# Clifford-based spectral action and renormalization group analysis of the gauge couplings

## TL;DR

This paper investigates whether Clifford algebra-extended spectral actions can unify gauge couplings through RG analysis, concluding that the minimal framework is insufficient for unification.

## Contribution

It introduces a RG analysis of Clifford-based spectral actions, showing that additional scalar fields do not achieve gauge coupling unification within the minimal model.

## Key findings

- No mass hierarchy configuration leads to unification.
- The minimal spectral action framework is inadequate for unification.
- Additional model modifications are necessary for unification.

## Abstract

The Spectral Action Principle in noncommutative geometry derives the actions of the Standard Model and General Relativity (along with several other gravitational terms) by reconciling them in a geometric setting, and hence offers an explanation for their common origin. However, one of the requirements in the minimal formalism, unification of the gauge coupling constants, is not satisfied, since the basic construction does not introduce anything new that can change the renormalization group (RG) running of the Standard Model. On the other hand, it has been recently argued that incorporating structure of the Clifford algebra into the finite part of the spectral triple, the main object that encodes the complete information of a noncommutative space, gives rise to five additional scalar fields in the basic framework. We investigate whether these scalars can help to achieve unification. We perform a RG analysis at the one-loop level, allowing possible mass values of these scalars to float from the electroweak scale to the putative unification scale. We show that out of twenty configurations of mass hierarchy in total, there does not exist even a single case that can lead to unification. In consequence, we confirm that the spectral action formalism requires a model-construction scheme beyond the (modified) minimal framework.