Induced Gauge Theory on a Noncommutative Space

TL;DR

This paper develops a gauge theory on a noncommutative space by coupling a scalar field with an oscillator potential, deriving a candidate renormalisable gauge action from 1-loop divergences.

Contribution

It introduces a gauge-invariant coupling in a renormalisable noncommutative scalar field model and proposes a new gauge action based on 1-loop divergence analysis.

Findings

Derived a gauge field dynamics from divergent 1-loop terms.

Proposed a candidate renormalisable noncommutative gauge action.

Utilized matrix basis for divergence extraction.

Abstract

We consider a scalar $\phi^4$ theory on canonically deformed Euclidean space in 4 dimensions with an additional oscillator potential. This model is known to be renormalisable. An exterior gauge field is coupled in a gauge invariant manner to the scalar field. We extract the dynamics for the gauge field from the divergent terms of the 1-loop effective action using a matrix basis and propose an action for the noncommutative gauge theory, which is a candidate for a renormalisable model.