Renormalizability conditions for almost-commutative geometries

TL;DR

This paper establishes graph-theoretical conditions for the renormalizability of spectral actions in almost-commutative geometries, with implications for the Standard Model and beyond.

Contribution

It introduces graph-theoretical criteria based on Krajewski diagrams to determine renormalizability of geometries in spectral action frameworks.

Findings

Conditions for renormalizability are formulated using Krajewski diagrams.

The Standard Model satisfies these renormalizability conditions.

Potential to identify new renormalizable field theories via geometric criteria.

Abstract

We formulate conditions for almost-commutative (spacetime) manifolds under which the asymptotically expanded spectral action is renormalizable. These conditions are of a graph-theoretical nature, involving the Krajewski diagrams that classify such geometries. This applies in particular to the Standard Model of particle physics, giving a graph-theoretical argument for its renormalizability. A promising potential application is in the selection of physical (renormalizable) field theories described by almost-commutative geometries, thereby going beyond the Standard Model.