Parameter restrictions in a non-commutative geometry model do not survive standard quantum corrections

TL;DR

This paper examines a simple non-commutative geometry model with fermions, gauge fields, and scalars, revealing that parameter restrictions do not remain stable under standard quantum corrections, challenging their physical viability.

Contribution

It demonstrates that parameter relations inspired by non-commutative geometry models are not preserved under one-loop quantum corrections, highlighting limitations in their renormalization.

Findings

Parameter restrictions are not renormalization-group invariant.

Quantum corrections break the relations among coupling constants.

The model's parameter relations cannot be maintained after quantum corrections.

Abstract

We have investigated the standard one-loop quantum corrections for a particularly simple non-commutative geometry model containing fermions interacting with a unique abelian gauge field and a unique scalar through Yukawa couplings. In this model there are certain relations among the different coupling constants quite similar to the ones appearing in the Connes-Lott version of the standard model. We find that it is not possible to implement those relations in a renormalization-group invariant way.