Toward gauge independent study of confinement in SU(3) Yang-Mills theory

TL;DR

This paper introduces a gauge-invariant lattice formulation of SU(3) Yang-Mills theory that preserves color symmetry and allows for the study of quark confinement via dual superconductivity without gauge fixing.

Contribution

It proposes a new non-linear variable change in lattice SU(3) Yang-Mills theory that maintains color symmetry and enables gauge-invariant monopole definitions, extending previous SU(2) work.

Findings

Preliminary numerical results support the formulation's validity.

The new approach allows gauge-invariant monopole detection.

It offers a promising framework for studying confinement mechanisms.

Abstract

Dual superconductivity is believed to be a promising mechanism for quark confinement and has been investigated on a lattice effectively by a particular gauge called the maximal Abelian (MA) gauge. We propose a new formulation of SU(3) Yang-Mills theory on a lattice based on a non-linear change of variables where the new field variables are expected to reduce to those of the Cho-Faddeev-Niemi- Shabanov decomposition in the continuum limit. By introducing a new variable, say color field, carrying the color direction with it, this formulation enables us to restore and maintain color symmetry that was lost in the conventional MA gauge due to the naive separation of the gauge potential into diagonal and off-diagonal components. An advantage of this formulation is that we can define gaugeinvariant magnetic monopoles without relying on specific gauges to investigate quark confinement from the viewpoint of dual superconductivity. In this talk, we will present the relevant lattice formulation to realize the above advantages and preliminary results of numerical simulations to demonstrate the validity of this formulation. This SU(3) formulation is an extension of the SU(2) version already proposed by us in the previous conference.