Solitons, monopoles and duality: from sine-Gordon to Seiberg-Witten

TL;DR

This paper provides a pedagogical introduction to Seiberg-Witten theory, covering solitons, monopoles, and duality, with detailed explanations suitable for graduate students, and discusses the exact solutions for N=2 supersymmetric Yang-Mills theories.

Contribution

It offers a clear, accessible overview of Seiberg-Witten theory and its foundational concepts, emphasizing pedagogical clarity and including solutions for various gauge groups.

Findings

Exact Seiberg-Witten solution for SU(2) gauge group

Illustration of solitons and monopoles in supersymmetric theories

Discussion of dualities and confinement mechanisms

Abstract

An elementary introduction into the Seiberg-Witten theory is given. Many efforts are made to get it as pedagogical as possible, within a reasonable size. The selection of the relevant material is heavily oriented towards graduate students. The basic ideas about solitons, monopoles, supersymmetry and duality are reviewed from first principles, and they are illustrated on the simplest examples. The exact Seiberg-Witten solution to the low-energy effective action of the four-dimensional N=2 supersymmetric pure Yang-Mills theory with the gauge group SU(2) is the main subject of the review. Other gauge groups are also considered. Some related issues (like adding matter, confinement, string dualities) are outlined.