Higher-derivative gauge theories from noncommutative geometry

TL;DR

This paper reviews the interpretation of the spectral action in noncommutative geometry as a higher-derivative gauge theory, discusses superrenormalizability, and clarifies previous conflicting claims about these results.

Contribution

It clarifies the connection between spectral action and higher-derivative gauge theories and defends the superrenormalizability results against prior misinterpretations.

Findings

Spectral action corresponds to a higher-derivative Yang-Mills theory

The higher-derivative theory is superrenormalizable

Resolves previous conflicting claims about the results

Abstract

In this short note we review the interpretation of the spectral action for the Yang-Mills system in noncommutative geometry as a higher-derivative gauge theory, adopting an asymptotic expansion in a cutoff parameter. We recall our previous results on superrenormalizability of the resulting higher-derivative Yang-Mills gauge theory and confront this with [6] where these very results were erroneously claimed to be incorrect. We explain how their approach differs from ours, thus clarifying the apparent mismatch.