  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.
