On the Problem of Renormalizability in Non-Commutative Gauge Field Models - A Critical Review

TL;DR

This paper critically reviews the challenges in developing renormalizable non-commutative gauge field theories, highlighting the UV/IR mixing problem and discussing potential solutions, with a focus on scalar models and the difficulties in gauge theories.

Contribution

It provides a comprehensive analysis of the obstacles in formulating renormalizable non-commutative gauge models and explores possible approaches to overcome these issues.

Findings

Few renormalizable models exist, mainly scalar field theories on four-dimensional non-commutative space.

UV/IR mixing is a major obstacle in constructing gauge theories.

The paper sketches potential strategies to address renormalizability challenges.

Abstract

When considering quantum field theories on non-commutative spaces one inevitably encounters the infamous UV/IR mixing problem. So far, only very few renormalizable models exist and all of them describe non-commutative scalar field theories on four-dimensional Euclidean Groenewold-Moyal deformed space, also known as `theta-deformed space'. In this work we discuss some major obstacles of constructing a renormalizable non-commutative gauge field model and sketch some possible ways out.