Center vortex model for the infrared sector of SU(3) Yang-Mills theory: Topological susceptibility

TL;DR

This paper investigates the topological susceptibility in an SU(3) vortex model for infrared Yang-Mills theory, comparing results with lattice data and analyzing temperature dependence and deviations.

Contribution

It introduces a hypercubic lattice implementation of vortex surfaces with color structure to compute topological susceptibility in SU(3) Yang-Mills theory.

Findings

Quantitative agreement with lattice results in the confined phase

Rapid fall-off of susceptibility in the deconfined phase

Deviations possibly due to model artefacts or vortex dynamics

Abstract

The topological susceptibility of the SU(3) random vortex world-surface ensemble, an effective model of infrared Yang-Mills dynamics, is investigated. The model is implemented by composing vortex world-surfaces of elementary squares on a hypercubic lattice, supplemented by an appropriate specification of vortex color structure on the world-surfaces. Topological charge is generated in this picture by writhe and self-intersection of the vortex world-surfaces. Systematic uncertainties in the evaluation of the topological charge, engendered by the hypercubic construction, are discussed. Results for the topological susceptibility are reported as a function of temperature and compared to corresponding measurements in SU(3) lattice Yang-Mills theory. In the confined phase, the topological susceptibility of the random vortex world-surface ensemble appears quantitatively consistent with Yang-Mills theory. As the temperature is raised into the deconfined regime, the topological susceptibility falls off rapidly, but significantly less so than in SU(3) lattice Yang-Mills theory. Possible causes of this deviation, ranging from artefacts of the hypercubic description to more physical sources, such as the adopted vortex dynamics, are discussed.