A formulation of the Yang-Mills theory as a deformation of a topological field theory based on background field method and quark confinement problem

TL;DR

This paper reformulates Yang-Mills theory as a deformation of a topological quantum field theory using the background field method, providing insights into quark confinement and gluon mass generation.

Contribution

It introduces a novel reformulation of Yang-Mills theory based on topological configurations and background fields, linking gauge fixing to topological and geometric structures.

Findings

Identification of Yang-Mills with a deformed topological theory

Proposal of a numerical simulation to test the scheme

Connection between gauge fixing and global topology

Abstract

By making use of the background field method, we derive a novel reformulation of the Yang-Mills theory which was proposed recently by the author to derive quark confinement in QCD. This reformulation identifies the Yang-Mills theory with a deformation of a topological quantum field theory. The relevant background is given by the topologically non-trivial field configuration, especially, the topological soliton which can be identified with the magnetic monopole current in four dimensions. We argue that the gauge fixing term becomes dynamical and that the gluon mass generation takes place by a spontaneous breakdown of the hidden supersymmetry caused by the dimensional reduction. We also propose a numerical simulation to confirm the validity of the scheme we have proposed. Finally we point out that the gauge fixing part may have a geometric meaning from the viewpoint of global topology where the magnetic monopole solution represents the critical point of a Morse function in the space of field configurations.