New features of the maximal abelian projection

TL;DR

This paper investigates the decomposition of SU(2) gauge fields into monopole and non-monopole components after fixing the Maximal Abelian gauge, revealing their distinct roles in confinement and string fluctuations.

Contribution

It introduces a method to decompose nonabelian gauge fields into monopole and modified components, analyzing their separate contributions to the static potential in lattice gauge theory.

Findings

Monopole potential is linear and confining.

Modified nonabelian potential is nonconfining.

Sum of potentials closely approximates the full nonabelian potential.

Abstract

After fixing the Maximal Abelian gauge in SU(2) lattice gauge theory we decompose the nonabelian gauge field into the so called monopole field and the modified nonabelian field with monopoles removed. We then calculate respective static potentials and find that the potential due to the modified nonabelian field is nonconfining while, as is well known, the monopole field potential is linear. Furthermore, we show that the sum of these potentials approximates the nonabelian static potential with 5% or higher precision at all distances considered. We conclude that at large distances the monopole field potential describes the classical energy of the hadronic string while the modified nonabelian field potential describes the string fluctuations. Similar decomposition was observed to work for the adjoint static potential. A check was also made of the center projection in the direct center gauge. Two static potentials, determined by projected $Z_2$ and by modified nonabelian field without $Z_2$ component were calculated. It was found that their sum is a substantially worse approximation of the SU(2) static potential than that found in the monopole case. It is further demonstrated that similar decomposition can be made for the flux tube action/energy density.