Bosonic Spectral Action Induced from Anomaly Cancelation

TL;DR

This paper demonstrates that the bosonic spectral action in noncommutative geometry can be derived from the cancellation of the scale anomaly in the fermionic action, linking quantum fermions to the standard model and gravity.

Contribution

It introduces a method to derive the bosonic spectral action via anomaly cancellation, unifying fermionic and bosonic actions in noncommutative geometry.

Findings

Bosonic spectral action can be obtained from fermionic anomaly cancellation.

The regularization approach aligns bosonic and fermionic actions.

Standard model coupled with gravity emerges from quantum fermion effects.

Abstract

We show how (a slight modification of) the noncommutative geometry bosonic spectral action can be obtained by the cancelation of the scale anomaly of the fermionic action. In this sense the standard model coupled with gravity is induced by the quantum nature of the fermions. The regularization used is very natural in noncommutative geometry and puts the bosonic and fermionic action on a similar footing.