Induced Gauge Theory on a Noncommutative Space

TL;DR

This paper computes the one-loop effective action for a scalar field with gauge coupling on a four-dimensional noncommutative space, proposing a candidate for a renormalisable noncommutative gauge theory.

Contribution

It introduces a new noncommutative gauge theory action derived from one-loop divergences, aiming for renormalisability in four dimensions.

Findings

Derived the effective action on noncommutative space

Proposed a candidate renormalisable gauge theory

Identified divergent terms leading to the gauge action

Abstract

We discuss the calculation of the 1-loop effective action on four dimensional, canonically deformed Euclidean space. The theory under consideration is a scalar $\phi^4$ model with an additional oscillator potential. This model is known to be re normalisable. Furthermore, we couple an exterior gauge field to the scalar field and extract the dynamics for the gauge field from the divergent terms of the 1-loop effective action using a matrix basis. This results in proposing an action for noncommutative gauge theory, which is a candidate for a renormalisable model.