Lorentz signature and twisted spectral triples

TL;DR

This paper demonstrates that twisting the spectral triple of the Standard Model naturally produces the Krein space linked to Lorentzian spacetime signature, revealing a connection between twist and Wick rotation.

Contribution

It introduces a novel approach to relate spectral triple twisting with Lorentzian signature and Wick rotation in the Standard Model framework.

Findings

Twisting spectral triples yields Krein spaces for Lorentzian signature.

Spectral action analysis for fermions and bosons supports the twist-Lorentzian link.

Establishes a connection between twist and Wick rotation in spectral geometry.

Abstract

We show how twisting the spectral triple of the Standard Model of elementary particles naturally yields the Krein space associated with the Lorentzian signature of spacetime. We discuss the associated spectral action, both for fermions and bosons. What emerges is a tight link between twist and Wick rotation.