Quark confinement and gauge invariant monopoles in SU(2) YM

TL;DR

This paper reviews a new gauge-invariant lattice formulation of SU(2) Yang-Mills theory that defines magnetic monopoles and demonstrates their dominance in confinement, aligning with results previously seen only in specific gauges.

Contribution

It introduces a gauge-invariant monopole definition and shows monopole dominance in string tension, advancing understanding of quark confinement without gauge fixing.

Findings

Gauge-invariant magnetic monopole current with quantized magnetic charge.

Demonstration of monopole dominance in the string tension.

Reproduction of Abelian gauge results in a gauge-invariant framework.

Abstract

We give a short review of recently obtained results on a new lattice formulation of the non-linear change of variables which was once called the Cho--Faddeev--Niemi decomposition in SU(2) Yang-Mills theory. Based on this formulation, we proposed a new gauge-invariant definition of the magnetic monopole current which guarantees the magnetic charge quantization. We also demonstrated the magnetic monopole dominance in the string tension in SU(2) Yang-Mills theory on a lattice. Our formulation enables one to reproduce in the gauge-invariant way remarkable results obtained so far only in the Maximally Abelian gauge.