  SU($N_c$) gauge theories containing matter fields may be invariant under
transformations of some subgroup of the $\mathbb{Z}_{N_c}$ center; the maximum
such subgroup is $\mathbb{Z}_{p}$, with $p$ depending on $N_c$ and the
representations of the various matter fields in the theory. Confining SU($N_c$)
gauge theories in either 3+1 or 2+1 space-time dimensions and with matter
fields in any representation have string tensions for representation $R$ given
by $\sigma_R =\sigma_f \, \, \frac{p_R (p-p_R) \, \, g\left (p_R (p-p_R) \right
)}{(p-1) \, \, g(p -1 )} $ with $p_R={n_R \, \rm mod}(p)$, where $\sigma_f $ is
the string tension for the fundamental representation, $g$ is a positive finite
function and $n_R$ is the n-ality of $R$. This implies that a necessary
condition for a theory in this class to have an area law is invariance of the
theory under a nontrivial subgroup of the center. Significantly, these results
depend on $p$ regardless of the value of $N_c$.
