On twisting real spectral triples by algebra automorphisms

TL;DR

This paper explores how to systematically twist real spectral triples using algebra automorphisms, analyzing the effects on metric fluctuations and potential implications for the spectral standard model.

Contribution

It introduces a natural method to define twisted counterparts for any real graded spectral triple and studies the impact of twisting on metric fluctuations and physical models.

Findings

Twisting affects metric fluctuations in spectral triples.

A framework for twisting real spectral triples is established.

Potential applications to the spectral standard model are discussed.

Abstract

We systematically investigate ways to twist a real spectral triple via an algebra automorphism and in particular, we naturally define a twisted partner for any real graded spectral triple. Among other things we investigate consequences of the twisting on the fluctuations of the metric and possible applications to the spectral approach to the standard model of particle physics.