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New Monopoles in Non-Abelian Gauge Theories

Liping Zou, Pengming Zhang, Y. M. Cho

TL;DR

The work identifies multiple new monopole solutions across non-Abelian gauge theories: in the standard model, both Cho-Maison monopoles and electromagnetically neutral monopoles with distinct dressings; in the Georgi-Glashow model, Wu-Yang monopoles dressed by $W$ bosons; and in QCD, a chromonic Wu-Yang monopole. Central to the construction is the Abelian decomposition, which reveals two independent monopole topologies and a mixing of currents that links the electroweak and hypercharge sectors, enabling two types of monopole topology within a single framework. The authors provide explicit ansätze, discuss the energy structure (often with divergent classical energies for certain solutions) and offer mass estimates suggesting potential experimental accessibility for some monopole types (e.g., neutral standard-model monopoles around a few TeV). The results imply deep connections between topology, gauge structure, and low-energy phenomena, with possible applications to condensed matter analogs and spintronics, and motivate further studies of monopole stability and detection prospects. All mathematical notation is kept precise, highlighting charges, couplings, and topological charges with $ $ delimiters throughout.

Abstract

The monopoles play important roles in physics. In this work we discuss the new monopoles in non-Abelian gauge theories, the standard model, the Georgi-Glashow model, and QCD. The standard model has two totally different types of monopoles, the Cho-Maison type monopoles which have the weak boson dressing and the electromagnetically neutral magnetic monopoles (the naked one and the one with the W boson dressing) which carries the neutral magnetic charge $4π/\bae$. The Georgi-Glashow model has a new monopole, the Wu-Yang monopole which has the W boson dressing, in addition to the well known 'tHooft-Polyakov monopole. And QCD has a new monopole, the Wu-Yang monopole which has the chromon dressing. We show how to construct the new monopoles and clarify the origin of the topology of the new monopoles. The new monopoles could have deep implications not just in high energy physics but also in low energy physics.

New Monopoles in Non-Abelian Gauge Theories

TL;DR

The work identifies multiple new monopole solutions across non-Abelian gauge theories: in the standard model, both Cho-Maison monopoles and electromagnetically neutral monopoles with distinct dressings; in the Georgi-Glashow model, Wu-Yang monopoles dressed by bosons; and in QCD, a chromonic Wu-Yang monopole. Central to the construction is the Abelian decomposition, which reveals two independent monopole topologies and a mixing of currents that links the electroweak and hypercharge sectors, enabling two types of monopole topology within a single framework. The authors provide explicit ansätze, discuss the energy structure (often with divergent classical energies for certain solutions) and offer mass estimates suggesting potential experimental accessibility for some monopole types (e.g., neutral standard-model monopoles around a few TeV). The results imply deep connections between topology, gauge structure, and low-energy phenomena, with possible applications to condensed matter analogs and spintronics, and motivate further studies of monopole stability and detection prospects. All mathematical notation is kept precise, highlighting charges, couplings, and topological charges with delimiters throughout.

Abstract

The monopoles play important roles in physics. In this work we discuss the new monopoles in non-Abelian gauge theories, the standard model, the Georgi-Glashow model, and QCD. The standard model has two totally different types of monopoles, the Cho-Maison type monopoles which have the weak boson dressing and the electromagnetically neutral magnetic monopoles (the naked one and the one with the W boson dressing) which carries the neutral magnetic charge . The Georgi-Glashow model has a new monopole, the Wu-Yang monopole which has the W boson dressing, in addition to the well known 'tHooft-Polyakov monopole. And QCD has a new monopole, the Wu-Yang monopole which has the chromon dressing. We show how to construct the new monopoles and clarify the origin of the topology of the new monopoles. The new monopoles could have deep implications not just in high energy physics but also in low energy physics.

Paper Structure

This paper contains 7 sections, 75 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Abelian Decomposition of the Standard Model
  3. Cho-Maison Monopole: A Review
  4. New Monopoles in Standard Model
  5. New Monopole in Georgi-Glashow Model
  6. Chromonic Monopole in QCD
  7. Discussion

Figures (3)

  • Figure 1: The new monopole solutions in the standard model. The W boson profile of the neutral magnetic monopole is shown in red curve, which should be compared with the W and Higgs boson profiles of the Cho-Maison monopole shown in black curves. Notice that the same red curve also describes the W boson profile of the new Cho-Maison monopole which has only the W boson dressing.
  • Figure 2: The new monopole solutions in Georgi-Glashow model. The black curves represent the well known 'tHooft-Polyakov monopole, and the blue curve represents the Wu-Yang monopole which has the W boson dressing.
  • Figure 3: The new monopole solution in QCD, the Wu-Yang monopole which has the chromon dressing. The black curve represents the chromon profile, and the red curve represents the chromon profile $f$ in log scale.