Large N Limit of SO(N) Gauge Theory of Fermions and Bosons

In this paper we study the large Nc limit of SO(Nc) gauge theory coupled to a Majorana field and a real scalar field in 1 + 1 dimensions extending ideas of Rajeev[1]. We show that the phase space of the resulting classical theory of bilinears, which are the mesonic operators of this theory, is OSp1(H|H)/U(H+|H+), where H|H refers to the underlying complex graded space of combined one-particle states of fermions and bosons and H+|H+ corresponds to the positive frequency subspace. In the begining to simplify our presentation we discuss in detail the case with Majorana fermions only (the purely bosonic case is treated in [2]). In the Majorana fermion case the phase space is given by O1(H)/U(H+), where H refers to the complex one-particle states and H+ to its positive frequency subspace. The meson spectrum in the linear approximation again obeys a variant of the ’t Hooft equation. The linear approximation to the boson/fermion coupled case brings an additonal bound state equation for mesons, which consists of one fermion and one boson, again of the same form as the well-known ’t Hooft equation.