Yang-Mills theory as an Abelian theory without gauge fixing

TL;DR

This paper introduces a nonlocal variable change to reveal an Abelian structure within Yang-Mills theories without gauge fixing, uncovering topological features and monopole-like defects, and discusses implications for duality and solitons.

Contribution

It proposes a novel nonlocal transformation to expose Abelian features in Yang-Mills theories, avoiding gauge fixing and analyzing topological and monopole structures.

Findings

Maxwell field contains topological degrees of freedom from Yang-Mills fields.

't Hooft's monopole projection independence is proved for certain projections.

Discussion of partial duality and massive knot-like solitons.

Abstract

A general procedure to reveal an Abelian structure of Yang-Mills theories by means of a (nonlocal) change of variables, rather than by gauge fixing, in the space of connections is proposed. The Abelian gauge group is isomorphic to the maximal Abelian subgroup of the Yang-Mills gauge group, but not its subgroup. A Maxwell field of the Abelian theory contains topological degrees of freedom of original Yang-Mills fields which generate monopole-like and flux-like defects upon an Abelian projection. 't Hooft's conjecture that ``monopole'' dynamics is projection independent is proved for a special class of Abelian projections. A partial duality and a dynamical regime in which the theory may have massive excitations being knot-like solitons are discussed.