Large N limit of SO(N) scalar gauge theory

TL;DR

This paper investigates the large N limit of SO(N) gauge theory with a real scalar, revealing a classical phase space structure and deriving a version of the 't Hooft equation in this context.

Contribution

It introduces the phase space structure of the large N limit of SO(N) scalar gauge theory and derives the 't Hooft equation analog in this setting.

Findings

Phase space is Sp_1(H)/U(H_+) in the large N limit.

Derivation of a 't Hooft-like equation for the theory.

Connection between classical phase space and known two-dimensional QCD results.

Abstract

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.