  In the large $N_c$ limit of QCD, baryons can be modeled as solitons, for
instance, as Skyrmions. This modeling has been justified by Witten's
demonstration that all properties of baryons and mesons scale with $N_c^{-1/2}$
in the same way as the analogous meson-based soliton model scales with a
generic meson-meson coupling constant $g$. An alternative large $N_c$ limit
(the orientifold large $N_c$ limit) has recently been proposed in which quarks
transform in the two-index antisymmetric representation of $SU(N_c)$. By
carrying out the analog of Witten's analysis for the new orientifold large
$N_c$ limit, we show that baryons and solitons can also be identified in the
orientifold large $N_c$ limit. However, in the orientifold large $N_c$ limit,
the interaction amplitudes and matrix elements scale with $N_c^{-1}$ in the
same way as soliton models scale with the generic meson coupling constant $g$
rather than as $N_c^{-1/2}$ as in the traditional large $N_c$ limit.
