Abelianization of QCD in the Maximally Abelian Gauge and the Nambu-'t Hooft Picture for Color Confinement

TL;DR

This paper investigates how QCD simplifies to an abelian theory in the maximally abelian gauge, providing evidence for monopole condensation and the dual Higgs mechanism as explanations for color confinement.

Contribution

It demonstrates the abelianization of QCD in the MA gauge, showing monopole condensation and the dual Higgs mechanism through lattice QCD simulations.

Findings

Off-diagonal gluons acquire a large effective mass (~1 GeV).

Infrared QCD behaves like an abelian theory due to off-diagonal gluon suppression.

Monopole condensation leads to magnetic screening (~0.5 GeV).

Abstract

We study the Nambu-'t Hooft picture for color confinement in terms of the abelianization of QCD and monopole condensation in the maximally abelian (MA) gauge. In the MA gauge in the Euclidean metric, the off-diagonal gluon amplitude is strongly suppressed, and then the off-diagonal gluon phase shows strong randomness, which leads to rapid reduction of the off-diagonal gluon correlation. In SU(2) and SU(3) lattice QCD in the MA gauge with the abelian Landau gauge, the Euclidean gluon propagator indicates a large effective mass of the off-diagonal gluon as $M_{\rm off} \simeq 1 {\rm GeV}$ in the intermediate distance as $0.2{\rm fm} \le r \le 0.8{\rm fm}$. Due to the infrared inactiveness of off-diagonal gluons, infrared QCD is well abelianized like nonabelian Higgs theories in the MA gauge. We investigate the inter-monopole potential and the dual gluon field $B_\mu$ in the MA gauge, and find longitudinal magnetic screening with $m_B \simeq$ 0.5 GeV in the infrared region, which indicates the dual Higgs mechanism by monopole condensation. We define the ``gluonic Higgs scalar field'' providing the MA projection, and find the correspondence between its hedgehog singularity and the monopole location in lattice QCD.