Center Vortices and Monopoles without lattice Gribov copies

TL;DR

This paper introduces a smooth gauge fixing method on the lattice that eliminates ambiguities, revealing center vortices and monopoles as gauge defects, and supports the equivalence of string tensions in the continuum limit.

Contribution

It presents a novel Laplacian Center Gauge that avoids lattice Gribov copies and unifies the description of vortices and monopoles.

Findings

Support for equality of $Z_N$ and SU(N) string tensions in the continuum limit

Demonstration of gauge defects as local features in the new gauge

Validation of the gauge's effectiveness in SU(2) and SU(3) simulations

Abstract

We construct a smooth gauge for the adjoint field which is free of ambiguities on the lattice. In this Laplacian Center Gauge, center vortices and monopoles appear together as local gauge defects. A numerical study of center vortices in SU(2) and SU(3) supports equality of the $Z_N$ and SU(N) string tensions in the continuum limit, and only then.