersymmetric solitons, especially BPS states, provide valuable insights into non-Abelian gauge theories and quantum chromodynamics, highlighting recent advances and their implications.

Contribution

It summarizes major recent progress in understanding critical BPS solitons in supersymmetric theories and their role in elucidating non-supersymmetric gauge dynamics.

Findings

Insights into non-Abelian strings and confined monopoles in N=2 theories

Reduction of supersymmetry levels and its effects

Domain walls as D brane prototypes

Abstract

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.