Induced QCD at Large N

TL;DR

This paper introduces a new large N lattice gauge model where Yang-Mills interactions are induced by heavy scalar fields, revealing two phases and deriving exact equations in the weak coupling phase.

Contribution

It proposes a novel induced QCD model at large N and derives exact integral equations for the vacuum and excitation spectrum in the weak coupling phase.

Findings

Identified two phases with different properties at large N.

Derived exact nonlinear integral equations for the vacuum and excitations.

Suggested potential for further analysis of the strong coupling phase.

Abstract

We propose and study at large N a new lattice gauge model , in which the Yang-Mills interaction is induced by the heavy scalar field in adjoint representation. At any dimension of space and any $ N $ the gauge fields can be integrated out yielding an effective field theory for the gauge invariant scalar field, corresponding to eigenvalues of the initial matrix field. This field develops the vacuum average, the fluctuations of which describe the elementary excitations of our gauge theory. At $N= \infty $ we find two phases of the model, with asymptotic freedom corresponding to the strong coupling phase (if there are no phase transitions at some critical $N$). We could not solve the model in this phase, but in the weak coupling phase we have derived exact nonlinear integral equations for the vacuum average and for the scalar excitation spectrum. Presumably the strong coupling equations can be derived by the same method.