Concepts in Gauge Theory Leading to Electric--Magnetic Duality

TL;DR

This paper introduces fundamental concepts in gauge theory from both physical and mathematical perspectives, demonstrating how they lead to a nonabelian electric-magnetic duality and exploring its implications in quantum field theory.

Contribution

It presents a nonabelian generalization of electric-magnetic duality derived from core gauge theory concepts, linking physical intuition with mathematical structure.

Findings

Nonabelian electric-magnetic duality derived from gauge theory concepts

Implications of duality in quantum field theory

Connections between physical and mathematical perspectives in gauge theory

Abstract

Gauge theory, which is the basis of all particle physics, is itself based on a few fundamental concepts, the consequences of which are often as beautiful as they are deep. In this short lecture course I shall try to give an introduction to these concepts, both from the physical and mathematical points of view. Then I shall show how these considerations lead to a nonabelian generalization of the well-known electric--magnetic duality in electromagnetism. I shall end by sketching some of the many consequences in quantum field theory that this duality engenders in particle physics. These are notes from a lecture course given in the Summer School on {\em Geometric Methods in Quantum Field Theory}, Villa de Leyva, Colombia, July 1999, as well as a series of graduate lectures given in Oxford in Trinity Term of 1999 and 2000.