Large $N$ Matrix Models and $q$-Deformed Quantum Field Theories

TL;DR

This paper explores the connection between large N $SU(N)$ gauge theories and $q$-deformed quantum field theories, revealing how master fields obey $q$-deformed relations and exhibit non-Abelian gauge symmetry in a Boltzmannian Fock space.

Contribution

It introduces a novel framework linking large N gauge theories with $q$-deformed quantum fields, including the formulation of master fields with $q=0$ and their gauge symmetries.

Findings

Master fields satisfy $q$-deformed commutation relations with $q=0

Master fields are realized in Boltzmannian Fock space

Gauge symmetry persists despite non-Lie algebra values

Abstract

Recently it was shown that an asymptotic behaviour of $SU(N)$ gauge theory for large $N$ is described by q-deformed quantum field. The master fields for large N theories satisfy to standard equations of relativistic field theory but fields satisfy $q$-deformed commutation relations with $q=0$. These commutation relations are realized in the Boltzmannian Fock space. The master field for gauge theory does not take values in a finite-dimensional Lie algebra however there is a non-Abelian gauge symmetry. The gauge master field for a subclass of planar diagrams, so called half-planar diagrams, is also considered. A recursive set of master fields summing up a matreoshka of 2-particles reducible planar diagrams is briefly described.