Reformulating SU(N) Yang-Mills theory based on change of variables

TL;DR

This paper introduces a reformulation of SU(N) Yang-Mills theory using new variables to better understand low-energy phenomena like quark confinement through topological degrees of freedom.

Contribution

It presents a novel reformulation based on a nonlinear change of variables, enabling gauge-invariant analysis of magnetic monopoles, vortices, and dual superconductivity.

Findings

Explicit extraction of topological degrees of freedom

Gauge-invariant understanding of dual superconductivity

Clarification of quark confinement mechanism

Abstract

We propose a new version of SU(N) Yang-Mills theory reformulated in terms of new field variables which are obtained by a nonlinear change of variables from the original Yang-Mills gauge field. The reformulated Yang-Mills theory enables us to study the low-energy dynamics by explicitly extracting the topological degrees of freedom such as magnetic monopoles and vortices to clarify the mechanism for quark confinement. The dual superconductivity in Yang-Mills theory is understood in a gauge-invariant manner, as demonstrated recently by a non-Abelian Stokes theorem for the Wilson loop operator, although the basic idea of this reformulation is based on the Cho-Faddeev-Niemi decomposition of the gauge potential.