Lattice construction of Cho-Faddeev-Niemi decomposition and gauge invariant monopole

TL;DR

This paper introduces a lattice implementation of the Cho-Faddeev-Niemi decomposition for SU(2) Yang-Mills fields, preserving gauge invariance and proposing a new gauge-invariant monopole definition validated through numerical comparisons.

Contribution

It provides the first lattice construction of the decomposition that maintains color symmetry and introduces a gauge-invariant monopole current definition.

Findings

Preserves global SU(2) gauge invariance on the lattice.

Proposes a gauge-invariant magnetic monopole current.

Validates the new monopole definition against the DeGrand-Toussaint method.

Abstract

We present the first implementation of the Cho--Faddeev--Niemi decomposition of the SU(2) Yang-Mills field on a lattice. Our construction retains the color symmetry (global SU(2) gauge invariance) even after a new type of Maximally Abelian gauge, as explicitly demonstrated by numerical simulations. Moreover, we propose a gauge-invariant definition of the magnetic monopole current using this formulation and compare the new definition with the conventional one by DeGrand and Toussaint to exhibit its validity.