Potentials between static SU(3) sources in the fat-center-vortices model

TL;DR

This paper investigates the potentials between static SU(3) sources using the fat-center-vortices model, finding qualitative agreement with Casimir scaling at intermediate distances but noting significant quantitative deviations and the need for additional physical input.

Contribution

It provides a detailed analysis of static SU(3) potentials within the fat-center-vortices model, highlighting where it aligns with and diverges from expected Casimir scaling behavior.

Findings

Qualitative agreement with Casimir scaling at intermediate distances

Quantitative deviations from Casimir scaling are larger than in simulations

Screening occurs for zero-triality representations at large distances

Abstract

The potentials between static sources in various representaions in SU(3) are calculated based on the fat-center-vortices model of Faber, Greensite and Olejnik. At intermediate distances, most distributions of the flux within vortices lead to potentials that are qualitatively in agreement with ``Casimir scaling,'' which says that the string tension is proportional to the quadratic operator of the representation. However, at the quantitative level, violations of Casimir scaling are generally much larger than those seen in numerical simulations, indicating that additional physical input to the fat-center-vortices model is required. At large distances, screening occurs for zero-triality representations; for the representations with non-zero triality the string tension equals that of the fundamental representation. Some rather ``unphysical,'' flux distributions can lead to violations of Casimir scaling at intermediate distances and violations of the expected ordering of representations at large distances.