  The nucleon's strange quark content comes from closed quark loops, and hence
should vanish at leading order in the traditional large $N_c$ (TLNC) limit.
Quark loops are not suppressed in the recently proposed orientifold large $N_c$
(OLNC) limit, and thus the strange quark content should be non-vanishing at
leading order. The Skyrme model is supposed to encode the large $N_c$ behavior
of baryons, and can be formulated for both of these large $N_c$ limits. There
is an apparent paradox associated with the large $N_c$ behavior of strange
quark matrix elements in the Skyrme model. The model only distinguishes between
the two large $N_c$ limits via the $N_c$ scaling of the couplings and the
Witten-Wess-Zumino term, so that a vanishing leading order strange matrix
element in the TLNC limit implies that it also vanishes at leading order in the
OLNC limit, contrary to the expectations based on the
suppression/non-suppression of quark loops. The resolution of this paradox is
that the Skyrme model does not include the most general type of meson-meson
interaction and, in fact, contains no meson-meson interactions which vanish for
the TLNC limit but not the OLNC. The inclusion of such terms in the model
yields the expected scaling for strange quark matrix elements.
