Quantization of a gauge theory on a curved noncommutative space

TL;DR

This paper investigates the quantization of a gauge theory on a curved noncommutative space, identifying divergences and necessary counterterms for renormalization, thus advancing understanding of quantum gauge theories in noncommutative geometries.

Contribution

It introduces a quantization framework for a gauge analog of the Grosse-Wulkenhaar model on curved noncommutative space, detailing divergence structure and renormalization requirements.

Findings

Identified divergent one-loop contributions to Green functions.

Found five counterterms needed for renormalization.

All divergences are logarithmic.

Abstract

We study quantization of a gauge analogon of the Grosse-Wulkenhaar model: we find divergent one-loop contributions to the 1-point and 2-point Green functions. We obtain that five counterterms are necessary for renormalization and that all divergences are logarithmic.