  We study Casimir scaling and renormalization properties of Polyakov loops in
different irreducible representations in SU(N) gauge theories; in particular,
we investigate the approach to the large-N limit, by performing lattice
simulations of Yang-Mills theories with an increasing number of colors, from 2
to 6. We consider the twelve lowest irreducible representations for each gauge
group, and find strong numerical evidence for nearly perfect Casimir scaling of
the bare Polyakov loops in the deconfined phase. Then we discuss the
temperature dependence of renormalized loops, which is found to be
qualitatively and quantitatively very similar for the various gauge groups. In
particular, close to the deconfinement transition, the renormalized Polyakov
loop increases with the temperature, and its logarithm reveals a characteristic
dependence on the inverse of the square of the temperature. At higher
temperatures, the renormalized Polyakov loop overshoots one, reaches a maximum,
and then starts decreasing, in agreement with weak-coupling predictions. The
implications of these findings are discussed.
