Large N limit of SO(N) gauge theory of fermions and bosons

Abstract

In this paper we study the large N_c limit of SO(N_c) gauge theory coupled to a Majorana field and a real scalar field in 1+1 dimensions extending ideas of Rajeev. We show that the phase space of the resulting classical theory of bilinears, which are the mesonic operators of this theory, is OSp_1(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 our earlier work). In the Majorana fermion case the phase space is given by O_1(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.