The Simple Center Projection of SU(2) Gauge Theory

TL;DR

This paper introduces a simple, gauge-invariant method for center projection in SU(2) lattice gauge theory, demonstrating center dominance and analyzing topological objects with a more straightforward approach.

Contribution

The paper proposes a new gauge-invariant Simple Center Projection method, simplifying the extraction of center vortices and monopoles while confirming their role in confinement.

Findings

Center dominance observed with the new projection method.

Behavior of vortices and monopoles aligns with maximal center gauge results.

Extraction procedure is numerically simpler than traditional methods.

Abstract

We consider the SU(2) lattice gauge model. We propose a new gauge invariant definition of center projection, which we call the Simple Center Projection. We demonstrate the center dominance, i.e., the coincidence of the projected potential with the full potential up to the mass renormalization term at low energies. We also consider the center vortices and the center monopoles ({\em nexuses}). It turns out that the behavior of such objects qualitatively coincides with the behavior of the vortices and monopoles in the Maximal Center gauge. The connection of the condensation of nexuses with the dual superconductor theory is discussed. Numerically the procedure of extracting the center vortices proposed in this paper is much simpler than the usual Maximal Center Projection.