C-projection and monopole condensation in QCD

Y M Cho

doi:10.1142/s2010194514602105

Abstract

We show that the monopole condensation is responsible for the confinement. To demonstrate this we present a new gauge invariant integral expression of the one-loop QCD effective action which has no infra-red divergence, and show that the color reflection invariance ("the C-projection") assures the gauge invariance and the stability of the monopole condensation.

Highlights

One of the most challenging problems in theoretical physics is the confinement problem in quantum chromodynamics (QCD)
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]
Imposing the color reflection invariance on the gluon functional determinant which assures the gauge invariance, we obtain a new infra-red finite integral expression of QCD effective action. From this we show that a stable monopole condensation takes place and becomes the true vacuum of QCD

Summary

Introduction

One of the most challenging problems in theoretical physics is the confinement problem in quantum chromodynamics (QCD). Imposing the color reflection invariance (the C-parity) on the gluon functional determinant which assures the gauge invariance, we obtain a new infra-red finite integral expression of QCD effective action From this we show that a stable monopole condensation takes place and becomes the true vacuum of QCD. We have two different Abelian decompositions imposing the same isometry using two different bases, without changing the physics This tells that the color reflection (8) which originally was introduced as a gauge transformation becomes a discrete symmetry of RCD, ECD, and ACD after the Abelian decomposition.[2, 3]. After the Abelian decomposition the color reflection invariance plays the role of the non-Abelian gauge invariance As importantly this tells that in QCD the monopole is equivalent to the antimonopole. These are the lessons from the above analysis which we have to keep in mind in the followings

QCD Effective Action

Monopole Condensation

Discussion