Topological properties of the SU(3) random vortex world-surface model

TL;DR

This paper develops a method to compute topological charge and susceptibility in the SU(3) random vortex world-surface model, extending previous SU(2) work, and evaluates these properties across different phases of Yang-Mills theory.

Contribution

It introduces a proper treatment of vortex color structure at branchings for SU(3), enabling topological charge calculation in this more complex setting.

Findings

Topological susceptibility is computed for SU(3) vortex configurations.

The model captures topological properties in both confined and deconfined phases.

Extension of vortex models to SU(3) with topological charge considerations.

Abstract

The random vortex world-surface model is an infrared effective model of Yang-Mills dynamics based on center vortex degrees of freedom. These degrees of freedom carry topological charge through writhe and self-intersection of their world-surfaces. A practical implementation of the model realizes the vortex world-surfaces by composing them of elementary squares on a hypercubic lattice. The topological charge for specifically such configurations is constructed in the case of SU(3) color. This necessitates a proper treatment of vortex color structure at vortex branchings, a feature which is absent in the SU(2) color case investigated previously. On the basis of the construction, the topological susceptibility is evaluated in the random vortex world-surface ensemble, both in the confined low-temperature as well as in the deconfined high-temperature phase.