A Universal Action Formula

TL;DR

This paper proposes a universal action formula for noncommutative geometries based on spectral triples, unifying gravity and the standard model through a new symmetry principle involving algebra automorphisms.

Contribution

It introduces a novel spectral action formula that is a geometric invariant and incorporates a symmetry principle unifying gravity with the standard model.

Findings

Unified action for gravity and standard model at high energy scale

Spectral action based on Dirac operator spectrum as a geometric invariant

New symmetry principle combining diffeomorphisms and internal symmetries

Abstract

A universal formula for an action associated with a noncommutative geometry, defined by a spectal triple $(\Ac ,\Hc ,D)$, is proposed. It is based on the spectrum of the Dirac operator and is a geometric invariant. The new symmetry principle is the automorphism of the algebra $\Ac $ which combines both diffeomorphisms and internal symmetries. Applying this to the geometry defined by the spectrum of the standard model gives an action that unifies gravity with the standard model at a very high energy scale.