One-loop structure of the U(1) gauge model on the truncated Heisenberg space

TL;DR

This paper computes one-loop divergences in a U(1) gauge theory on a noncommutative geometric space, revealing nonlocal divergences and discussing their implications for model improvement.

Contribution

It provides the first detailed calculation of one-loop divergences in a gauge theory on the truncated Heisenberg space, extending the Grosse-Wulkenhaar model.

Findings

Identified divergent nonlocal terms of the form $ox^{-1}$ and $ox^{-2}$

Confirmed the BRST invariance of the gauge-fixed theory

Discussed potential modifications to address nonlocal divergences

Abstract

We calculate divergent one-loop corrections to the propagators of the U(1) gauge theory on the truncated Heisenberg space, which is one of the extensions of the Grosse-Wulkenhaar model. The model is purely geometric, based on the Yang-Mills action; the corresponding gauge-fixed theory is BRST invariant. We quantize perturbatively and, along with the usual wave-function and mass renormalizations, we find divergent nonlocal terms of the $\Box^{-1}$ and $\Box^{-2}$ type. We discuss the meaning of these terms and possible improvements of the model.