  In this paper we study the large $N_c$ limit of SO(N_c) gauge theory coupled
to a real scalar field following ideas of Rajeev. We see that the phase space
of this resulting classical theory is Sp_1(H)/U(H_+) which is the analog of the
Siegel disc in infinite dimensions. The linearized equations of motion give us
a version of the well-known 't Hooft equation of two dimensional QCD.
