Discrete Noncommutative Gauge Theory

TL;DR

This paper reviews the connections between matrix models and noncommutative gauge theories, introduces a lattice formulation, and explores properties like UV/IR mixing, Morita equivalence, and matter coupling, advancing understanding of noncommutative quantum field theories.

Contribution

It constructs a lattice version of noncommutative Yang-Mills theory and establishes Morita equivalence with twisted reduced models, providing new insights into noncommutative gauge theories.

Findings

Demonstrates UV/IR mixing in noncommutative gauge theories

Establishes Morita equivalence between models with and without matter

Proves equivalence of planar loop renormalizations in QCD

Abstract

A review of the relationships between matrix models and noncommutative gauge theory is presented. A lattice version of noncommutative Yang-Mills theory is constructed and used to examine some generic properties of noncommutative quantum field theory, such as UV/IR mixing and the appearence of gauge-invariant open Wilson line operators. Morita equivalence in this class of models is derived and used to establish the generic relation between noncommutative gauge theory and twisted reduced models. Finite dimensional representations of the quotient conditions for toroidal compactification of matrix models are thereby exhibited. The coupling of noncommutative gauge fields to fundamental matter fields is considered and a large mass expansion is used to study properties of gauge-invariant observables. Morita equivalence with fundamental matter is also presented and used to prove the equivalence between the planar loop renormalizations in commutative and noncommutative quantum chromodynamics.