  The leading, planar diagrams of the $1/N_c$ expansion and the usual string
description suggest that quarks propagate on the boundary of a two-dimensional
world surface. We restrict the quarks to the boundary of the world surface by
giving them infinitely large mass on the interior of the surface and zero mass
on its boundary and show that in this picture the QCD $\theta$--vacua can be
represented by the self-intersection number (or equivalently by the first Chern
number of the normal bundle) of the surface.
