Topological Quantum Field Theory and Seiberg-Witten Monopoles

TL;DR

This paper introduces a topological quantum field theory that reproduces Seiberg-Witten invariants for four-manifolds and extends to a three-dimensional invariant related to Casson's invariant, providing new insights into manifold topology.

Contribution

It presents a novel topological quantum field theory framework for Seiberg-Witten invariants and derives a new three-dimensional invariant with a geometric interpretation.

Findings

Reproduces Seiberg-Witten invariants via a topological quantum field theory

Derives a new three-manifold invariant related to Casson's invariant

Provides a geometric interpretation of the 3D quantum field theory

Abstract

A topological quantum field theory is introduced which reproduces the Seiberg-Witten invariants of four-manifolds. Dimensional reduction of this topological field theory leads to a new one in three dimensions. Its partition function yields a three-manifold invariant, which can be regarded as the Seiberg-Witten version of Casson's invariant. A Geometrical interpretation of the three dimensional quantum field theory is also given.