Revisiting the Wu-Yang Monopole: classical solutions and conformal invariance

TL;DR

This paper revisits the Wu-Yang monopole in SU(2) Yang-Mills theory, discovering new finite-energy solutions and exploring conformal invariance to understand monopole configurations and their potential role in quark-gluon plasma transition.

Contribution

It introduces new classical monopole solutions with finite energy by leveraging conformal invariance and scale-breaking techniques in pure Yang-Mills theory.

Findings

Found new classical solutions with finite energy

Identified monopole configurations relevant to plasma transition

Demonstrated the role of conformal invariance in solution scale setting

Abstract

he Wu-Yang monopole for pure SU(2) Yang-Mills theory is revisited. New classical solutions with finite energy are found for a generalized Wu-Yang configuration. Our method relies on known asymptotic series solutions and explores the conformal invariance of the theory to set the scale for the monopole configurations. Furthermore, by breaking the scale invariance of the pure Yang-Mills theory by a term which simulates the coupling to quark fields, four different monopole configurations with an energy of 2.9 GeV and spatial extent of 1.2 fm, 1.4 fm, 2.4 fm and 2.6 fm are obtained. These configurations may play a role in the transition to the plasma phase.