The Donaldson-Witten Invariants in Pure QCD with Order and Disorder 't Hooft-like Operators

TL;DR

This paper explores the connection between non-local flux operators in pure SU(2) Yang-Mills theory with a theta-term and Witten's four-manifold invariants, revealing new insights into topological aspects of gauge theories.

Contribution

It introduces a gauge-invariant framework for electric and magnetic flux operators in pure Yang-Mills theory and links their Green functions to topological invariants of four-manifolds.

Findings

Green functions related to flux operators are connected to Witten's invariants

Provides a gauge-invariant description of 't Hooft operators in pure YM

Establishes a bridge between gauge theory and four-manifold topology

Abstract

We study the first-order formalism of pure four-dimensional ${\rm SU}(2)$ Yang--Mills theory with theta-term. We describe the Green functions associated to electric and magnetic flux operators \`a la 't~Hooft by means of gauge-invariant non-local operators. These Green functions are related to Witten's invariants of four-manifolds.