The Spectral Action Principle

TL;DR

The paper introduces a spectral action principle for noncommutative spaces that reproduces the standard model coupled with gravity and predicts relations among coupling constants at high energy.

Contribution

It formulates a new spectral action principle applicable to noncommutative geometries, linking the standard model with gravity and unifying coupling constants.

Findings

Reproduces the standard model coupled to Einstein and Weyl gravity

Predicts gauge coupling relations similar to $SU(5)$

Identifies Higgs self-coupling relations at high energy

Abstract

We propose a new action principle to be associated with a noncommutative space $(\Ac ,\Hc ,D)$. The universal formula for the spectral action is $(\psi ,D\psi) + \Trace (\chi (D /$ $\Lb))$ where $\psi$ is a spinor on the Hilbert space, $\Lb$ is a scale and $\chi$ a positive function. When this principle is applied to the noncommutative space defined by the spectrum of the standard model one obtains the standard model action coupled to Einstein plus Weyl gravity. There are relations between the gauge coupling constants identical to those of $SU(5)$ as well as the Higgs self-coupling, to be taken at a fixed high energy scale.