New Results in Topological Field Theory and Abelian Gauge Theory

TL;DR

This paper reviews recent advances in topological field theory, duality in Maxwell theory, and introduces Seiberg-Witten invariants, providing foundational background and encouraging further exploration in four-dimensional gauge theories.

Contribution

It presents a comprehensive overview of duality in Maxwell theory and introduces Seiberg-Witten invariants, connecting topological field theory with four-manifold invariants.

Findings

Duality in Maxwell theory on arbitrary four-manifolds

Introduction of Seiberg-Witten invariants as topological invariants

Educational background material on topological gauge theories

Abstract

These are the lecture notes of a set of lectures delivered at the 1995 Trieste summer school in June. I review some recent work on duality in four dimensional Maxwell theory on arbitrary four manifolds, as well as a new set of topological invariants known as the Seiberg-Witten invariants. Much of the necessary background material is given, including a crash course in topological field theory, cohomology of manifolds, topological gauge theory and the rudiments of four manifold theory. My main hope is to wet the readers appetite, so that he or she will wish to read the original works and perhaps to enter this field.