Center vortex model for the infrared sector of SU(4) Yang-Mills theory: String tensions and deconfinement transition

TL;DR

This paper develops a vortex model for SU(4) Yang-Mills theory's infrared sector, capturing confinement and deconfinement phenomena, but requiring more complex tuning than for lower color numbers, indicating the importance of additional vortex structures.

Contribution

It introduces a vortex world-surface model for SU(4) Yang-Mills theory that accounts for the increased complexity of vortex dynamics at higher color numbers.

Findings

Reproduces lattice data for SU(4) confinement and deconfinement.

Requires more complex action and tuning than SU(2) and SU(3).

Signatures of additional vortex structures emerge at four colors.

Abstract

A random vortex world-surface model for the infrared sector of SU(4) Yang-Mills theory is constructed, focusing on the confinement properties and the behavior at the deconfinement phase transition. Although the corresponding data from lattice Yang-Mills theory can be reproduced, the model requires a more complex action and considerably more tuning than the SU(2) and SU(3) cases studied previously. Its predictive capabilities are accordingly reduced. This behavior has a definite physical origin, which is elucidated in detail in the present work. As the number of colors is raised in Yang-Mills theory, the corresponding infrared effective vortex description cannot indefinitely continue to rely on dynamics determined purely by vortex world-surface characteristics; additional color structures present on the vortices begin to play a role. As evidenced by the modeling effort reported here, definite signatures of this behavior appear in the case of four colors.