Dimensional Transmutation by Monopole Condensation in QCD

TL;DR

This paper demonstrates that monopole condensation, rather than Abelian dominance, is responsible for color confinement in QCD, supported by a gauge-invariant effective action and invariance principles.

Contribution

It introduces a gauge-invariant integral expression for the one-loop QCD effective action and establishes monopole dominance as the mechanism for confinement.

Findings

Monopole condensation causes confinement in QCD.

A new gauge-invariant effective action expression is derived.

Critical defects in previous SNO effective action calculations are identified.

Abstract

We compare two competing conjectures of the color confinement in QCD, the monopole condensation and the Abelian dominance, and show that it is the monopole condensation which 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. With this we show that, just as the GSO-projection restores the supersymmetry and modular invariance in NSR string theory, the color reflection invariance ("the C-projection") assures the gauge invariance and the stability of the monopole condensation. This establishes the monopole dominance in QCD. In doing so we point out critical defects in the calculation of the Savvidy-Nielsen-Olesen (SNO) effective action.