The equivalence of the SU(N) Yang Mills Theory with a Purely Fermionic Model

TL;DR

This paper explores the conditions under which a purely fermionic model with current-current interactions can be equivalent to a renormalizable, asymptotically free SU(N) gauge theory, providing insights into gauge theory formulations.

Contribution

It establishes the specific conditions for the equivalence between a fermionic model and an SU(N) gauge theory, advancing understanding of gauge theory origins.

Findings

Identifies criteria for fermionic models to match SU(N) gauge theories.

Shows how current-current interactions can lead to asymptotic freedom.

Provides a framework for connecting fermionic models with gauge theories.

Abstract

We investigate the detailed conditions under which a purely fermionic model with current-current interaction goes over to a renormalizable, asymptotically free SU$(N)$ gauge theory.