Contributions of the Cartan generators in potentials between static sources

TL;DR

This paper examines how different Cartan generators influence static potentials in SU(3) gauge theory, showing that including multiple generators improves the potential's behavior and matches known scaling laws.

Contribution

It introduces a method to incorporate multiple Cartan generators in the domain model of center vortices, improving the accuracy of static potential predictions.

Findings

Including only H8 causes concavities in higher representation potentials.

Adding H3 eliminates these concavities and aligns with N-ality.

Potentials with only H8 match Casimir scaling better at intermediate distances.

Abstract

We investigate the contributions of the Cartan generators in the static potentials for various representations in the framework of the domain model of center vortices for SU(3) gauge theory. Using the center domains with the cores corresponding to only one Cartan generator H8, already given as a particular proposal, leads to some concavities in the potentials for higher representations. Furthermore, the string tension of the fundamental representation is the same at Casimir scaling and N-ality regimes. We add the contribution of the other Cartan generator H3 to the potentials and therefore these shortcomings can be eliminated. However, we discuss that at intermediate range of distances the potentials induced by only H8 agree with the Casimir scaling better than those corresponding to both Cartan generators.