Topological susceptibility in the SU(3) random vortex world-surface model

TL;DR

This paper develops a method to compute topological susceptibility in SU(3) vortex models, accounting for complex color structures at branchings, and analyzes its temperature dependence across different phases.

Contribution

It introduces a novel treatment of color structures at vortex branchings in SU(3) and applies it to evaluate topological susceptibility in the vortex model.

Findings

Topological susceptibility varies with temperature in the vortex model.

The method successfully distinguishes between confined and deconfined phases.

Results align with expectations from infrared Yang-Mills dynamics.

Abstract

The topological charge is constructed for SU(3) center vortex world-surfaces composed of elementary squares on a hypercubic lattice. In distinction to the SU(2) case investigated previously, it is necessary to devise a proper treatment of the color structure at vortex branchings, which arise in the SU(3) case, but not for SU(2). The construction is used to evaluate the topological susceptibility in the random vortex world-surface model of infrared Yang-Mills dynamics. Results for the topological susceptibility are reported as a function of temperature, including both the confined as well as the deconfined phase.