Non-Abelian Monopoles on Four-Manifolds

TL;DR

This paper introduces a non-abelian extension of monopole equations on four-manifolds, explores the moduli space of solutions, and constructs a related topological quantum field theory, broadening the scope of Donaldson theory.

Contribution

It develops a non-abelian generalization of Witten monopole equations and constructs a corresponding topological quantum field theory using the Mathai-Quillen formalism.

Findings

Analysis of SU(2) monopoles on Kähler manifolds

Construction of the associated moduli space

Development of a new topological quantum field theory

Abstract

We present a non-abelian generalization of Witten monopole equations and we analyze the associated moduli problem, which can be regarded as a generalization of Donaldson theory. The moduli space of solutions for SU(2) monopoles on K\"ahler manifolds is discussed. We also construct, using the Mathai-Quillen formalism, the topological quantum field theory corresponding to the new moduli problem. This theory involves the coupling of topological Yang-Mills theory to topological matter in four dimensions