Noncommutative geometry, Grand Symmetry and twisted spectral triple

TL;DR

This paper explores a noncommutative geometric framework for the standard model, introducing twisted spectral triples to derive an extra scalar field and address technical issues, aligning theoretical predictions with experimental data.

Contribution

It proposes a novel use of twisted spectral triples within noncommutative geometry to derive the sv scalar field and resolve unbounded term problems in the grand symmetry model.

Findings

Derived the sv scalar field from a grand algebra

Resolved unbounded vectorial terms using twisting

Achieved Higgs mass prediction compatible with 126 GeV

Abstract

In the noncommutative geometry approach to the standard model we discuss the possibility to derive the extra scalar field sv- initially suggested by particle physicist to stabilize the electroweak vacuum - from a "grand algebra" that contains the usual standard model algebra. We introduce the Connes-Moscovici twisted spectral triples for the Grand Symmetry model, to cure a technical problem, that is the appearance, together with the field sv, of unbounded vectorial terms. The twist makes these terms bounded, and also permits to understand the breaking making the computation of the Higgs mass compatible with the 126 GeV experimental value.