Renormalization of the spectral action for the Yang-Mills system

TL;DR

This paper proves that the spectral action for the Yang-Mills system on flat 4D space is renormalizable and superrenormalizable, revealing its favorable behavior as a higher-derivative gauge theory.

Contribution

It demonstrates the renormalizability of the spectral action for Yang-Mills systems, interpreting it as a higher-derivative gauge theory and establishing its superrenormalizability.

Findings

Spectral action is superrenormalizable.

One-loop effective action is BRST-invariant.

Spectral action behaves well under renormalization.

Abstract

We establish renormalizability of the full spectral action for the Yang-Mills system on a flat 4-dimensional background manifold. Interpreting the spectral action as a higher-derivative gauge theory, we find that it behaves unexpectedly well as far as renormalization is concerned. Namely, a power counting argument implies that the spectral action is superrenormalizable. From BRST-invariance of the one-loop effective action, we conclude that it is actually renormalizable as a gauge theory.