Abelian Decomposition and Monopole Condensation in QCD

Y.M Cho,Y Aharonov,L Bravina,S Kabana

doi:10.1051/epjconf/201818202029

Abstract

We demonstrate the monopole condensation in QCD using the Abelian decomposition. The Abelian decomposition decomposes the gluons to the color neutral binding gluons (the neurons and the monopoles) and the colored valence gluons (the chromons), and shows that QCD can be viewed as the restricted QCD (RCD) made of the binding gluons which has the chromons as colored source. This simplifies the QCD dynamics greatly. In the perturbative regime this decomposes the gluon propagater to the neuron propagaters and the chromon propagaters, and simplifies the Feynman diagram. In the non-perturbative regime this allows us to calculate the QCD effective potential gauge independently, and demonstrate the monopole condensation unambiguously.

Highlights

One of the most challenging problems in theoretical physics is the confinement problem in quantum chromodynamics (QCD)
It has long been argued that the confinement in QCD can be triggered by the monopole condensation [1,2,3]
A natural way to establish the monopole condensation in QCD is to show that the quantum fluctuation triggers a phase transition similar to the dimensional transmutation observed in massless scalar QED [6]

Summary

Introduction

One of the most challenging problems in theoretical physics is the confinement problem in quantum chromodynamics (QCD). It tells that the Abelian potential is made of two parts, the non-topological Maxwell part and the topological monopole part [2, 3] This allows us to test the Abelian dominance and the monopole condensation gauge independently. With this we can pinpoint exactly what is responsible for the confinement. The Abelian decomposition decomposes the gluons (in general the non-Abelian gauge potentials) to two different types, the color neutral binding gluons called the neurons and the colored valence gluons called the chromons, gauge independently This is very important in hadron spectroscopy because the chromons, just like the quarks, can form the color singlet bound states and become the constituent of hadrons. In this talk we discuss the Abelian decomposition of QCD and show how it can be used to demonstrate the monopole condensation gauge independently

Abelian decomposition: A Review

Abelian Dominance and Monopole Condensation in QCD

QCD Effective Action and Monopole Condensation

Discussions