Loop Calculations for the Non-Commutative U(1) Gauge Field Model with Oscillator Term

TL;DR

This paper investigates the renormalizability of a non-commutative U(1) gauge theory with an oscillator term by performing explicit one-loop calculations and proposing modifications to the action.

Contribution

It provides the first detailed one-loop analysis of a non-commutative U(1) gauge model with an oscillator term and discusses necessary action modifications for renormalizability.

Findings

One-loop graphs computed explicitly.

Identified modifications needed for renormalizability.

Insights into the structure of non-commutative gauge theories.

Abstract

Motivated by the success of the non-commutative scalar Grosse-Wulkenhaar model, a non-commutative U(1) gauge field theory including an oscillator-like term in the action has been put forward in arXiv:0705.4205. The aim of the current work is to analyze whether that action can lead to a fully renormalizable gauge model on non-commutative Euclidean space. In a first step, explicit one-loop graph computations are hence presented, and their results as well as necessary modifications of the action are successively discussed.