An Unorthodox Introduction to Supersymmetric Gauge Theory

TL;DR

This paper provides an accessible overview of supersymmetric gauge theories, emphasizing scaling and renormalization group flow, and explores phenomena like solitons, duality, and nonrenormalization in abelian and non-abelian contexts.

Contribution

It introduces supersymmetric gauge theories with a focus on scaling, nonrenormalization theorems, and dualities, including detailed analysis of three- and four-dimensional models.

Findings

Three-dimensional supersymmetric QED exhibits solitons and duality.

Nonrenormalization theorems constrain quantum corrections.

Features of abelian theories extend to non-abelian cases.

Abstract

Numerous topics in three and four dimensional supersymmetric gauge theories are covered. The organizing principle in this presentation is scaling (Wilsonian renormalization group flow.) A brief introduction to scaling and to supersymmetric field theory, with examples, is followed by discussions of nonrenormalization theorems and beta functions. Abelian gauge theories are discussed in some detail, with special focus on three-dimensional versions of supersymmetric QED, which exhibit solitons, dimensional antitransmutation, duality, and other interesting phenomena. Many of the same features are seen in four-dimensional non-abelian gauge theories, which are discussed in the final sections. These notes are based on lectures given at TASI 2001.