Improving Center Vortex Detection by Usage of Center Regions as Guidance for the Direct Maximal Center Gauge

Rudolf Golubich,Manfried Faber

doi:10.3390/particles2040030

Abstract

The center vortex model of quantum chromodynamic states that vortices, a closed color-magnetic flux, percolate the vacuum. Vortices are seen as the relevant excitations of the vacuum, causing confinement and dynamical chiral symmetry breaking. In an appropriate gauge, as direct maximal center gauge, vortices are detected by projecting onto the center degrees of freedom. Such gauges suffer from Gribov copy problems: different local maxima of the corresponding gauge functional can result in different predictions of the string tension. By using nontrivial center regions—that is, regions whose boundary evaluates to a nontrivial center element—a resolution of this issue seems possible. We use such nontrivial center regions to guide simulated annealing procedures, preventing an underestimation of the string tension in order to resolve the Gribov copy problem.

Highlights

First proposed by Hooft [1] and Cornwall [2] the center vortex model gives an explanation of confinement in non-Abelian gauge theories
Orders of phase transitions in SU(2) and SU(3); Casimir scaling of heavy-quark potential, see [4]; Spontaneous breaking of scale invariance, see [5]; Chiral symmetry breaking, see [6,7] → quark condensate; but suffers from Gribov copy problems: predictions concerning the string tension depend on the specific implementation of the gauge fixing procedure, see [8,9]
We show that by preserving nontrivial center regions, the loss of the vortex finding property is prevented and the full string tension can be recovered

Summary

Introduction

First proposed by Hooft [1] and Cornwall [2] the center vortex model gives an explanation of confinement in non-Abelian gauge theories. It states that the vacuum is a condensate of quantized magnetic flux tubes, the so-called vortices. Orders of phase transitions in SU(2) and SU(3); Casimir scaling of heavy-quark potential, see [4]; Spontaneous breaking of scale invariance, see [5]; Chiral symmetry breaking, see [6,7] → quark condensate; but suffers from Gribov copy problems: predictions concerning the string tension depend on the specific implementation of the gauge fixing procedure, see [8,9].

Methods

Results

Conclusion