Reducible Connections in Massless Topological QCD and 4-manifolds

TL;DR

This paper investigates the role of reducible connections in massless topological QCD, linking it to 4-manifold invariants and revealing identities among U(1) topological invariants without relying on duality or Higgs mechanisms.

Contribution

It introduces a novel analysis of reducible connections in massless topological QCD and connects vacuum expectation values to Donaldson, Abelian, and non-Abelian monopole theories.

Findings

Separation of vacuum expectation value into three parts

Identification of identities among U(1) topological invariants

Analysis conducted without duality or Higgs mechanism

Abstract

A role of reducible connections in Non-Abelian Seiberg-Witten invariants is analyzed with massless Topological QCD where monopole is extended to non-Abelian groups version. By giving small external fields, we found that vacuum expectation value can be separated into a part from Donaldson theory, a part from Abelian Monopole theory and a part from non-Abelian monopole theory. As a by-product, we find identities of U(1) topological invariants. In our proof, the duality relation and Higgs mechanism are not necessary.