Compact lattice formulation of Cho-Faddeev-Niemi decomposition: string tension from magnetic monopoles

TL;DR

This paper introduces a new compact lattice formulation of the Cho-Faddeev-Niemi decomposition in SU(2) Yang-Mills theory, enabling gauge-invariant magnetic monopole definitions and demonstrating monopole dominance in string tension.

Contribution

It presents a compact lattice formulation that improves previous non-compact models and provides a gauge-invariant way to define magnetic monopoles in Yang-Mills theory.

Findings

Magnetic monopole dominance in string tension demonstrated

Gauge-invariant magnetic monopole current defined

Reproduces Abelian projection results in a gauge-invariant manner

Abstract

In this paper we begin on a new lattice formulation of the non-linear change of variables called the Cho--Faddeev--Niemi decomposition in SU(2) Yang-Mills theory. This is a compact lattice formulation improving the non-compact lattice formulation proposed in our previous paper. Based on this formulation, we propose a new gauge-invariant definition of the magnetic monopole current which guarantees the magnetic charge quantization and reproduces the conventional magnetic-current density obtained in the Abelian projection based on the DeGrand--Toussaint method. Finally, we demonstrate 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.